Classically, damping force is described as a function of velocity in the linear theory of mechanical models. In this work, a memory-dependent derivative model with respect to displacement is proposed to describe damping in various oscillatory systems of complex dissipation mechanisms where memory effects could not be ignored. A memory-dependent derivative is characterized by its time-delay and kernel function K(x, t) which can be chosen freely. Thus, it is superior to the fractional derivative in that it provides more access into memory effects and thus better physical meaning. To elucidate this, an equation of motion is proposed based on the prototype mass-spring model. The analytical solution is then attempted by the Laplace transform method. Due to the complexity of finding the inverse Laplace transform, a numerical inversion treatment is carried out using the fixed Talbot method and also compared with the finite difference discretization to validate the method. The calculations show that the response function is sensitive to different choices of and K(x, t). It is found that this proposed model supports the existence of memory-dependence in the structure of the material. The interesting case of resonance where the response function is classically increased rapidly is found to be weakened by an appropriate choice of and K(x, t).
A new shaft element is proposed for viscoelastic rotors in a spinning frame considering the shear deformation in addition to bending deformation. The Maxwell–Wiechert model is considered here to replicate linear viscoelastic behavior. This model considers additional internal damping displacement variables between elastic and viscous elements and the stress depends not only on the elastic strain and elastic strain rate, but also on additional strains and their rates corresponding to the damping variables. The present work assumes that these additional strains can be derived from continuous fictitious displacement variables, which in turn are interpolated from their nodal values using the Timoshenko beam shape functions. Therefore, in addition to the standard degrees of freedom for a three-dimensional shaft, extra degrees of freedom are defined at the nodes. The finite element matrices are assembled in state space. The time domain equations are then used for stability analysis and computation of response to a unit step load and an unbalance.
A typical engine front end accessory drive system (FEADS) is mathematically modeled through Hamilton’s principle and Newton’s second law. In this model, the belt’s flexural rigidity and pulley’s eccentricity are considered. Eccentricities of the pulleys are introduced into governing motion equations of the belt spans through the boundary conditions and then transformed to external forces acting on the belt spans. Vibration modes and natural frequencies of the FEADS are calculated by the state-space technique of the complex mode theory. Dynamic responses of the FEADS at different rotational rates of the crankshaft are calculated by solving the spatially discretized governing equations obtained by Galerkin method. The modeling and solution methods are formulated and programmed in a general purposed code. The study shows that the typical resonance and beat phenomenon happen in a certain portion of the belt spans at a certain rotational rate by the excitations of the pulley’s eccentricity. According to the modal analysis and dynamic response analysis, an optimization method based on a genetic algorithm is proposed. By comparing the vibration amplitudes of belt spans before and after optimization at different rotational rates, this optimization method is verified to be effective in reducing transverse vibrations of the belt spans.
In this work, a boundary layer control scheme for one-dimensional wave propagation problems is presented that provides reflection-less absorption of incident waves in numerical simulations. The desired absorption properties are formulated as an optimization problem. By using the dispersion relation to predict the unbounded wave propagation as a reference trajectory, a constant-gain state-feedback boundary layer controller is found. Since no additional auxiliary variables are introduced, this approach is highly computationally efficient, making it suitable for simulations under real-time requirements. The performance of the boundary layer controller is first evaluated and demonstrated on the scalar wave equation (vibrating string), for which reference absorbing boundary conditions are well established. Afterward, the moving Euler–Bernoulli beam under axial tension is considered, for which a good absorbing performance is achieved.
Virtual hybrid simulation is a computationally-efficient method that enables coupling of two or more finite element analysis programs. In this study, benefits of this technique in predicting both cyclic and seismic response of a one-story one-bay frame equipped with a Triangular-plate Added Damping and Stiffness (TADAS) damper are evaluated. For this purpose, a detailed FE model of the damper is built in Abaqus to take into account precise modelling of its hysteretic behavior as well as a number of important features related to the geometric characteristics of the including parts of the device, while the remainder of the structure is modelled in OpenSees. Continuous exchange of the data between the coupled codes is conducted through the software framework, OpenFresco. Comparison of the results with experimental outcomes is presented, which proves the ability of the introduced technique in modelling the behavior of such structures in an efficient manner while preserving sufficient accuracy. At the end, a series of dynamic virtual hybrid simulations of the frame are performed which provide useful insights into design of TADAS frames.
A methodology has been proposed to estimate non-proportional viscous damping matrix of beams from measured complex eigendata using finite element model updating technique. Representation of damping through a proportional damping matrix ignoring the complexity of eigenvectors may not be appropriate when external damping devices are employed. The current literature of determination of non-proportional damping matrix demands measurement of a large number of complex modes which is extremely difficult in practice. A gradient based finite element model updating algorithm implementing inverse eigensensitivity method has been presented through a series of numerically simulated cantilever beams. The method can accurately predict the non-proportional damping matrix even if the measured eigenvectors are polluted with random noise. The novelty of the current method is that it can sustain a high level of modal and coordinate sparsity in measurement. The method assumes prior determination or updating of the mass and stiffness matrices.
We use a hybrid local meshless method to solve the distributed optimal control problem of a system governed by parabolic partial differential equations with Caputo fractional time derivatives of order α (0, 1]. The presented meshless method is based on the linear combination of moving least squares and radial basis functions in the same compact support, this method will change between interpolation and approximation. The aim of this paper is to solve the system of coupled fractional partial differential equations, with necessary and sufficient conditions, for fractional distributed optimal control problems using a combination of moving least squares and radial basis functions. To keep matters simple, the problem has been considered in the one-dimensional case, however the techniques can be employed for both the two- and three-dimensional cases. Several test problems are employed and results of numerical experiments are presented. The obtained results confirm the acceptable accuracy of the proposed method.
In this article, free vibration of functionally graded (FG) viscoelastic nanobeams embedded in viscoelastic foundation exposed to hygro-thermal loading is investigated based on nonlocal strain gradient elasticity theory and a higher order refined beam theory which captures shear deformation influences without the need for any shear correction factor. Also, the exact position of neutral axis is determined. The visco-Pasternak foundation is consists of parallel springs and dashpots as well as a shear layer. Temperature-dependent material properties of FGM beam are graded across the thickness based on the power-law form. Hamilton’s principle is used to obtain nonlocal governing equations of embedded strain gradient viscoelastic nanobeam which are solved analytically for various boundary conditions. The results are validated with those available in the literature. The impacts of visco-Pasternak foundation parameters, structural damping coefficient, hygro-thermal loading, nonlocal stress parameter, nonlocal gradient parameter, power-law exponent, mode number, boundary conditions and slenderness ratio on the damping frequency of nanoscale viscoelastic FG beams are evaluated.
The problem of flutter is an important topic involving aeroelastic analysis. The first approach to studying this problem was proposed by Theodore Theodorsen in 1935 and, since that publication, Theodorsen's theory has been extensively used by many researchers. However, it is common to find typographical errors in the definitions of the coefficients introduced by Theodorsen to determine the aerodynamic forces in a typical section airfoil. In this context, this paper summarizes the most common typographical errors found in the literature and includes mathematical demonstrations to clarify the correct form of those coefficients.
The presented paper is concerned with the propagation of Rayleigh waves in an orthotropic elastic half-space overlaid by an orthotropic elastic layer of arbitrary thickness. The layer and the half-space may be compressible or incompressible and they are in sliding contact with each other. The main aim of the paper is to derive explicit exact secular equations of the wave for four possible combinations: both the layer and the half-space are compressible or incompressible, one is compressible and the other is incompressible. When the layer and the half-space are both compressible, the explicit secular equation is derived by using the effective boundary condition method. For the three remaining cases, the explicit secular equations are deduced directly from this secular equation by using the incompressible limit technique. Based on the obtained secular equations, the effect of incompressibility and the sliding contact on the Raleigh wave propagation is considered through some numerical examples. It is shown that the incompressibility (of half-spaces and coating layers) and the sliding contact strongly affects the Raleigh wave velocity.
In the present study, viscously damped free and forced vibrations of a rectangular membrane are investigated using a closed form exact method. The method is exact and yields closed form expressions for the vibratory displacements. This is in contrast with the well known eigenfunction superposition method which requires expressing the distributed forcing functions and the displacement response functions as infinite sums of free vibration eigenfunctions. Instead of undamped natural frequencies which are typically computed and applied in the free and forced vibrations, damped natural frequencies are done. The damped natural frequency equation and the critical viscous damping equation are exactly derived. In the damped free vibration, effects of viscous damping on natural frequencies and mode shapes are studied. Some contour plots of damped mode shapes are given. Accurate displacement amplitude vs. forcing frequency curves showing the forced response due to distributed loading are displayed.
This paper proposes a new adaptive neural network integral sliding-mode controller using a bat algorithm (BA-ANNISMC) to control a biped robot. The conventional integral sliding-mode controller (ISMC) is discontinuous in nature due to the combination of nominal control and discontinuous feedback control. The phenomenon of chattering occurs when there is a discontinuity in feedback control. An adaptive neural network is applied to estimate the unknown disturbances to the system. Therefore, by using an adaptive neural network, the chattering phenomena will be eliminated. The proposed controller parameters are tuned using a bat algorithm. The stability of the adaptive neural network integral sliding-mode controller (ANNISMC) is proved by Lyapunov theory. In order to show the effectiveness of the proposed controller, its performance is compared with three other controllers such as a conventional sliding-mode controller (SMC), ISMC and ANNISMC. The results of the numerical simulation clearly indicate the effectiveness of the BA-ANNISMC controller when considering chattering reduction.
In railway transport, braking and traction forces mainly depend on the normal force and the adhesion coefficient between the wheel and the rail. Considering the restrictions on controlling the normal force, maximization of adhesion coefficient seems to be the only way of increasing braking and tractive efforts. Moreover, efficient utilization of adhesion can also reduce operating costs by avoiding early wheel and rail damages and minimizing trip time. However, the adhesion between the rail and the wheel is a highly dynamic function of many parameters, such as environmental conditions, speed, and slip ratio. Unfortunately, there is not yet any sufficiently accurate and reliable way of obtaining these parameters. In this paper, an event-based control scheme is presented to maximize adhesion utilization without necessitating any of the aforementioned parameters. The results obtained with the proposed method are compared with some of the experimentally proven and industrially applied successful methods for different driving scenarios and wheel–rail conditions.
Detecting structural damage in operational conditions still encounters some difficulties, especially in early-stage, as environmental varieties impose challenges in real engineering applications and may require large computational efforts in the structural health monitoring and potential maintenance. Unlike conventional strategies employing frequency response function or response data, a damage detection methodology is addressed in this study by employing transmissibility functions that retains a strong interrelation with structural damage or deterioration, in order to avoid the measurement of excitation, together with principal component analysis that leads to reduction in computational costs. In this procedure, transmissibility is extracted from the structural responses and main features are selected by principal component analysis for less computational costs. Then, via distance measures damage indicators are constructed for both intact and damaged states, and finally a numerical simulation with a clamped-clamped beam and a four-story benchmark are adopted to verify the applicability of the proposed procedure. The results demonstrate a good performance in structural damage detection.
Dynamic characteristics extracted from ambient and forced vibration tests are always associated with some level of uncertainties because of unknown nature of applied forces, existence of ambient noises as well as measurement errors. Stochastic Subspace Methods are among the most accurate and consistent methods within the domain of operational modal analysis. In this research, a new technique for Operational Modal Analysis is proposed using Stochastic Realization Theory and Canonical Correlation Analysis, which in comparison with previous methodologies, identification process are directly performed in the prediction space by extracting orthonormal vectors of data space. Considering its optimized nature, the proposed method is expected to have superior accuracy in terms of elimination of unstable poles as well as low time consumption analysis. To indicate the efficiency and accuracy of the proposed algorithm, it is applied to reanalyze the results of the forced vibration tests performed on the Shahid-Rajaee arch dam in northern Iran. These tests were conducted via steady-state sinusoidal stimulation method. More accurate natural frequencies are obtained compared to those of previously reported results, besides the fact that the first three modes of the structure were identified by the new approach, while they were not observed via the previous one. In order to examine the capabilities of the proposed method for processing of ambient vibration records, the dynamic characteristics of the Pacoima dam was identified using the recorded responses during 2001 earthquake in San Fernando, California. The results indicated good accuracy in the obtained frequencies and damping ratios compared to those obtained via data driven subspace method. Time consumption of identification process were reduced significantly (up to 50%) for both case studies indicating a faster convergence rate provided by the proposed method.
This paper deals with the analysis of stability and dynamics of simply supported micro-plate, actuated by suddenly applied electrostatic forces on both sides and subjected to proportional-derivative control. The Galerkin decomposition is used to obtain the modal equation of the system. Using both a continuous time approach with delay and discrete time approach, the stability analysis is presented in order to obtain the stability boundary and stability charts in the parameter space of control gains. The bifurcation diagram and time series are used to confirm the existence of the Hopf bifurcation and to analyse the pull-in instability. By applying the proportional derivative control to the system under study, the vibrations are controlled and it is found that the control voltage generated digitally is more effective compared to the voltage generated continuously.
In this paper, a new family of wavelets derived from the underdamped response of second-order Linear-Time-Invariant (LTI) systems is introduced. The most important criteria for a function or signal to be a wavelet is the ability to recover the original signal back from its continuous wavelet transform. We show that it is possible to recover back the original signal once the Second-Order Underdamped LTI (SOULTI) wavelet is applied to decompose the signal. It is found that the SOULTI wavelet transform of a signal satisfies a linear differential equation called the reconstructing differential equation, which is closely related to the differential equation that produces the wavelet. Moreover, a time-frequency resolution is defined based on two different approaches. The new transform has useful properties; a direct relation between the scale and the frequency, unique transform formulas that can be easily obtained for most elementary signals such as unit step, sinusoids, polynomials, and decaying harmonic signals, and linear relations between the wavelet transform of signals and the wavelet transform of their derivatives and integrals. The results obtained are presented with analytical and numerical examples. Signals with constant harmonics and signals with time-varying frequencies are analyzed, and their evolutionary spectrum is obtained. Contour mapping of the transform in the time-scale and the time-frequency domains clearly detects the change of the frequency content of the analyzed signals with respect to time. The results are compared with other wavelets results and with the short-time fourier analysis spectrograms. At the end, we propose the method of reverse wavelet transform to mitigate the edge effect.
This paper presents a linear matrix inequality based Proportional-Integral-Derivative (PID) type
In this article, electro-thermo-mechanical vibrational behavior of functionally graded piezoelectric (FGP) plates with porosities is explored via a refined four-variable plate theory for the first time. Uniform, linear and nonlinear temperature changes are considered in this study. Electro-elastic material properties of porous FGP plate vary across the thickness based on modified power-law model. The governing equations derived from Hamilton’s principle are solved analytically. The exactness of solution is confirmed by comparing obtained results with those provided in the literature. Influences of applied voltage, porosity distribution, thermal loadings, material gradation, plate geometrical parameters and boundary conditions on the vibrational behavior of FGP plates are discussed. These results can be applied for accurate design of smart structures made of functionally graded piezoelectric materials by considering porosity distribution.
This paper focuses on the problem of parametrically excited doubly curved sandwich shells with carbon nanotubes reinforced composite (CNTRC) facesheets subjected to in-plane periodic load. The panels consist of cylindrical and spherical shells modeled using QUAD-8 element which was developed using higher-order shear flexible theory. The formulation considers the secondary effects such as the influence of in-plane and rotary inertia terms, and the aerodynamic pressure when the panel is exposed to air flow. The governing equations developed are solved based on eigenvalue approach. The limits of the principal instability zone predicted here are graphically represented using excitation frequencies against the load amplitudes. The results of this study are tested against the available solutions in the literature. A detailed study considering various design parameters including structural theories on the dynamic instability boundaries and its associated origin of instability regions is conducted. These parameters include the CNT volume content, thermal environment, aspect ratio, thickness ratio of core and facesheet, and radius of curvature.
The present article deals with optimal vibration energy harvesting from an axially functionally graded (FG) non-prismatic piezolaminated beam using genetic algorithm (GA). Geometric nonlinear based finite element (FE) formulation using Newmark method in conjunction with Newton-Raphson method is formulated to solve the obtained governing equation. A two noded beam element with two degrees of freedom (DOF) at each node is used in the present FE formulation. The FG material (i.e. non-homogeneity) in the axial direction is considered which varies (continuously decreasing from root to tip of such cantilever beam) using a proposed power law formula. The various cross section profiles (such as linear, parabolic and cubic) are modelled using the Euler-Bernoulli beam theory. The effects of nonlinearity on the responses (such as displacement, voltage and output power) are deliberated with arbitrary power gradient index. The effects of tapers (both width and height in length directions) on the output power and voltage are analysed. A real-coded genetic algorithm based constrained optimization technique is also proposed to determine the best possible design variables for optimal power harvesting within the allowable limits of ultimate stress of beam and breakdown voltage of PZT sensor.
We consider a stochastic optimal feedback control problem for a single-degree-of-freedom vibrational system, where uncertainty is described by two independent noises. The first of them is induced by the control actions and called internal, whereas the second one acts externally. The drift vector also depends on the control function. The set of pointwise control constraints is assumed to be bounded. The minimization functional is taken as the mean system response energy. The Cauchy problem for the corresponding Hamilton–Jacobi–Bellman (HJB) equation without the control constraints is first investigated. This allows us to find the sought-for feedback control strategy in a specific domain of the space of state and time variables. Then a proper extension to the remaining parts of the space is constructed, and the optimality of the resulting global feedback control strategy is proved. The obtained control law is compared with the dry friction and saturated viscous friction control laws.
A new 1-3 viscoelastic composite material (VECM) layer is designed for improved active constrained layer damping (ACLD) treatment of vibration of a functionally graded (FG) circular cylindrical shell. Besides this improved active damping treatment, another objective of this study is to control all the modes of vibration of the shell effectively using the treatment (active constrained layer damping) in layer-form throughout the outer shell-surface. In this design of active constrained layer damping treatment in layer-form, its (active constrained layer damping) necessary conformability with the curved host shell-surface is ensured by the use of a vertically reinforced 1-3 piezoelectric composite (PZC) constraining layer, whereas the effective control of several modes of vibration of the shell is achieved by the use of electrode-patches over the surfaces of the constraining layer. A fruitful strategy in the arrangement of electrode-patches is proposed for effective control of several modes of vibration of the shell using one configuration of the electrode-patches. An electric potential function is assumed for this use of electrode-patches and a geometrically nonlinear coupled electro-visco-elastic incremental finite element model of the overall shell is developed for its analysis in the frequency-domain. The analysis reveals significant improvement of active damping characteristics of the active constrained layer damping layer for the use of the present 1-3 viscoelastic composite material layer instead of the traditional monolithic viscoelastic material (VEM) layer. The analysis also reveals the suitability of the present strategy of arrangement of electrode-patches for achieving aforesaid control-activity of the ACLD layer. The effects of temperature in the host functionally graded shell and different geometric parameters in the design of the 1-3 viscoelastic composite material layer on the damping characteristics of overall shell are also presented.
In this study, the divergence and flutter instability of a cantilever piezoelectric carbon nanotube (CNT) conveying flowing fluid is investigated by considering surface effects. The size-dependent governing differential equation of a piezoelectric CNT is derived using a Newtonian method based on the Eringen nonlocal elasticity theory and in conjunction with the Euler–Bernoulli beam model. The extended Galerkin method is employed to transform the partial differential equation into a set of ordinary differential equations. The resulting eigenvalue problem is solved numerically to determine the effect of nonlocal parameter, various values of piezoelectric voltage, and surface effects on the divergence and flutter instability of a CNT conveying a fluid. Results show that by increasing the voltage from negative values to positive values, the nondimensional critical velocity of the fluid flow decreases. In addition, it should be noted that the effects of the nonlocal parameter lead to a reduction of the flutter and divergence stability of the CNT. Finally, this research can be used to design fluid-conveying nanodevices based on piezoelectric CNTs.
A new formulation is introduced to study the free vibration behavior of a statically loaded beam with geometric nonlinearity. The tangent stiffness of the statically loaded beam is used to investigate the free vibration behavior of the beam about its loaded configuration. The problem is formulated for a linearly tapered beam, and a uniform beam is obtained as a special case. Energy principles based on the variational approach are used to derive the governing equations for the static and dynamic problems. The Ritz method of approximate displacement field is followed to solve the governing equations. The Ritz coefficients are used to derive the tangent stiffness of the loaded beam. Components of the tangent stiffness matrix are derived for a Timoshenko beam with von Kármán-type nonlinearity. Illustrative results are presented for four different classical boundary conditions having in-plane restraint. Results for the first two modes of transverse vibration are presented in the nondimensional deflection-frequency plane. Validation of the work is carried out using finite element software ANSYS. The formulation is new of its kind and can be used for any displacement-based problem following the Ritz method.
In this study, a novel fuzzy robust fault estimation scheme is developed for a class of nonlinear systems when both fault and disturbance are considered. The proposed scheme includes component fault with a nonlinear distribution matrix; as a result, the Takagi–Sugeno model is used to create multiple models. While the Takagi–Sugeno model is used for only the nonlinear distribution matrix of the fault signal, a larger category of nonlinear systems will be considered. This paper presents the problem of robust fault estimation based on fuzzy nonlinear observers, the first one is a fuzzy unknown input observer and the other one is a fuzzy sliding mode observer. The approach decoupled the faulty subsystem from the rest of the system through a series of transformations. Then, the objective is to design a fuzzy unknown input observer guaranteeing the asymptotic stability of the error dynamic using the Lyapunov method and completely removing disturbances; meanwhile, a fuzzy sliding mode observer is designed for a faulty subsystem to generate an estimation of fault based on a quadratic Lyapunov function and some matrices inequality convexification techniques. The sliding motion affects only the faulty subsystem through a novel reduced order fuzzy sliding mode observer; meanwhile, all disturbances are completely removed by fuzzy unknown input observer. Sufficient conditions are established in order to guarantee the convergence of the state estimation error and the results are formulated in the form of linear matrix inequalities. Thus, an exact fault estimator is determined on the basis of linear matrix inequality conditions while the estimation fault is completely insensitive to the disturbance. Finally, a simulation study on an electromagnetic suspension system is presented to demonstrate the g performance of the results compared with a pure sliding mode observer.
An exact free vibration and buckling analysis of a tapered beam-column with general connections is calculated. All structural elements are made of functionally graded material. In this study, a power function is assumed for the variation of the elastic modulus along the cross-section’s height. Extensional-coupling effects are considered in the proposed formulation. By solving the related fourth-order differential equation, the exact answers are obtained. The Bessel functions are utilized in this solution. In addition, the effect of connection flexibility is assessed by considering rotational and transitional springs at the two ends of the element. The suggested stiffness matrix can analyze the free vibration and buckling of a frame made of functionally graded material tapered beam-columns with semi-rigid connections and supports. To validate the proposed formulation, several benchmarks and novel examples are separately analyzed. All numerical findings clearly demonstrate the usefulness of the authors’ scheme.
Among the chatter suppression techniques in milling, active fixtures seem to be the most industrially oriented, mainly because these devices could be directly retrofittable to a variety of machine tools. The actual performances strongly depend on fixture design and the control logic employed. The usual approach in the literature, derived from general active vibration control applications, is based on the employment of adaptive closed-loop controls aimed at mitigating the amplitude of chatter frequencies with targeted counteracting vibrations. Whilst this approach has proven its effectiveness, a general application would demand a wide actuation bandwidth that is practically impeded by inertial forces and actuator-related issues. This paper presents the study of the performance of alternative open-loop actuation strategies in suppressing chatter phenomena, aiming at limiting the required actuation bandwidth. A dedicated time-domain simulation model, integrating fixture dynamics and the features of piezoelectric actuators, is developed and experimentally validated in order to be used as a testing environment to assess the effectiveness of the proposed actuation strategies. An extensive numerical investigation is then carried out to highlight the most influential factors in assessing the capability of suppressing chatter vibrations. The results clearly demonstrated that the regenerative effect could be effectively disrupted by actuation frequencies close to half the tooth-pass frequency, as long as adequate displacement is provided by the actuators. This could sensibly increase the critical axial depth of cut and hence improve the achievable material removal rate, as discussed in the paper.
A vibration model of the powertrain can be used to predict its dynamic behavior when excited by fluctuations in the engine torque and speed. The torsional vibration resulting from torque and speed fluctuations increases the rattle noise in the gearbox and it should be controlled or minimized in order to gain acceptance by clients and manufactures. The fact that the proprieties of the torsional damper integrated into the clutch disc alter the dynamic characteristic of the system is important in the automotive industry for design purposes. In this study, bench test results for the characteristics of a torsional damper for a clutch system (torsional stiffness and friction moment) and powertrain torsional vibration measurements taken in a passenger car were used to verify and calibrate the model. The adjusted model estimates the driveline natural frequency and the time response vibration. The analysis uses order tracking signal processing to isolate the response from the engine excitation (second-order). It is shown that a decrease in the stiffness of the clutch disc torsional damper lowers the natural frequency and an increase in the friction moment reduces the peak amplitude of the gearbox torsional vibration. The formulation and model adjustment showed that a nonlinear model with three degrees of freedom can represent satisfactorily the powertrain dynamics of a front-wheel drive passenger car.
The performance index of both the state and control variables with a constrained dynamic optimization problem of a fractional order system with fixed final Time have been considered here. This paper presents a general formulation and solution scheme of a class of fractional optimal control problems. The method is based upon finding the numerical solution of the Hamilton–Jacobi–Bellman equation, corresponding to this problem, by the Legendre–Gauss collocation method. The main reason for using this technique is its efficiency and simple application. Also, in this work, we use the fractional derivative in the Riemann–Liouville sense and explain our method for a fractional derivative of order of
A procedure based on the concept of full-discretization and numerical integration is established in this work for the stability analysis of periodic distributed-delay oscillators governed by delay integro-differential equations (DIDEs). DIDEs can be found as models of mechanical systems suffering from distributed-delay feedback, such as regenerative machine tool vibrations modeled by distributed force and wheel shimmy. Unstable vibrations in such systems are systematically avoided/controlled if the boundaries between the stable and unstable subspaces are established. The presented method involves the two-stage application of numerical integration to the governing DIDE. While the first-stage application discretizes and converts the distributed delay to fine series of short discrete delays, the second-stage application results in discrete solutions paving the way for a new method of constructing a finite monodromy operator. The error and convergence of the method are studied. It is found that the presented method is of the same convergence as that of the well-accepted first-order semi-discretization method, but more computationally efficient in terms of time savings. A number of case study DIDEs that have already been studied in the literature using methods of semi-discretization and spectral finite elements are studied with the presented method. It is seen that the presented method is valid as it produces stability results that compare well with those of the earlier works.
The three-dimensional sono-elasticity method recently developed by Zou ((2014) Three-dimensional sono-elasticity of ships. PhD Dissertation, China Ship Scientific Research Center, China) and Wu ((1984) Hydroelasticity of floating bodies. PhD Dissertation, Brunel University, UK) is employed to explore the acoustic and vibrational characteristics of a propeller–shaft–hull coupled system. The acoustic field can be solved by introducing Green’s function for the ideal compressible fluid together with the Price–Wu generalized fluid–structure interface boundary conditions. The vibration of a ship structure is governed by the generalized equations, including added mass, damping and restoring coefficients. In order to discover the mechanisms underlying the acoustic and vibrational characteristics of the propeller–shaft–hull coupled system, numerical models for hull structures with a shaft and without a shaft are designated. Through modal analysis, the correlations of the line spectra of acoustic radiation and the corresponding vibration modes of the hull are clearly identified. Through further numerical analysis, the appropriate location of the base for the thrust bearing and installation schemes are recommended.
The aim of this paper is to study the behavior of the torsional surface wave in a heterogeneous initially stressed vertical fluid-saturated anisotropic layer sandwiched between inhomogeneous and homogeneous porous half-spaces. It has been considered that the mass density and rigidity of the upper half-space and intermediate layer are space dependent. The proposed model is solved to obtain different dispersion relations for the torsional surface wave in a heterogeneous poroelastic medium lying between two half-spaces. The influence of compressive stress and heterogeneity on torsional surface wave dispersion is shown numerically. It has been observed that heterogeneity, porosity, initial stress of the layer and inhomogeneity of the upper and porosity of lower half-spaces affect the torsional wave speed much. The wave analysis further indicates that the torsional surface waves travel faster in elastic half-spaces in comparison than in the fluid-saturated porous layer.
In this paper, a longitudinal model of a space launch vehicle was developed using the Lagrange mechanism and a free–free Euler–Bernoulli beam model. The aim was to propose a model including one flexible mode plus a nonlinear aerodynamic coefficient for nonlinear control design. We then studied the output feedback problem raised by using such a nonlinear model. The main achievement is to propose a new finite-time state observer when the measured outputs are corrupted by an unidentified flexible mode. This effect may destabilize a classical backstepping control law applied to the rigid model. To achieve this, a backstepping control law was redesigned to damp out the flexible mode, once measured and characterized. Hence a new adaptive finite time observer was developed. Closed-loop simulations show the effectiveness of the observer in combination with a redesigned backstepping control law when sensors and the launcher nozzle are collocated.
In this paper, three controllers are investigated for active vibration control of a pedestrian walkway structure. They comprise direct velocity feedback, observer-based and independent modal space controllers that are implemented in single-input single-output (SISO), multi-SISO and multiple-input multiple-output (MIMO) configurations. The objective of the SISO controller schemes is to compare vibration mitigation performances arising from global control versus selective control of structural resonant frequencies in a given frequency bandwidth. The objectives set out for the multi-SISO and MIMO controllers are to realize global control within the same frequency bandwidth considered in the SISO studies. A novel aspect of these latter studies is the independent control of selected resonant frequencies at different locations on the structure with the aim of imposing global control.
Vibration mitigation performances are evaluated using frequency response function measurements and uncontrolled and controlled responses to a synthesized walking excitation force. In the SISO studies, selective control of specific resonant frequencies has a slight degradation in the global vibration mitigation performance, although it reflects better performance around the target frequencies. For the multi-SISO and MIMO controller studies, the selective control of the two lowest and dominant frequencies of the structure at two different locations still offers comparative vibration mitigation performances with the controllers considered as global in the sense that they target both structural frequencies at both locations. Attenuations of between 10 and 35 dB are achieved.
In this work, the horizontal nonlinear response of a three-degree-of-freedom vertical transportation model excited by guide rail deformations is investigated. The equation of motion contains nonlinearities in the form of Duffing stiffness for the translational spring in tilting motion of the cabin. In order to improve the comfort for passengers a control strategy based on the State-dependent Ricatti Equation (SDRE) is proposed. Numerical simulations are performed to study the nonlinear behavior of the adopted mathematical model. In addition, we test the robustness of the SDRE control technique considering parametric errors and noise. The obtained results confirm that the proposed strategy can be effective in controlling the response of the system.
A dynamic stiffness formulation is developed for both in-plane and bending vibrations of plates with two opposite edges simply supported. The bending motions of plates are described in terms of Leissa’s displacement functions while the in-plane motions take the forms take the forms that were proposed by Bercin and Langley. Using Projection Method, the forces and their corresponding displacements along plate junctions are projected onto a set of orthogonal functions, by which means the well-known spatial dependence difficulties can be overcome, and, as a result, local dynamic stiffness matrix is obtained. Classical finite element technique is utilized to assemble local stiffness matrix into global coordinates. Finally, dynamics of an L-shaped plate is addressed, within which conversion of in-plane and bending motions occurs. Our numerical results are in good agreement with those obtained from finite element method, which demonstrates that this dynamic stiffness formulation has great potential in modeling the dynamics of built-up plate structures, especially in characterizing the in-plane waves, bending waves, and their mutual conversions along plate junctions.
A coupled lateral-torsional nonlinear dynamic model with 16-degree-of-freedom (16-DOF) of gear-rotor-bearing transmission system (GRBTS) is developed after comprehensive considering the nonlinear features associated with time-varying meshing stiffness, backlash, transmission error, friction force, input/output load, gravity and gear eccentricity. Based on the nonlinear differential equations, the coupled multi-body dynamic responses of the GRBTS are demonstrated using the Runge-Kutta numerical method, and the effects of friction coefficient and mean load on the dynamic characteristics are investigated. The results show that the friction force could enlarge the vibration amplitude and affect the low frequency components seriously. The mean load excitation has a complicated influence on the coupled GRBTS, and the torsional vibration is the dominate response. Whereas the mean load excitation has a certain extent vibration suppression, and light load and heavy load could no longer effectively control the nonlinear vibration of the GRBTS. With the increasing of rotational speed, the friction coefficient and mean load ranges of the chaotic behavior widen and the chaotic characteristics strengthens. It is shown that small parameter random perturbation might be propagated in the vibration system and lead to relatively large vibration of the system. The contribution to provide a reference for the design and study of gear system.
In this paper, a new numerical method for solving fractional optimal control problems by using hybrid functions is presented. The Riemann–Liouville fractional integral operator for hybrid functions is utilized to reduce the solution of optimal control problems to a nonlinear programming one, to which existing, well-developed algorithms may be applied. The method is computationally very attractive and gives very accurate results.
In this paper, a finite element model updating method using frequency response functions is experimentally validated. The method is a sensitivity-based model updating approach which utilizes a pseudo-linear sensitivity equation. The method is robust against the adverse effects of incomplete measurement, measurement errors and modeling errors. The experimental setup consists of a free-free aluminum beam, where changes are introduced by reducing the stiffness and attaching lumped mass at certain parts of the beam. The method is applied to identify the location and amount of the changes in structural parameters. The results indicate that the location and the size of different level of changes in the structure can be properly identified by the method. In addition, a study is done on the influence of the number of impacts and sensors on the quality of the identified parameters.
In this paper, free vibration analysis of magneto-electro-elastic (MEE) cylindrical composite panel reinforced by various distributions of carbon nanotubes (CNTs) considering open and closed circuits boundary conditions based on the first order shear deformation theory (FSDT) is carried out. Carbon nanotubes (CNTs) in Poly-vinylidene fluoride (PVDF) matrix are arranged and different distribution patterns of CNTs including uniform distribution (UD), FG-V, FG-A, FG-X and FG-O are employed. The Young’s and shear moduli are obtained using the extended mixture rule. Also, the material properties of magneto-electric fiber reinforced composite are estimated by mixture rule. By employing energy method and Hamilton’s principle, the equations of motion for cylindrical composite panel reinforced by CNTs are derived. In this paper, the effects of the volume fraction, various distributions of CNTs including uniform and functionally graded (FG) distributions, angle orientation, two elastic foundation parameters, aspect ratio (length-to-thickness ratio), radius-to-thickness ratio, and the multi-physical fields with open and closed circuits boundary conditions on the natural frequency of MEE cylindrical composite panel are considered. These effects play an important role on the natural frequencies. Moreover, the numerical results of this research can be used to manufacturing process design and optimization MEE cylindrical composite panel under multi-physical fields and the previous results can be used in order to prevent the resonance phenomenon.
The paper develops a new topology for a three phase multilevel inverter with a view to reduce the number of switches in the path of the current. It encompasses a mechanism to reach the desired target voltage and in turn enable the three phase induction motor to operate at the specified speed. The formulation incorporates the theory of an appropriate pulse width modulation strategy to ensure the elimination of higher frequency components of the output voltage. The use of relatively smaller number of carriers in the process of generating the switching pulses serves to enhance the output voltage spectrum. The intriguing merits of the phase disposition over the other modulation schemes enable to arrive at a nearly sinusoidal voltage. The performance obtained from the prototype substantiate the MATLAB based simulation results and establish the ability of the series parallel switched multilevel inverter topology to offer an improved performance for the induction motor.
In this paper, the influence of clutch disk pre-damper mechanism constituents on the idle rattle phenomenon was investigated with an analytical model containing a new time-varying gear mesh stiffness function. Comparing experimental results to simulation results for the same excitation input was the key implementation for the validation of proposed model. The engine speed fluctuations represented in the simulation was imported from a speed measurement of a diesel engine in the test bench.
In this paper the noise propagation through a solid medium is considered to study how the parameters of the statistical model change. In particular the external and internal sound fields of a box are taken into account. It is experimentally shown that the variance of the real and the imaginary parts of the external stationary random noise change differently while going through the box walls. The generalized Rayleigh distribution is shown to be more suitable to model the noise inside the cavity instead of the classical Rayleigh distribution. Starting from this outcome it has been studied how this noise affects a signal.
It is known that a signal modulus affected by stationary random noise can be described by using the Rice distribution if the real and imaginary parts of the noise are statistically independent and identically distributed with zero mean and equal variances. Otherwise the less popular generalized Rice distribution must be used. The main differences of using the Rice or the generalized Rice distributions are shown by considering phasors both with constant and variable phases. In this paper it is shown that the bias estimation depends on the phase of the phasor if the variances of the real and imaginary parts are different and a numerical quantification is given.
The attained results are useful when performing measurements of the sound pressure field due to a sound source inside a cavity affected by external noise.
This work addresses the control of a pinned-pinned beam represented by the fourth order partial differential equation commonly known as the Euler–Bernoulli beam model. The system under consideration has pinned boundary conditions on one end (displacement and bending moment fixed at zero) and controlled boundary conditions on the other end (displacement and bending moment are prescribed by control functions). There are also unknown bounded disturbances included on the controlled boundary. A backstepping control technique which introduces arbitrary damping into the system is discussed, and a method for applying this control in the presence of unknown disturbances is developed using sliding mode control theory. Sliding mode controllers are developed in a way that does not create a chattering effect, which is a common issue with sliding mode control. Simulation results are presented to show how the system dampens out vibrations at an arbitrarily determined rate and how the control functions respond to unmodeled disturbances.
A nonlinear saturation controller (NSC) is applied in this work to reduce the oscillations of a rotating blade dynamical system running at unsteady rotating speed. The controller is coupled quadratically to the main system by designing its natural frequency to be one half of the main system natural frequency. This is done to setup an energy bridge between them to make use of saturation phenomenon. That phenomenon is advantageous when the excitation force increases; the whole energy in the main system is channeled to the controller. The two system modes of vibrations are found to be linearly coupled powerfully, so the controller is applied only to the first mode and, consequently, the second mode tracks it. The multiple scales perturbation technique (MSPT) is adopted to derive the steady state equations that describe the modulations of amplitudes and phases of the system before and after control. Then, a stability analysis is achieved via Lyapunov’s indirect method to determine the stable and unstable solutions depending on the real parts of the Jacobian matrix eigenvalues. Time history and different response curves of the controlled system are included for showing the controller effect. Eventually, validation curves and comparison with previously published work are included.
This study proposes a new method for reducing the shock vibration response of an Unmanned Aerial Vehicle (UAV) during the landing process by means of the momentum exchange principle (MEID). The performance of the impact damper is improved by adding a pre-straining spring to the damper system. This research discusses the theoretical application of the damper to the UAV landing gear system. The UAV dynamics is first modeled as a simple lumped mass translational vibration system. Then we analyze a more complex two-dimensional model of UAV dynamics. This model consists of the main wheel, nose wheel and main body. Three cases of UAV landing gear mechanisms: without damper, with passive MEID (PMEID) and with pre-straining spring MEID (PSMEID) are simulated. The damper performance is evaluated from the maximum acceleration and force transmission to the main body. The energy balance calculation is conducted to investigate the performance of PSMEID. The simulation results show that the proposed PSMEID method is the most effective method for reducing the maximum acceleration and force transmission of UAV during impact landing.
The main motivation of this paper is to examine the effect of structural nonlinearities on the engineering demand parameters (EDPs) of seismically excited controlled plan-asymmetric buildings equipped with magneto-rheological dampers. The development of a robust control algorithm for asymmetric buildings due to the randomness of ground excitations and their torsional response has always been a significantly challenging task in the vibrations control of structures. While the control algorithm in a simple approach could be designed ignoring the dependency of stiff and flexible edges of EDPs, the present research aimed also to develop a control strategy that mitigates simultaneously asymmetric edge responses of the structure using the multi-input multi-output ability of fuzzy logic control algorithms. In order to alleviate all difficulties to design an admissible control algorithm and attain the desired level of performance, the nondominated sorting genetic algorithm-II is applied. The effectiveness of the proposed controller on the inelastic seismic behavior of a controlled plan-asymmetric one-story structure is evaluated through a parametric study in which asymmetry is considered in the form of unidirectional mass eccentricity. To take the inelastic behavior of a controlled asymmetric building’s members into account, fiber elements modeling is employed. The model was subjected to a uniaxial lateral disturbance, including ordinary and strong ground motions exciting both lateral and torsional motions.
Optimal control techniques (LQG, H, etc.) offer several advantages for active vibration control, such as possibility of trade-off between achievable vibration attenuation and required control inputs, simultaneous suppression of multiple modes, unified and systematic controller design procedure for MIMO systems. However, a major limitation in their application has been the phenomena of spillover. For optimal controllers robustness to spillover is achieved by rolling-off controller response. In this paper, a novel criterion of sensors placement to minimize roll-off requirement, for given actuator locations, is proposed. As an illustration H control is applied for suppressing first two modes of a slewing spacecraft. Comparison of results obtained for sensor location based on proposed criterion with those of collocated sensor location showed: (a) for a given controller order, performance characteristics similar to collocated control with improved robustness to spillover can be obtained by using the proposed criterion of sensor placement; (b) with proposed placement criterion robustness to spillover can be maintained with lower order controller as compared with the minimum controller order required for collocated control.
The present paper investigates the efficacy of controlling friction induced vibration by normal load modulation. Friction-induced self-excited vibration, attributed to the low-velocity drooping characteristics of friction (Stribeck effect), is modelled by a mass-on-belt model where the normal force of the mass is being modulated based on the acceleration feedback followed by a second order filtering. Polynomial model is employed to study the friction phenomenon between the mass and the belt. The pole crossover design (to ensure faster transient and greater relative stability) is implemented to optimize the filter parameters with an independent choice of the belt velocity and control gain. These sets of optimized parameter values are then used to construct local stability boundaries in the plane of control parameters. Numerical simulations in a MATLAB SIMULINK model and bifurcation diagrams obtained in AUTO (while using belt velocity as the bifurcation parameter) indicate that a significantly small-amplitude limit cycle resulting from a supercritical Hopf bifurcation stabilizes the extreme low velocity region at higher values of the control gain. With the increase of the control gain the subcritical nature of Hopf bifurcation changes to a supercritical one. The efficacy of this optimization (based on numerical results) in the delicate low velocity region is also enclosed.
This paper presents efficient numerical techniques for solving fractional optimal control problems (FOCP) based on orthonormal wavelets. These wavelets are like Legendre wavelets, Chebyshev wavelets, Laguerre wavelets and Cosine And Sine (CAS) wavelets. The formulation of FOCP and properties of these wavelets are presented. The fractional derivative considered in this problem is in the Caputo sense. The performance index of FOCP has been considered as function of both state and control variables and the dynamic constraints are expressed by fractional differential equation. These wavelet methods are applied to reduce the FOCP as system of algebraic equations by applying the method of constrained extremum which consists of adjoining the constraint equations to the performance index by a set of undetermined Lagrange multipliers. These algebraic systems are solved numerically by Newton's method. Illustrative examples are discussed to demonstrate the applicability and validity of the wavelet methods.
The effects of the pseudoelastic hysteresis of shape memory alloy springs on the aeroelastic behavior of a typical airfoil section are numerically investigated for six different sets of alloy constitutive properties. A two-degree-of-freedom (namely, plunge and pitch) typical section is modeled. Shape memory alloy helical springs are considered in the pitch degree-of-freedom based on classical phenomenological models modified by the pure shear assumption. Tension–compression asymmetry and nonhomogeneous distributions of shear strain, shear stress and martensitic fraction in the cross-sectional area of the coiled shape memory alloy wire are considered. A linear model is used to determine the unsteady aerodynamic loads. Attractive alloy characteristics, which can enhance the aeroelastic behavior of the typical section at the flutter boundary and at the post-flutter regime, are identified and discussed in detail.
In this paper the forced vibration of a hydro-viscoelastic system consisting of a viscoelastic plate, compressible viscous fluid and rigid wall is considered. The focus is on the investigation of the influence of the rheological parameters of the plate material and the viscosity of the fluid on the frequency response of this system. The constitutive relations for the plate material are given through the fractional-exponential operators, and the exact equations of the visco-elastodynamics in the plane-strain state are employed for describing the plate motion. The fluid motion is described through the linearized Navier–Stokes equations and it is assumed that the velocity and force vectors are continuous across the interface plane between the fluid and the plate. Numerical results on the frequency response of the normal stress acting on the interface plane and of the normal velocity of the points of this plane are presented for various values of the rheological parameters of the plate material. These results are also distinguished with respect to inviscid and viscous fluid cases. As a result of the analyses of these results, corresponding conclusions are made on the influence of the rheological parameters of the plate material on the aforementioned frequency responses.
The aim of this paper is to validate the finite element formulations proposed in a companion paper for the study of the nonlinear dynamic behavior of cable structures. A well-known suspended cable in multiple 1:2 "internal resonance" conditions is herein considered. A uniform ice deposit, along the length of the cable, makes it prone to galloping vibrations under a steady wind flow. Different modeling strategies, relying on different assumptions regarding both the mechanical model as well as the aerodynamic response, are investigated and compared with results coming from analytical, semi-analytical and numerical models from the literature. The role of torsional and flexural stiffness terms, and of the initial undeformed configuration, is critically assessed. The results obtained show the significant effect coming from the adoption of a beam finite element formulation that includes the effect of torsional rotation in the evaluation of the aerodynamic loads.
It has been observed from failures of highway bridges during major earthquakes that skew bridges are among the most vulnerable to seismic loading. It has been shown that the coupling between the translational motions of the deck and the collision of the deck with the abutments are two major factors influencing the vulnerability of skew bridges. This paper studies the influence of deck–abutment collision (seismic pounding) on the coupled motions of decks of skew bridges during strong earthquakes using an analytical approach. A three-degree-of-freedom model is presented to study key dynamic features of skew bridges. It is assumed that the deck of the model is rigid and the columns remain elastic during the ground motion. Contact planes between the deck and the abutments are idealized by several contact points pairwise arrayed at the end-span expansion joints. The mechanism of energy absorption and dissipation during the contact duration is simulated through the implementation of a nonlinear contact element between the contact points. A parametric study has been carried out by varying different parameters, including the skew angle (β), the size of the gap between the deck and the abutments at the end-span expansion joints (gap), and the normalized stiffness eccentricity along the x-axis (ex/r). The results of this study show that the transverse displacements of acute corners of the deck and the rotation of the deck about the mass center noticeably increase with the increases of β and ex/r, and with the decrease of the gap.
In the presented study, a second-line back-up system for the seismic protection of cladding panels in RC precast buildings is first presented. The system consists of special anchoring elements and a rope restrainer. The latter is activated only in the case when the existing connections between the primary structure and the panel fail, resulting in the occurrence of relatively large impact forces in the restrainer and in the anchoring elements. In order to adequately design the constitutive parts of the system, a simple yet sufficiently accurate procedure for the estimation of the impact forces is needed. A relatively easy-to-use formula was therefore proposed for this purpose. Next, an extensive parametric study, using response history analysis (RHA), was performed and the influence of several parameters affecting the impact forces in the restrainers was studied. The results obtained in the study were used to evaluate the proposed analytical formula. Considering the simplicity of the proposed formula, its accuracy was good. It can therefore be applied to the design of short restrainers which could be used in reinforced concrete (RC) precast buildings for the protection of cladding panels against the effects of earthquakes.
Functionally graded SUS316-Al2O3 beams with ceramic content varying from 0 to 40% were prepared by a plasma spraying technique. Nonlinear finite element analysis was used to obtain the static deflection and free vibration of a clamped-free functionally graded beam. Von Kármán geometric nonlinearity and power law variation in material gradation through the beam thickness are considered in the analysis. The maximum error between the experimental and nonlinear finite element results for deflection is 6.68% and 14.31% on the fundamental frequency. Numerical results have also been attempted using ANSYS 3D solid element and they compare more closely with the experimental results.
Inducing sustained oscillations in a class of nonlinear discrete time systems is studied in this paper. The novelty of this paper is based on the proposed approach in generating stable oscillations according to limit cycle control. The limit cycle control is not formulated for nonlinear discrete time systems of any order and this paper concentrates on this issue. Considering the stable limit cycle as a positive limit set for the dynamical system, a nonlinear control law is designed to create the considered limit cycle in the phase trajectories of the closed-loop nonlinear discrete time system to achieve oscillations with the desirable amplitude and frequency. For this purpose, firstly, the limit cycle control is proposed for second-order nonlinear discrete time systems. The stability analysis of the generated limit cycle is done via a suitable Lyapunov function. Also, the domain of attraction of the created limit cycle is calculated. The proposed method is then extended for nonlinear discrete time systems of any order via the backstepping technique. Finally, computer simulations are performed for a practical example to demonstrate the ability of the designed controller in generating stable oscillations.
In this paper, we design learning law with high-order internal models for fractional order differential equations to track the varying reference accurately by adopting a few iterations in a finite time interval. We establish sufficient conditions of convergence for the P-type and PD-type updating law for different fractional order differential equations. Finally, we give some numerical examples to demonstrate the validity of the designed method.
Free vibration analysis of embedded functionally graded carbon nanotube-reinforced composite (FG-CNTRC) conical, cylindrical shells and annular plates is carried out using the variational differential quadrature (VDQ) method. Pasternak-type elastic foundation is taken into consideration. It is assumed that the functionally graded nanocomposite materials have the continuous material properties defined according to extended rule of mixture. Based on the first-order shear deformation theory, the energy functional of the structure is calculated. Applying the generalized differential quadrature method and periodic differential operators in axial and circumferential directions, respectively, the discretized form of the energy functional is derived. Based on Hamilton’s principle and using the VDQ method, the reduced forms of mass and stiffness matrices are obtained. The comparison and convergence studies of the present numerical method are first performed and then various numerical results are presented. It is found that the volume fractions and functionally grading of carbon nanotubes play important roles in the vibrational characteristics of FG-CNTRC cylindrical, conical shells and annular plates.
In adaptive control applications for noise and vibration, finite ımpulse response (FIR) or ınfinite ımpulse response (IIR) filter structures are used for online adaptation of the controller parameters. IIR filters offer the advantage of representing dynamics of the controller with smaller number of filter parameters than with FIR filters. However, the possibility of instability and convergence to suboptimal solutions are the main drawbacks of such controllers. An IIR filtering-based Steiglitz–McBride (SM) algorithm offers nearly-optimal solutions. However, real-time implementation of the SM algorithm has never been explored and application of the algorithm is limited to numerical studies for active vibration control. Furthermore, the prefiltering procedure of the SM increases the computational complexity of the algorithm in comparison to other IIR filtering-based algorithms. Based on the lack of studies about the SM in the literature, an SM time-domain algorithm for AVC was implemented both numerically and experimentally in this study. A methodology that integrates frequency domain IIR filtering techniques with the classic SM time-domain algorithm is proposed to decrease the computational complexity. Results of the proposed approach are compared with the classical SM algorithm. Both SM and the proposed approach offer multimodal vibration suppression and it is possible to predict the performance of the controller via simulations. The proposed hybrid approach ensures similar vibration suppression performance compared to the classical SM and offers computational advantage as the number of control filter parameters increases.
The optimal control for vibration suppression of a plate by distributed piezoelectric actuators is considered. A performance index in the form of a weighted quadratic functional of the dynamic response of a rectangular simply supported plate will be minimized within a prescribed time duration using piezoelectric patches (voltages). The minimization of the performance index over these voltages is subject to the equation of motion governing the plate's structural vibration and a set of initial and boundary conditions. The solution method is a combination of modal space expansion and direct state parameterization. Modal space expansion will transform the optimal control of a distributed parameter system into the optimal control of a lumped parameter system. Using Legendre wavelets, the quadratic optimization problem is transformed into a mathematical programming problem, where the objective is to minimize a set of unknown coefficients to obtain the optimal trajectory and the optimal control. Numerical examples will be provided to illustrate the effectiveness and the efficiency of the proposed method.
Model uncertainties and actuator delays are two factors that degrade the performance of active structural control systems. A new robust control system is proposed for control of an active tuned mass damper (AMD) in a high-rise building. The controller comprises a two-loop sliding model controller in conjunction with a dynamic state predictor. The sliding model controller is responsible for model uncertainties and the state predictor compensates for the time delays due to actuator dynamics and process delay. A reduced model that is validated against experimental data was constructed and equipped with an electro-mechanical AMD system mounted on the top storey. The proposed controller was implemented in the test structure and its performance under seismic disturbances was simulated using a seismic shake table. Moreover, robustness of the proposed controller was examined via variation of the test structure parameters. The shake table test results reveal the effectiveness of the proposed controller at tackling the simulated disturbances in the presence of model uncertainties and input delay.
Active magnetic bearings (AMBs) are often used to mitigate vibrations in turbines, compressors, machining spindles, etc. However, rotor-AMBs are inherent open-loop unstable systems, and hence it is an urgent yet challenging task to stabilize rotor-AMBs with external disturbances. A dual-mode predictive flexible rotor controller is developed hereby for a rotor-AMB system with input constraints. The method is afterwards proved to be capable of enlarging the region of attraction, and hence can effectively mitigate more-intensive vibrations excited by external disturbances, which is desirable in real applications. Finally, experiments are conducted on the rotor-AMB system to show the effectiveness of the proposed dual-mode predictive controller.
This paper presents the optimization of input amplitudes for mechanical control-affine systems with high-frequency, high-amplitude inputs. The problem consists of determining the input waveform shapes and the relative phases between inputs to minimize the input amplitudes while accomplishing some control objective. The effects of the input waveforms and relative phases on the dynamics are investigated using averaging. It is shown that of all zero-mean, periodic functions, square waves require the smallest amplitudes to accomplish a control objective. Using the averaging theorem the problem of input optimization is transformed into a constrained optimization problem. The constraints are algebraic nonlinear equalities in terms of the amplitudes of the inputs and their relative phases. The constrained optimization problem may be solved using analytical or numerical methods. A second approach uses finite Fourier series to solve the input optimization problem. This second approach confirms the earlier results concerning minimum amplitude inputs and is then applied to the problem of minimizing control energy.
The problem of the optimal semi-active control of a structure subjected to a moving load is studied. The control is realized by a change of damping of the structure’s supports. The objective is to provide a smooth passage for vehicles and extend the time needed for the safety service of the carrying structures. In contrast to the previous works of the author, in this paper, the model used takes into account time-varying passage speeds, which allows a broader application, in particular, to robotics. The study of the optimal control problem produces a practical condition that justifies whether, for a given set of parameters, the controlled system can outperform its passively damped equivalent. For the optimization, an efficient method of parametrized switching times is developed and tested via a numerical example. The designed optimal control is examined on a real test stand. The experiments are carried out for three different passage scenarios. In terms of the assumed metrics the proposed method outperforms the passive case by over 40%.
This paper studies the effects of an external mean flow and an internal air-gap mean flow on sound transmission through a double-wall thick cylindrical shell. Due to the major influence of some effective terms such as membrane, bending, transverse shearing and rotational inertia on thick-walled shell, three-dimensional theory of elasticity is used to obtain the governing equations of motion. Therefore, Newton’s second law is utilized to develop the equilibrium equations for an infinitesimal element in cylindrical coordinates. Then, the equations of motion related to the circular hollow cylinders are solved using Helmholtz potentials for arbitrary values of physical and geometrical parameters. In addition, by coupling of both inner and outer shells, a modal transfer matrix is created. This modal matrix stands for the global dynamic equilibrium of the double-wall cylinder. Moreover, the sound transmission Loss of the double-wall cylinder excited by an acoustic oblique plane wave with two angles of incident (i.e. elevation and azimuth angles) is predicted. Due to lack of studies in the field of sound transmission through the thick-walled shell, the results obtained in this study are compared with those from other researchers for a thin cylindrical shell. These results indicate an excellent agreement in comparison with each other. Furthermore, the results reveal that with thickening of the shell, critical and coincidence frequencies are getting closer to ring frequency. Moreover, the effects of external and air-gap flows on TL behave in similar way whereas the Mach number is positive. In addition, an improvement of transmission loss can be found whereas the Mach number is negative; particularly this enhancement is more specified for the external flow. Finally, the results indicate that where both external and air-gap fluids simultaneously flow in opposite directions
This paper considers experiments on the control of a helicopter gearbox hybrid electromagnetic suspension. As the new generation of helicopters includes variable engine revolutions per minute (RPMs) during flight, it becomes relevant to add active control to their suspension systems. Most active system performance derives directly from the controller construction, its optimization to the system controlled, and the disturbances expected. An investigation on a feedback and feedforward filtered-x least mean square (FXLMS) control applied to an active DAVI suspension has been made to optimize it in terms of narrow-band disturbance rejection. In this paper, we demonstrate the efficiency of a new hybrid active suspension by combining the advantages of two different approaches in vibration control: resonant absorbers and active suspensions. Here, a hybrid active suspension based on the passive vibration filter called DAVI is developed. The objective of this paper is to prove the relevancy of coupling a resonant vibration absorber with a control actuator in order to create an active suspension with larger bandwidth efficiency and low energy consumption. The simulations and experimentation achieved during this suspension system development support this hypothesis and illustrate the efficiency and low energy cost of this smart combination.
In this study, a robust finite time Takagi-Sugeno fuzzy control method for hydro-turbine governing system (HTGS) is investigated. Firstly, the mathematical model of HTGS is introduced, and on the basis of Takagi-Sugeno (T-S) fuzzy rules, the T-S fuzzy model of HTGS is presented. Secondly, based on finite time stability theory, a novel finite time Takagi-Sugeno fuzzy control method is designed for the stability control of HTGS. Thirdly, the relatively loose sufficient stability condition is acquired, which could be transformed into a group of linear matrix inequalities (LMIs) via Schur complement as well as the strict mathematical derivation is given. Furthermore, the control method could resist random disturbances, which shows the good robustness. Simulation results indicate the designed finite time T-S fuzzy control scheme works well compared with the conventional method. The approach proposed in this paper is easy to implement and also provides reference for relevant hydropower systems.
For output-feedback control of linear time-varying (LTV) and nonlinear systems, this paper focuses on control based on the forward propagating Riccati equation (FPRE). FPRE control uses dual difference (or differential) Riccati equations that are solved forward in time. Unlike the standard regulator Riccati equation, which propagates backward in time, forward propagation facilitates output-feedback control of both LTV and nonlinear systems expressed in terms of a state-dependent coefficient (SDC). To investigate the strengths and weaknesses of this approach, this paper considers several nonlinear systems under full-state-feedback and output-feedback control. The internal model principle is used to follow and reject step, ramp, and harmonic commands and disturbances. The Mathieu equation, Van der Pol oscillator, rotational-translational actuator, and ball and beam are considered. All examples are considered in discrete time in order to remove the effect of integration accuracy. The performance of FPRE is investigated numerically by considering the effect of state and control weightings, the initial conditions of the difference Riccati equations, the domain of attraction, and the choice of SDC.
Stiffness properties of interfacial engineering surfaces are of great importance to the dynamic performance of relevant mechanical systems. Normal contact stiffness and oil film stiffness of line contact problems are studied in this work analytically and numerically. The Hertzian contact theory and the Yang–Sun method are applied to predict the contact stiffness, while the empirical elastohydrodynamic lubrication (EHL) film thickness method and the complete numerical EHL model are used to predict the oil film stiffness. The numerical model mainly consists of the Reynolds equation; the film thickness equation, in which the regular surface roughness is taken into consideration; the force balance equation; and the viscosity-pressure equation. The effects of the normal load, rolling speed, regular surface waviness, and starved lubrication level on the oil film stiffness are investigated.
The interest of studying fractional systems of second order in electrical and mechanical engineering is first illustrated in this paper. Then, the stability and resonance conditions are established for such systems in terms of a pseudo-damping factor and a fractional differentiation order. It is shown that a second-order fractional system might have a resonance amplitude either greater or less than one. Moreover, three abaci are given allowing the pseudo-damping factor and the differentiation order to be determined for, respectively, a desired normalized gain at resonance, a desired phase at resonance, and a desired normalized resonant frequency. Furthermore, it is shown numerically that the system root locus presents a discontinuity when the fractional differentiation order is an integral number.
The paper deals with attenuation of transversal vibrations of a clamped-clamped beam loaded by a rigid mass at beam mid-point and excited by vertical force acting at beam mid-point. The novelty of treated approach is the use of a ferromagnetic conductor as the principal damping device. This is a different approach from that one used in contemporary research papers. Beyond vibration attenuation a concurrent shift in damped natural frequency due to the negative stiffness is observable. The theoretical results are complemented by measurements on a test stand. Up to 10 dB attenuation of the most marked resonance peak and frequency shift by up to 5 % to lower frequency was observed.
There are several methods to reduce the seismic damages in liquid storage tanks. One of these methods is to use passive control devices, in particular seismic base isolators. Among the different base isolation systems, the Friction Pendulum System (FPS) whose period does not depend on the weight of the system is more appropriate for isolation of liquid storage tanks. The aim of this paper is to investigate the effects of peak ground acceleration (PGA) and pulselike characteristics of earthquakes on the seismic behavior of steel liquid storage tanks base isolated by FPS bearings. In addition, impact effects of the slider with the side retainer are investigated, as well as effects of tank aspect ratio, isolation period and friction coefficient. The obtained results of tanks with different aspect ratios indicate that the responses get more reduced due to isolation under far-field ground motions compared to near-fault ground motions. It is also seen that the response of a base isolated tank is affected when contact takes place with the side retainer of the FPS.
The main goal of this paper is to present an automatic approach for the dynamic modeling of the oblique impact of a multi-flexible-link robotic manipulator. The behavior of a multi-flexible-link system confined inside a closed environment with curved walls can be completely expressed by two distinct mathematical models. A set of differential equations is employed to model the system when it has no contact with the curved walls (Flight phase); and a set of algebraic equations is used whenever it collides with the confining surfaces (Impact phase). In this article, in addition to the Assumed Mode Method (AMM), the Euler-Bernoulli Beam Theory (EBBT), and the Newton’s kinematic impact law, the Gibbs-Appell (G-A) formulation has been employed to derive the governing equations in both phases. Also, instead of using 3 x 3 rotational matrices, which involves lengthy kinematic and dynamic formulations for deriving the governing equations, 4 x 4 transformation matrices have been used. Moreover, for the systematic modeling of flexible multiple links through the space, two virtual links have been added to the n real links of a manipulator. Finally, two case studies have been simulated to demonstrate the validity of the proposed approach.
The objective of this paper is to present a supervised multi-level fuzzy controller to control the deflection of an electrostatically actuated microplate within and beyond its pull-in range. The mode shapes of the microplate are derived using Extended Kantorovich Method (EKM) which are shown to be in great agreement with finite element results. Using open loop simulations, it is shown that the first mode shape is effectively the dominant one. Then by utilizing a single mode approximation along with employing the Lagrange equation, the dynamic behavior of the microplate is described in modal space by an ordinary differential equation. By static and dynamic simulations, dependence of the plate deflection on the applied voltage is identified linguistically. Then based on the linguistic description of the system, a fuzzy controller is designed to stabilize the microplate at desired deflections. To improve the performance specifications of the closed-loop system, another fuzzy controller at a higher level is proposed to adjust the parameters of the main controller in real time. To guarantee the stability of the closed-loop system, a non-fuzzy supervisory unit is attached to the control architecture. The simulations results reveal that by using the presented single level and supervised adaptive controllers, the control objective is met effectively with good performance specifications. It is also observed that adding a second level and a supervisory unit to the main controller can reduce the overshoot and the settling time for within and beyond pull-in stabilization of electrostatically actuated microplates in following the step commands. Excellent performance of the system in the presence of the proposed controller is further demonstrated using multiple step and also sinusoidal commands. The qualitative knowledge resulting from this research can be generalized and used for development of efficient controllers for N/MEMS actuators and electrostatically actuated nano/micro positioning systems.
This paper is on the natural frequency and mode shape computation of frame structures with column cracks. First, a model of intact frame structures is built to perform vibration analysis. Beam elements are considered as lumped masses and rotational springs at the storey levels of frames. Equivalent model of columns and lumped mass-stiffness effects of beams have been combined to carry out continuous solution for the anti-symmetric mode in-plane vibrations of frames. In addition, frame systems with multiple column cracks are analyzed in terms of anti-symmetric mode vibration characteristics. Cracks are considered as massless rotational springs in compliance with the local flexibility model. Compatibility and continuity conditions are satisfied at crack and storey locations of the equivalent column, modeled using the Euler–Bernoulli beam theory. The proposed method is tested for single-storey single- and multi-bay, H-type and double-storey single-bay frame systems with intact and cracked columns. Results are validated by those given in the current literature and/or obtained by the finite element analyses.
Vehicle stability largely depends on the vibration of the steering system. A four degrees of freedom dynamic model of an automotive steering system with a magneto-rheological damper is presented in this study. Firstly, an equivalent mathematical model of the steering system is developed. The nonlinear equation of motion obtained from the dynamic model is then linearized around its equilibrium point to make it suitable for the design of an appropriate controller for vibration suppression. In this work, a new type of adaptive sliding mode controller is designed for control of the magneto-rheological damper and hence to control unwanted vibration. It is shown that the proposed control logic is very effective for settling steering motion near the equilibrium position. The shimmy vibrations of the wheels are reduced by a considerable amount and the steering system becomes stable. In addition, a comparative work is undertaken between the proposed controller and an ordinary sliding mode controller to demonstrate the advantage of the proposed methodology.
Fundamentally, second-order model is the foundation of describing the dynamic characteristics of many mechanical and electrical systems. This paper investigates a parametric identification scheme for single degree-of-freedom second-order model in which the model parameters are subject to normal variation. By utilizing frequency response magnitude and phase angle measurements, we construct a linear-in-the-parameters model and build a related maximum likelihood estimator for both parametric means as well as variances. The validity of the approach is demonstrated through a collection of case analyses, and the results show considerable levels of accuracy in the presence of sufficient data.
Semi-active and active suspensions can improve both ride comfort and handling compared to passive suspensions. The authors have proposed a suspension comprising a pneumatic system capable of changing the stiffness of the suspension and a semi-active magnetorheological damper capable of controlling the suspension damping. Eight configurations of this magnetorheological/pneumatic suspension result from combining two possible stiffnesses (compliant and stiff) and four possible means of producing damping (constant low, constant high, on-off skyhook control and on-off balance control). The minimization of a cost function, which considers both ride comfort and handling, leads to decision maps which indicate the most appropriate configuration depending on vehicle velocity and two pieces of information about the road: the international roughness index and the curve radius. All this information can be gathered from a GPS system and toggling between set-ups is fast, efficient, and easily done by simply opening or closing pipes in the pneumatic system and modifying the current supply in the magnetorheological dampers. The proposed magnetorheological/pneumatic suspension achieves the same roll angle levels as in a comparable passive vehicle while improving ride comfort by reducing acceleration by up to 30%.
The complete nonlinear dynamics of an active magnetic bearing (AMB) with proportional and derivative controller is revisited analytically. Through the stability analysis of the second-order nonlinear differential equation governing the dynamics of the system, a state diagram is obtained in the proportional gain and precontrol current space. This diagram is fundamental and may help in making important design decisions namely in the identification of a controller for the complete range of the rotor mass, in order to ensure structural stability. In particular, we find that there exists a threshold for the proportional gain whose expression depends both on the inner radius of the bearing and on the bias current, and below which no stable dynamics of the system can occur. In the operating range, we show that the system exhibits a rich dynamics characterized by the possibility for the existence of many kinds of nonlinear localized excitations in the transient state, which may lead to an irregular or a chaotic behavior of the shaft. In this regime, the expressions of the critical running speed obtained by means of the Melnikov theory indicate its dependence on the AMB characteristic parameters.
As a form of passive control, padding rubber layers onto the most heavily deformed zones of a system can improve the dynamic behavior and the acoustic comfort of a vehicle system. This paper proposes an extensive hybrid modal synthesis method in order to study coupled fluid-structure systems, in retaining a few degrees of freedom. Modal criteria, corresponding to noise transmission paths between substructures in the system, have been derived to characterize the dynamic phenomenon from a modal view. These criteria were then substituted by Kriging interpolation models to avoid prohibitive simulation steps during optimization of the complex system. Once the mathematical models of the investigated modal criteria were established and the multi-objective functions for rubber characteristics defined, an approximate optimal solution leading to superior dynamic performance could be obtained based on a genetic algorithm. The analytical results and numerical experiments conducted have also justified the efficiency of our proposed strategy.
Many devices and processes utilize self-excited oscillation to enhance performance. Recently, much research work has been devoted to the induction of self-excited oscillation in mechanical systems by nonlinear feedback. The present paper investigates the efficacy of a displacement feedback technique in generating self-excited oscillation at the desired mode(s) in a multiple degrees-of-freedom mechanical system. The controller couples the system with a bank of second-order filters and generates the required control force as a nonlinear function of the filter output. The describing function method theoretically explores the dynamics of the system with the control law. The control cost of the controller is studied for the proper choice of the filter parameters. The analytical results are substantiated by the numerical simulation results. The present study reveals that the proposed control laws, if used in an appropriate way, can generate self-excited oscillation in the system at the desired mode(s).
This paper is concerned with the measure of degree of controllability (DOC) for linear system with external disturbance. A new measure of DOC, in which the initial condition is regarded as a random vector, is proposed in this paper by solving the fixed-time expected minimum-energy transfer control problem. Since this new measure is dependent on the statistical information of initial condition rather than its estimated value, it is more suitable to apply the proposed measure in the design and optimization of the structural parameters of controlled plants. Furthermore, the simulations on the NREL (National Renewable Energy Laboratory) CART3 wind turbine demonstrate that the relation of the proposed measure to turbine parameters (including rotor inertia and optimum tip speed ratio) coincides with that of the MPPT efficiency to turbine parameters. This indicates that the proposed measure is applicable to guide the design and optimization of the structural parameters of wind turbines. Meanwhile, a mass-spring-damper system is also simulated to validate the proposed measure.
In this paper, the effects of high-static low-dynamic stiffness (HSLDS) isolators on the supports of a continuous rotating shaft for vibration control of a rotary system under mass eccentricity force are investigated. The rotating shaft is modeled using the Euler–Bernoulli beam theory. HSLDS isolators have a linear damping and linear and nonlinear (cubic) equivalent stiffness. Isolators are positioned on the supports of the rotating shaft, so that their forces are applied in radial directions. Equations of motion are extracted using the extended Hamilton principle and they are analyzed using the multiple scale method; then, the steady-state solutions and stability are studied. The effects of variations in linear and nonlinear parameters of the isolators on the static load bearing, resonant peak, frequency band of isolation and hardening nonlinearity are considered, in order to design an appropriate HSLDS isolator and to set its parameters in an optimal way. Investigating the effects of the cubic stiffness and damping values on bifurcations of the system, one may observe that inappropriate setting of these parameters causes strong or weak nonlinearity in the system and, consequently, HSLDS isolators perform less effectively than a linear one does. Then, the results are verified through analyzing the time history of the rotary system under study.
A robust nonfragile observer-based controller for a linear time-invariant system with structured uncertainty is introduced. The
In this paper, a passive/active hybrid vibration isolator is proposed to isolate micro-vibration. The passive element of the isolator is a spring-damper constructed with oil-filled corrugated pipes and the active one is an inertial actuator. A numerical model of the isolator is established through theoretical modeling of the stiffness and damping of the spring-damper and the subsystem synthesis method. On the basis of this model, frequency response functions of the disturbance and control channels are computed to describe the characteristics of the isolator. An adaptive control method based on the least mean squares algorithm is adopted to suppress transmission of micro-vibration caused by tonal, chirp or random disturbances. To verify the modeling as well as the isolation performance, tests and experiments are carried out and the results show that the computation of stiffness is effective and the passive element of the isolator has a reasonable amplification factor and a decreasing slope of –40 dB/decade. Furthermore, the active element is able to achieve remarkable attenuation of random and tonal disturbances.
Based on the nonlinear characteristics of permanent magnet synchronous motor (PMSM), a nonlinear speed and direct torque control (DTC) using sliding mode backstepping method for PMSM is presented in this paper. The sliding mode speed controller is implemented with exponential reaching law to improve the robustness of the system, and further a step-by-step recursive design for backstepping torque and flux controllers is presented. The system stability with proposed scheme is mathematically proved using Lyapunov stability criteria. At the same time, the load torque is observed with the extended state observer (ESO), and is fed-forward to the controller for rejecting the load disturbance and to mitigate the chattering affect due to the sliding mode controller. Finally, simulation test results are demonstrated to support the effectiveness and feasibility of the proposed strategy.
This paper addresses an on-off damping tuned liquid column damper (TLCD) regulated by a general controller. This general controller can represent many conventional controllers such as groundhook, skyhook, bang-bang, or linear clipping controller. Due to the on-off damping and quadratic damping of the TLCD the system is complex nonlinear. To cope with those nonlinearities, this paper presents a simple approximated solution by solving a scalar algebraic equation. Outcomes of numerical simulations verify the proposed approximated solution. Moreover, the approximated solution is useful to clarify the condition of robust controllers, to speed up the optimization of the general controller, and to conduct any parametric study. Based on a parametric study, an empirical formula for the optimized parameters of the general on-off damping controller is derived. In a case study of an earthquake excited five degree-of-freedom shear frame the simplicity, robustness, and effectiveness of the semi-active TLCD with optimized parameters is illustrated, considering limited noisy measurements, time delay, modeling error, and nonlinear TLCD behavior.
The assimilation of path planning and motion control is a crucial capability for autonomous vehicles. Pure pursuit controllers are a prevalent class of path tracking algorithms for front wheel steering cars. Nonetheless, their performance is rather limited to relatively low speeds. In this paper, we propose a model predictive active yaw control implementation of pure pursuit path tracking that accommodates the vehicle’s steady state lateral dynamics to improve tracking performance at high speeds. A comparative numerical analysis was under taken between the proposed strategy and the traditional pure pursuit controller scheme. Tests were conducted for three different paths at iteratively increasing speeds from 1 m/s up to 20 m/s. The traditional pure pursuit controller was incapable of maintaining the vehicle stable at speeds upwards of 5m/s. The results show that implementing receding horizon strategy for pure pursuit tracking improves their performance. The contribution is apparent by preserving a relatively constant controller effort and consequently maintaining vehicle stability for speeds up to 100Km/h in different scenarios. A
Seismic response of base isolated steel liquid storage tanks is investigated in this study by a stochastic approach in frequency domain. For the purpose of evaluating different frequency contents of seismic events on the responses of fixed and isolated tanks, the earthquake excitation is characterized by power spectral density function. Since earthquake is a random process, stochastic seismic analysis is used and root mean square response predicts behavior of system properly. Two types of isolation system are assumed and nonlinear behavior of base isolation systems are developed by an iterative statistical linearization scheme. The study demonstrates the influence of each characteristic parameter of the storage tanks and isolation system and also excitation features. It is confirmed that near-fault earthquake excitations amplify the overall response of the system. Base isolation is known as an effective technique to reduce responses appropriately. It is demonstrated that the sloshing responses of the tanks is significantly reduced by sliding bearing. Further, excitation parameters, PGV/PGA ratio of records and pulse period in near-fault ground motions, that represent differences in two sets of earthquakes are defined to recognize variation of responses.
This paper considers dampers comprising collections of viscoelastic particles that are subjected to vibrations whose amplitude is such that slip between particles is negligible. Energy dissipation occurs primarily by viscoelastic processes within each particle and is maximized when standing waves are set up in the granular medium. In this work, the medium is represented as an equivalent viscoelastic solid and predictions of performance employ models constructed using standard finite element software. Two numerical approaches are considered: one uses the Direct Frequency Response and the other uses standard modal analysis in conjunction with analytical expressions for energy dissipation based on the wave equation. The performance of these prediction techniques is compared with measured behavior from experiments on a box-shaped structure and a hollow composite tube assembly. The computational efficiency of the modal technique allowed a brief investigation of the effects of uncertainties in the actual nature of the granular arrangement. Results show that both prediction methods give a reasonable level of accuracy. Differences between predicted and measured behavior are shown to be of the same order as the uncertainty in the prediction itself. For the systems considered, it is shown that the methods are appropriate for acceleration amplitudes up to almost that of gravity.
To study the energy dissipation mechanism of nonobstructive particle dampers (NOPDs) and provide guidance to the application of NOPDs, the dense granular flow theory was introduced to establish a quantitative energy dissipation model for NOPDs. The convection movement of the particles under vibrational excitations was studied using the discrete element method, and the Prandtl mixing length theory was adopted to modify the constitution law of dense granular flows. The pressure of the granular flow was obtained by equivalenting the vibrational excitation to a body force acted on particles. Theoretical results showed that the energy dissipation rate of the NOPD was increased with the vibration intensity and decreased with the granular diameter. It also indicated that particles near the side wall and the bottom of the damper dissipated more energy than those particles in other regions. The theoretical model was verified by simulation and experimental result. The results may provide a new approach to studying the energy dissipation mechanism of NOPD and give some guidance to enhancing the damping performance of NOPD in engineering practices.
Sudden torque changes and torque fluctuations caused by a traction motor in HEV (hybrid electric vehicle) can result in a driveline oscillation. This paper focuses on the HEV launch vibration in pure electric mode while only the electric motor is generating output torque. A relevant mathematical model has been built based on the working principle. According to the model, the torsional vibration characteristics of the electric propulsion system have been analyzed. Two active control methods, feed-forward control (FFC) and pole placement (PP) have been applied to suppress the HEV launch vibration. However, such longitudinal vibration may still be perceived by passengers, though they can attenuate the vibration to some extent. Therefore another method, wave superposition control strategy (WSCS), has been proposed to suppress the vibration more effectively. In order to prove the control effectiveness of WSCS, all these three active control methods have been applied in simulation for a comprehensive comparison of the vibration suppression effect. Simulation results demonstrate that compared with FFC and PP, WSCS minimizes the overshoot of wheel angular acceleration (WAA) most and doesn’t have much effect on the system response quickness, which can be regarded as the most effective control method.
A new mixed method for nonlinear fuzzy free vibration analysis of nanobeams on nonlinear elastic foundation is introduced. The governing equations are derived based on the first-order shear deformation theory (FSDT) in conjunction with the von-Kármán’s assumptions and the Eringen’s nonlocal elasticity theory. The differential quadrature method (DQM) is employed to discretize the governing equations and the related boundary conditions. The direct displacement control iterative method is used to solve the discretized system of equations. The fuzzy transformation method (FTM) is coupled with the solution to incorporate effects of different uncertainties such as the small scale effect parameter, nonlinear elastic foundation parameters and vibration amplitude of the nanobeam. Applicability, rapid rate of convergence and high accuracy of the presented method are shown and significant effects of the nonlinearity on the response of nanobeams are investigated via solving some examples.
This paper presents the modeling and simulation results of active noise control (ANC) in a small room using the wave-based approach defined by particle velocities and sound pressure within the defined boundary conditions. The ANC system excitation is a single-frequency noise with an adaptive feedforward configuration. The Finite Difference Time Domain (FDTD) algorithm is used to model the room acoustics due to a boxed loudspeaker of single frequency. A control system based on the filtered-x least mean-squared (FxLMS) algorithm is utilized to synthesize a cancelling noise using a secondary loudspeaker. The single channel system is modified into a multichannel system and genetic algorithm (GA) is used to optimize the sensors and actuators placements simultaneously. Numerical results are plotted to demonstrate the performance of the control system. These show that the numerical modelling technique can be used to combine room acoustic simulation and FxLMS adaptive control. This provides a way for the optimum placement of the microphones and loudspeakers before being used in a practical complex enclosure.
This paper presents an innovative method to achieve the simultaneous phase control of multiple resonance frequencies of a linear multi-degree-of-freedom system using only one sensor/actuator pair. Each frequency is manipulated independently by means of a PLL-based control loop which comprises a digital averaging phase detector that combines the two most crucial tasks, namely the phase shift measurement and the frequency separation. The properties of the controller are designed individually for each mode using a linearized model of the control system. The method is applicable to all kinds of oscillators where frequencies near the structure’s natural frequencies are to be controlled. To validate the results experimentally, the controller is implemented on a digital signal processor (DSP) and applied to a torsional oscillator. Investigating two different damping conditions, the simultaneous control of five resonance frequencies of the oscillator illustrates the effectiveness and stability of the multiple frequency tracking. The method is able to significantly improve the accuracy and versatility of sensor applications. As an example a method is presented that enables the direct determination of the modal damping by using two frequencies corresponding to one single vibration mode.
The KDamper is a novel passive vibration isolation and damping concept, based essentially on the optimal combination of appropriate stiffness elements, which include a negative stiffness element. The KDamper concept does not require any reduction in the overall structural stiffness, thus overcoming the corresponding inherent disadvantage of the "Quazi Zero Stiffness" (QZS) isolators, which require a drastic reduction of the structure load bearing capacity. Compared to the traditional Tuned Mass damper (TMD), the KDamper can achieve better isolation characteristics, without the need of additional heavy masses, as in the case of the T Tuned Mass damper. Contrary to the TMD and its variants, the KDamper substitutes the necessary high inertial forces of the added mass by the stiffness force of the negative stiffness element. Among others, this can provide comparative advantages in the very low frequency range.
The paper proceeds to a systematic analytical approach for the optimal design and selection of the parameters of the KDamper, following exactly the classical approach used for the design of the Tuned Mass damper. It is thus theoretically proven that the KDamper can inherently offer far better isolation and damping properties than the Tuned Mass damper. Moreover, since the isolation and damping properties of the KDamper essentially result from the stiffness elements of the system, further technological advantages can emerge, in terms of weight, complexity and reliability.
A simple vertical vibration isolation example is provided, implemented by a set of optimally combined conventional linear springs. The system is designed so that the system presents an adequate static load bearing capacity, whereas the Transfer Function of the system is below unity in the entire frequency range. Further insight is provided to the physical behavior of the system, indicating a proper phase difference between the positive and the negative stiffness elastic forces. This fact ensures that an adequate level of elastic forces exists throughout the entire frequency range, able to counteract the inertial and the external excitation forces, whereas the damping forces and the inertia forces of the additional mass remain minimal in the entire frequency range, including the natural frequencies.
It should be mentioned that the approach presented does not simply refer to discrete vibration absorption device, but it consists a general vibration absorption concept, applicable also for the design of advanced materials or complex structures. Such a concept thus presents the potential for numerous implementations in a large variety of technological applications, whereas further potential may emerge in a multi-physics environment.
The chaotic motions are investigated both analytically and numerically for a class of single-machine-infinite bus power systems. The mechanism and parametric conditions for chaotic motions of this system are obtained rigorously. The critical curves separating the chaotic and non-chaotic regions are presented. The chaotic feature of the system parameters is discussed in detail. It is shown that there exist chaotic bands for this system, and the bands vary with the system parameters. Some new dynamical phenomena are presented. Numerical results are given, which verify the analytical ones.
Wedge suspensions are critical systems for three-piece bogies. This paper proposes a methodology to optimize wedge suspensions using white-box suspension models, dynamic simulations of railway vehicle systems, parallel multi-objective Particle Swarm Optimization (pMOPSO), and parallel multi-objective Genetic Algorithm (pMOGA). Two types of original wedge suspensions with three different toe angle configurations were modeled and compared. Four case studies were carried out to prove the feasibility of the optimization methodology. A series of optimized designs were identified using the Pareto Front technique. Demonstrative optimized designs were compared with the original designs. Results show that wedge suspensions with the toe-in configuration provide better dynamic performance for freight wagons. Significant reductions to the maximum wheel/rail contact forces can be achieved by the optimized designs. Linear speed-up was achieved by using the parallel computing technique.
In this paper, vibration characteristics of magneto-electro-thermo-elastic functionally graded (METE-FG) nanobeams is investigated in the framework of third order shear deformation theory. Magneto-electro-thermo-elastic properties of FG nanobeam are supposed to vary smoothly and continuously along the thickness based on power-law form. To capture the small size effects, Eringen’s nonlocal elasticity theory is adopted. By using the Hamilton’s principle, the nonlocal governing equations are derived and then solved analytically to obtain the natural frequencies of METE-FG nanobeams. The reliability of proposed model and analytical method in predicting natural frequencies of METE-FG nanobeam is evaluated with comparison to some cases in the literature. Numerical results are provided indicating the influences of several parameters including magnetic potential, external electric voltage, temperature fields, power-law exponent, nonlocal parameter and slenderness ratio on the frequencies of METE-FG nanobeams. It is found that the vibrational behavior of METE-FG nanobeams is significantly impressed by these effects.
In this study, the free and forced vibration analysis of a micro scale Timoshenko beam resting on a Pasternak elastic foundation and subjected to a moving micro particle is presented. Based on the modified couple stress theory and employing Hamilton’s principle, the governing equations along with the boundary conditions are derived. A semi-analytical solution is obtained for the free vibration of the problem by expressing the dynamic lateral displacement and cross-section rotation in terms of the series of Legendre polynomials and extremizing the objective functional of the problem with respect to the unknown displacements and Lagrange multipliers. Correspondingly, the computed eigenvalue information of the system is utilized in the modal expansion technique to obtain the transient dynamic response. For comparison purposes, the free vibration frequencies of the micro beam and the dynamic deflections using the classical Timoshenko beam theory are compared with previously published studies and very good agreements have been observed. Furthermore, more numerical examples for natural frequencies and dynamic deflection of the beam are presented and the effects of some parameters, such as the material length scale parameter, the velocity of micro particle, the Pasternak elastic foundation parameters, shear deformation effects and boundary conditions are examined.
In this work, we study the effect of piezoelectric nonlinearity on shape and active vibration control of smart piezolaminated composite and sandwich shallow shells under strong field actuation. An efficient finite element model with advanced laminate kinematics and full electromechanical coupling is developed for this purpose. The nonlinearity is modeled using a rotationally invariant quadratic constitutive relationship for the piezoelectric material. For the laminate kinematics, a recently developed efficient layerwise theory, which is computationally as efficient as an equivalent single-layer theory, and has been shown to yield very accurate results in comparison with three-dimensional piezoelasticity based solutions for linear electromechanical response of hybrid laminated shells, has been employed. The nonlinear static response for shape control is obtained using the direct iteration method, and the active vibration control response with linear quadratic Gaussian controller is obtained by using the feedback linearization approach through control input transformation. It is shown that the linear model significantly overestimates the voltage required for shape or vibration control, when the applied electric field is beyond the threshold limit of the actuator. Thus, the use of the nonlinear model is essential for designing the control system utilizing the full actuation authority of the actuators. The effects of actuator thickness, radius of curvature to span ratio and applied loading on the relative difference between linear and nonlinear predictions are illustrated for shape and vibration control of smart cylindrical and spherical shells.
The cruise control problem of high speed trains (HSTs) is revisited in this paper. Despite the ongoing trend of using Lyapunov-based approaches, the concept of passivity is used as the basis of cruise controller design. To begin with, the Euler–Lagrange modeling of longitudinal motion of HST is introduced. Consequently, passivity properties of the system is investigated and it is shown that the system presents a strictly passive input–output map output. This property is utilized to design a controller based on an energy-shaping method. Since the controller benefits from the passivity property of the train, it is structurally simple and computationally efficient while ensuring asymptotic velocity tracking. In addition, as revealed in our robust analysis, the controller is capable of dealing with bounded perturbations. That is to say, boundedness of velocity tracking errors is guaranteed for sufficiently large control feedback gains. The obtained theoretical results have been verified by numerical simulation.
Missile vibration testing has undergone significant advances in the past decade. This has been the result of improvements in signal processing and test specification development, but more recently due to the implementation of Multi-Input Multi-Output (MIMO) testing. To date, much of the focus of MIMO testing has been on either a twin-shaker, single-axis configuration or multi-axis testing on a 3 or 6 Degree of Freedom (DOF) shaker system. There has been little attention to replication of the 3-dimensional operating deflection shapes that a missile system experiences during its carriage or operation.
This paper presents a systematic approach to 3-axis vibration testing, using current MIMO rectangular controller technology, and demonstrates through an experimental setup a near-3 fold improvement in matching the vibration response of the item under test over the more traditional single axis SISO and MIMO test methods.
This paper presents an adaptive fuzzy backstepping sliding mode control for multi-input and multi-output uncertain nonlinear systems in semi-strict feedback form. The systems are described by a discrete-time state equation with uncertainties viewed as the modeling errors and the unknown external disturbances, and the observation of the states is taken with independent measurement noises. Combining the adaptive fuzzy backstepping control with the sliding mode control approach for the comprehensive improvement in the stability and the robustness, the adaptive fuzzy backstepping sliding mode control is approximately designed where the design parameters are selected using an appropriate Lyapunov function. The uncertainities are approximated as fuzzy logic systems using the fuzzy inference approach based on the extended single input rule modules to reduce the number of the fuzzy IF-THEN rules. The estimates for the un-measurable states and the adjustable parameters are taken by the proposed simplified weighted least squares estimator. It is proved that the trajectory of the tracking error and the sliding surface is uniformly ultimately bounded. The effectiveness of the proposed approach is indicated through the simulation experiment of a simple numerical system.
Free vibration of a beam with multiple arbitrarily placed lateral viscous dampers is investigated to gain insight into the intrinsic dynamic features of non-proportional damped systems. In terms of virtual boundary condition method, complex modes of a damper-beam system are achieved, and the solution is also suitable for the beams that have different boundary conditions. The features of the wave numbers satisfying the frequency equation were discussed in theory. The orthogonality analysis conducted in this paper provides two orthogonality conditions for complex modes. Pseudoundamped natural frequencies, damping ratios and complex modes are surveyed via numerical study. The analysis on the evolution of complex modes shows that the increasing damping would lead to over damped modes, and the mode shape that corresponds to the small one of a pair of real-valued natural frequencies is close to the static deformation shape of a beam subjected to static forces located at the positions of the dampers. For the rest modes that would never be over damped with increasing damping, the mode shapes and corresponding psuedoundamped natural frequencies will converge to that of a beam with rolling supports located at where dampers are placed. The exact solution of free vibration of a multiple-span beam is presented in addition.
This paper concerns stochastic perturbations of piecewise-smooth ODE systems relevant for vibro-impacting dynamics, where impact events constitute the primary source of randomness. Such systems are characterized by the existence of switching manifolds that divide the phase space into regions where the system is smooth. The initiation of impacts is captured by a grazing bifurcation, at which a periodic orbit describing motion without impacts develops a tangential intersection with a switching manifold. Oscillatory dynamics near regular grazing bifurcations are described by piecewise-smooth maps involving a square-root singularity, known as Nordmark maps. We consider three scenarios where colored noise only affects impacting dynamics, and derive three two-dimensional stochastic Nordmark maps with the noise appearing in different nonlinear or multiplicative ways, depending on the source of the noise. Consequently the stochastic dynamics differs between the three noise sources, and is fundamentally different to that of a Nordmark map with additive noise. This critical dependence on the nature of the noise is illustrated with a prototypical one-degree-of-freedom impact oscillator.
The identification of nonlinear squeeze-film damper (SFD) bearings, typically used in aero-engines, has so far focused on their forward model (i.e. displacement input/force output). The contributions of this paper are the non-parametric identification of the inverse model of the SFD bearing (force input/displacement output) from empirical data, and its application to a nonlinear inverse rotor-bearing problem. This work is motivated by the need for a reliable substitute for internal instrumentation, to enable the identification of rotor unbalance using vibration data from externally mounted sensors, in applications where the rotor is inaccessible under operating conditions and there is no adequate linear connection between rotor and casing. The identification of the inverse model is fundamentally different from that of the forward model due to the need to account for system memory. A suitably trained Recurrent Neural network (RNN) is shown to be capable of identifying the inverse model of an actual SFD through two validation studies. In the first study, the RNN model satisfactorily predicted the SFD journal’s displacement time histories for given periodic time histories of the Cartesian SFD forces, although it could not predict the user-applied static offset in the SFD since it was not trained to do so. This was no limitation for the second study where, for both centred and non-centred SFD conditions, the RNN proved to be a reliable substitute for actual instrumentation as part of the inverse problem solution process for identifying the amplitudes and phases of the external excitation forces on a simple test rig.
A periodic bi-layer beam structure is proposed and the bandgap characteristic of flexural wave is studied in this paper. The single cell is made up of two bi-layer beams with four components. For the infinite structure, the flexural wave bandgap frequency algorithm is theoretically derived through Timoshenko beam theory, Hamilton principle, Bloch-Floquet theory and transfer matrix method. An analytical example is presented to illustrate the bandgap characteristic and FEA software simulation is conducted to demonstrate the validation of the algorithm. For the finite structure, the vibration transmission characteristic is studied with FEA software to show the flexural wave attenuation behavior of the periodic bi-layer beam. The results reveal that, the flexural wave is attenuated gradually in the stopband along the direction of wave propagation, while in the passband, it will propagate without attenuation. Comparisons with periodic single layer beam are studied to verify the convenience and flexibility of bi-layer beam. Finally, parametric influences on bandgaps are discussed, which will help the designers to make a better design for vibration reduction.
This paper presents the design of an L1 adaptive control system for the stabilization of a two-dimensional aeroelastic system with structural nonlinearities and unsteady aerodynamics, using a single trailing-edge control surface. This model describes the plunge and pitch motion of a prototypical wing. It is assumed that its parameters are unknown and external disturbances are present. The unsteady aerodynamics are modeled with an approximation to Theodorsen's theory. The system exhibits limit cycle oscillations beyond a critical speed. Based on the L1 adaptive control theory, a control law is developed for the trajectory control of the integral of the pitch angle. The control system includes a state predictor, a projection algorithm-based adaptation law designed based on the Lyapunov method, and a stabilizing control law. For the synthesis of the control law only the pitch angle and its derivative are measured. Simulation results show that in the closed-loop system, the aeroelastic vibrations are suppressed, despite parametric uncertainties and gust loads. Furthermore the performance limits of this L1 adaptive law with respect to the freestream velocity and strength of gust load are examined.
The generalized reflexive and anti-reflexive matrices have several applications in engineering and scientific computations. In the present paper, first we propose a conjugate direction (CD) algorithm for finding the generalized reflexive solution X and the generalized anti-reflexive solution Y of the coupled Sylvester matrix equations
This paper presents the results of an extensive series of experimental tests to identify the mechanical characteristics of a recently-proposed seismic isolation device known as the Roll- In-Cage (RNC) isolator. Several 1/10 reduced-scale experimental prototypes are examined considering different configurations, characteristics and construction materials. Cyclic horizontal displacement tests, varying the test parameters of shear displacement amplitude, axial load, and loading frequency are performed. The RNC isolator’s force-displacement relationship, shear stiffness and damping properties are investigated in terms of different test parameters. In addition, vertical cyclic displacement is applied to examine the RNC isolator’s capability to withstand vertical axial tension. Furthermore, tests at the ultimate-level consisting of an increasing monotonic shear loading beyond the bearing’s design displacement are also carried out to investigate its behavior after activating its self-stopping or buffer mechanism. Some experimentally obtained results are verified using numerical simulation models. A comparative analysis of the results is then performed to allow for highlighting the main features of the RNC isolator.
This work examines the elastic vibration of the ultrasonic stator subjected to piezoelectric bending excitation by focusing on two fundamental issues: general driving rule and vibration distortion. An elastic model of a cylindrical ultrasonic stator is developed by using Hamilton’s principle and solved by analytical approach. The results imply that a desired vibration can be aroused provided that an algebraic relation is satisfied by a suitable parameter combination. Traveling/standing wave is excited by conventional time-spatial voltage ones or even other ones. The relationships between the duty ratio of input voltage and wave distortion are identified as closed-form expression of basic parameters. The excitation’s average creates a stationary deflection but it can be neglected thanks to the sufficiently small amplitude it causes relative to that at the resonance frequency. The rotation reversion is realized by changing the duty ratio or excitation frequency but remarkable distortion and amplitude decrease occur, leading to the asymmetry between the forward and inversion. Main results are validated by the superposition approach and comparisons against the existing ones. Discussions on phasing effect and vibration distortion relative to other symmetric systems are also made. Main contributions are the general driving rule with non-/2 time-spatial phases and explanations on vibration distortion. These are achieved via the general time-spatial phasing in cyclically symmetric power-transmission systems.
In this paper we present a multidisciplinary modeling of a MEMS-based electrodynamic microsensor, when an additional vertical offset is defined, aiming acoustic applications field. The principle is based on the use of two planar inductors, fixed outer and suspended inner. When a DC current is made to flow through the outer inductor, a magnetic field is produced within the suspended inner one, located on a membrane top. In our modeling, the magnetic field curve, as a function of the vertical fluctuation magnitude, shows that the radial component was maximum and stationary for a specific vertical location. We demonstrate in this paper that the dynamic response of the electrodynamic microsensor was very appropriate for acting as a microphone when the membrane is shifted to a certain vertical position, which represents an improvement of the microsensor's basic design. Thus, a proposed technological method to ensure this offset of the inner inductor, by using wafer bonding method, is discussed. On this basis, the mechanical and electrical modeling for the new microphone design was performed using both analytic and Finite Element Method. Firstly, the resonance frequency was set around 1.6 kHz, in the middle of the acoustic band (20 Hz – 20 kHz), then the optimal location of the inner average spiral was evaluated to be around 200µm away from the diaphragm edge. The overall dynamic sensitivity was evaluated by coupling the lumped elements from different domains interfering during the microphone function. Dynamic sensitivity was found to be 6.3 μV/Pa when using 100 µm for both gap and vertical offset. In conclusion, a bandwidth of 37.6 Hz to 26.5 kHz has been found which is wider compared to some conventional microphones.
This study proposes skyhook and fuzzy logic based semi-active control strategies to isolate sprung mass motions of 8x8 military vehicle and provide ride quality, road holding and firing accuracy for a platform, removing the passivity constraints of semi-active suspension system. The governing differential equations of motion of 8x8 platform for semi-active vibration control are formulated analytically and validated under multi body dynamics environment. Sprung mass acceleration and displacement are measured on a quarter car set up experimentally to assess the efficacy of skyhook and fuzzy logic controllers. Control strategies, viz. continuous skyhook control, cascade loop control and cascade loop with ride control are implemented. Cascade loop with ride control is employed such that the outer loop stabilizes heave, pitch and roll motions of full vehicle whereas the inner loop, through fuzzy controller, isolates vehicle from uneven disturbances. Various parametric studies are also performed with 8x8 semi-active suspension systems in terms of stochastic road inputs to represent cross country terrain profile. Furthermore, effect of proposed strategies on ride comfort, road holding, amplitude and settling time of vehicle body motions after firing large projectile from gun and aiming accuracy of the fire control system are investigated. It is demonstrated that cascade loop with ride control in semi-active mode improves vehicle ride comfort and road holding and accuracy of fire control system and rate of fire of gun.
To improve the reliability of active electromagnetic suspension and reduce energy consumption, a hybrid electromagnetic suspension that consists of linear motor and passive damper in parallel is proposed in this paper. First, a dynamic model is established and passive energy regeneration and active control systems are built. Thereafter, energy regeneration, ride comfort, and driving safety are taken as control objects. The effect of damping values on different control objects are studied, and the best values are determined. Passive suspension is taken for comparison, and comparative simulation analysis is conducted. Finally, a bench test of 1/4 suspension is performed to verify the accuracy of the simulation results.
The bispectrum of rolling element bearing compound faults contains abundant fault characteristic information, and how to extract the fault feature effectively is a key problem. The fault diagnosis method of rolling element bearing compound faults based on Sparse No-Negative Matrix Factorization (SNMF)-Support Vector Data Description (SVDD) is proposed in the paper. The figure handling method SNMF is used firstly in fault feature extraction of the bispectrums of rolling element bearing different kinds of compound faults and the sparse coefficient matrices of the bispectrums are obtained. The sparse coefficient matrices are used as training and test input vectors of SVDD. At last, the three kinds of rolling element bearing compound faults (inner race outer race compound faults, outer race rolling element compound faults and inner race outer race rolling element compound faults) are classified correctly. In order to verify the advantages of the proposed method, the diagnosis results of the same three kinds of rolling element bearing compound faults based on No-Negative Matrix Factorization (NMF)-SVDD is used as comparison. The proposed method provides a new idea for fault diagnosis of rolling element bearing compound faults.
In this paper, the finite-time tracking control problem is discussed for extended nonholonomic chained-form systems with parametric uncertainty, unmodeled nonlinear dynamics and external uncertain time-varying disturbances. Two decoupled subsystems are considered, for which an anti-interference controller is proposed by combining finite-time stability control theory and chattering-free sliding-mode design strategy in the presence of the uncertainty, nonlinearity and perturbation. Moreover, for the corresponding closed-loop systems under the given control law, rigorous finite-time stability analysis is presented at the origin equilibrium point. Finally, the main conclusions are applied to the trajectory tracking control of dynamic nonholonomic mobile robots with visual servoing feedback, and the simulation results show the effectiveness of our control design approach.
Simulating the dynamic behavior and determining equivalent material properties for anisotropic models, superelements or structures subjected to preloads or friction remains a challenging issue. Amongst other practical applications, modeling interactions between the steel sheets in industrial magnetic cores of electric motor stators is a complex task, as it requires anticipating behavioral heterogeneities in the structure, and possibly represents significantly costly operations for performing modal or dynamic response simulations. In this article, a method for identifying equivalent material properties to anisotropic structures is developed, which is able to take into account the influence of preloads and friction on the material properties, later used in structural dynamics simulations. The proposed approach can be used with superelements, converting stiffness matrices into elasticity matrices. The method is first applied to a triclinic model, and recreates its elasticity matrix with little derivation. Then, an equivalent linear material is computed for a continuous structure under preloading. Compared at low frequencies, the vibration behavior of the preloaded structure and its equivalent effective media are in good agreement. The operation is repeated with a laminated stack under preloading. Again, the dynamic behavior of the equivalent structure shows good accuracy compared to the initial preloaded stack. Finally, the magnetic core of an electric machine stator is modeled with equivalent anisotropic material properties, accounting for friction and preload in the yoke's and the teeth's steel sheets. The simulation of the structure's low-frequency radial vibration modes is satisfying, and shows improvement compared to orthotropic properties.
Pounding between adjacent structures has been a concern in multi-span bridges in recent earthquakes. In this paper, a pounding mitigation strategy using magnetorheological dampers is proposed, and its performance is tested for a three-span bridge using a series of shake-table experiments. A new semi-active control algorithm called SMC-OPC is developed that is based on a clipped sliding mode control (SMC) with sliding surfaces designed using an optimal polynomial control (OPC) approach. The control design uses a stochastically linearized model of the nonlinear bridge with passive components of the magnetorheological dampers embedded to achieve a more representative system characterization. Optimal weighting matrices for the optimal polynomial control are found through a genetic algorithm. The proposed method along with uncontrolled, passive-off, and passive-on cases are tested on shake-tables for several scaled near-field Kobe ground motion records. Although no pounding is observed in all control cases for small earthquakes, significant pounding occurs in the uncontrolled and passive-off systems under large earthquakes. For these ground motions, the performance of the semi-active controller converges to that of the passive-on case but with noticeably reduced power consumption. The study shows that the use of magnetorheological dampers between adjacent spans is very effective in mitigating critical bridge responses especially under large earthquakes. In addition, the proposed SMC-OPC semi-active control strategy enables achieving balance among multiple performance objectives with significantly reduced power consumption as compared to passive-on case.
The present work is concerned with the study of reflection and transmission phenomena of dilatational waves at a plane interface between a microstretch elastic solid half-space and a microstretch liquid half-space. Eringen's theory of micro-continuum materials has been employed for addressing the mathematical analysis. Reflection and transmission coefficients, corresponding to various reflected and transmitted waves, have been obtained when a plane dilatational wave strikes obliquely at the interface after propagating through the solid half-space. It is found that the reflection and transmission coefficients are functions of the angle of incidence, the frequency of the incident wave and the elastic properties of the half-spaces. Numerical calculations have been carried out for a specific model by taking an aluminum matrix with randomly distributed epoxy spheres as the microstretch solid medium, while the microstretch fluid is taken arbitrarily with suitably chosen elastic parameters. The computed results obtained have been depicted graphically. The results of earlier studies have been deduced from the present formulation as special cases.
The acoustic behavior of a combustion engine is primarily dominated by the sound radiation of the oil pan. Therefore, the vibration behavior of the oil pan as the prominent noise emission source is investigated in this paper. The aim of this study is to present a new vibration reduction concept, which is based on the property of high damping possessed by granular materials. The efficiency of this concept is proven by measurements via a scanning laser vibrometer. Finally, it is shown that it is possible to create a lighter oil pan which shows much lower vibration amplitudes than the original one.
In this work, the variational iteration method (VIM) is used to solve a class of fractional optimal control problems (FOCPs). New Lagrange multipliers are determined and some new iterative formulas are presented. The fractional derivative (FD) in these problems is in the Caputo sense. The necessary optimality conditions are achieved for FOCPs in terms of associated Euler–Lagrange equations and then the VIM is used to solve the resulting fractional differential equations. This technique rapidly provides the convergent successive approximations of the exact solution and the solutions approach the classical solutions of the problem as the order of the FDs approaches 1. To achieve the solution of the FOCPs using VIM, four illustrative examples are included to demonstrate the validity and applicability of the proposed method.
This paper introduces a tilt integral derivative controller as the supplementary controller for load frequency control of a two-area interconnected power system. The optimal value of parameters of the tilt integral derivative controller is evaluated using constrained nonlinear optimization by means of a performance index-based method. The proposed tilt integral derivative control offers superior properties such as simple parameter tuning and its performance does not compromise the occurrence of any parameter variations in the system. To verify these features of the controller, the test system is subjected to step load disturbance and parameter variations that ensure the robustness of the tilt integral derivative controller. Comparative analysis with previously published work indicates that the proposed tilt integral derivative controller gives better performance and holds the property of robustness. Simulations have been performed using Matlab®.
In this paper, a boundary controller for a flexible manipulator is proposed based on a partial differential equation (PDE) robust observer. In the previous work we have proposed a PDE robust observer to estimate the infinite dimensional states of the flexible manipulator with unknown boundary disturbance and spatially distributed disturbance. On the basis of the proposed robust state observer, a boundary controller is designed to achieve the stability control, regulate the joint position and suppress elastic vibration in this paper. The stabilities of the proposed observer and the boundary controller are validated by theoretical analysis. Numerical simulations are provided to demonstrate the effectiveness of the closed-loop system.
This paper presents a modal analysis of different drivetrain configurations in electric vehicles; 1) an in -- wheel motor, 2) direct drive, and 3) an electric motor with a reduction gear and a differential gear. A specific simulation model was developed to analyze the vibrations while taking into account the traction motor, possible mechanical reduction gears, and the driveshaft, as well as a Rigid Ring Model (RRM) to describe the tire. On the basis of the simulation results, the frequency responses were calculated for each drivetrain configuration and also for a non-drive, free-rolling tire. The analyzed results show interesting differences between the different drivetrain configurations. However, most of the negative aspects can be compensated for if identified in the early design phase. For instance, the frequency response of the in-wheel motor configuration indicated that the vibrations that occur might cause negative effects in terms of driving comfort and wheel speed signal noise. The direct drive configuration has an additional mode at 24 Hz, and the differential configuration at 4 Hz. It is possible that these modes would resonate strongly if some drivetrain design parameters were poorly defined.
A range of methodologies exist for estimating nonlinear responses of structural systems using numerical simulations. However, efforts in relation to experimental methods in this regard still warrant further investigation. This paper presents an approach for assessing structural nonlinearities using the extremes of dynamic responses of the structural system under consideration. The approach allows revisiting and parameter tuning of theoretical models of structures based on experimental studies. A single degree of freedom system was excited in this study using broadband input excitations and the output dynamic responses were measured using different devices. The type and extent of experimentation required for implementation of the presented technique was investigated along with the effects of the estimates of the measured variables and the effects related to different measurement devices.
In this work a reliability based optimization (RBO) strategy of Tuned Mass Damper (TMD) parameters is presented. The strategy is based on an energetic approach. The strategy consists to optimize the TMD parameters so that we minimize the failure probability (objective function) characterized by the exceedence of the power dissipated in the primary structure of a certain threshold value during some interval time. The evaluation of the objective function is carried out using the classical Rice’s formula. The strategy is, firstly, applied to linear single-degree of freedom (SDOF) system, subjected to seismic motion, and then extended to linear multi-degree of freedom (MDOF) system. The use of the Rice’s formula requires the knowledge of the joint probability density function (PDF) of the considered processes; to this end, exact expression of the joint PDF is presented for the SDOF system and an approximation is presented for the evaluation of the failure probabilities for the MDOF system. By making use of the obtained joint PDF, for the SDOF system, as the a priori joint PDF, the approximation of the joint PDF, for the MDOF system, has been performed using the Minimum cross-entropy method (MinxEnt).
To highlight the good effectiveness of the proposed strategy, a ten-story shear building, subjected to different earthquakes, is considered. The obtained results are compared with other from literature, and it has been shown the superiority of the proposed strategy.
The Z-ram of a Portal Milling machine presents a weak point in the dynamic behaviour of the machine tool which makes it prone to the occurrence of chatter vibration. Since chatter vibrations directly limit the maximum allowable cutting depth during machining, an improvement in dynamic behaviour of the machine tools by means of active vibration control of the spindle will result in an increase of maximum cutting depth. An active vibration control of the Tool Center Point of a Portal Milling machine using four hydraulic compensation modules integrated in the Z-ram structure is proposed. A test bench for the Z-ram was constructed at Machine Tools Laboratory (WZL) of RWTH Aachen University and it’s modal analysis revealed the occurring dominant vibration mode. A polyreference-LSCF modal parameter estimation was employed for identification of the measured MIMO Frequency Response Functions (FRF) of the Z-ram test bench. Using this mathematical model, the MIMO controller was synthesized with the Glover-McFarlane
In this paper, a novel type of control strategy for the active control of uncertain civil structures is introduced. Robust time varying sliding sector for the active control of large, uncertain structures is proposed. The introduced method is chatter free and continuous. Chattering phenomenon is the main drawback in sliding mode controllers. This method is based on defining appropriate sliding sectors with their respective control rules. Sliding sector controller moves system’s states from outside the sector to inside of it with suitable control input. A large structure equipped with active tendons and with mass, stiffness and damping uncertainty is considered. The worst case design is considered where structure’s mass increases and its stiffness and damping coefficients decrease. Furthermore, by applying actuators’ failure, damage-tolerance capacity of the second-order sliding sector is investigated. The structure is subjected to different earth excitations to demonstrate the feasibility of proposed method under various earthquakes with different frequencies. The controlled responses of the structure are compared with LQR method which is a highly robust controller. Comparative results of the numerical simulation are presented to confirm the proposed method robustness and its ability to reduce the structures response under earthquake excitation, effectively.
A new hybrid vibration absorber, with detached passive and active parts, is designed, analyzed and tested. This is an alternative approach in case the traditional bundled hybrid vibration absorber with collocated active and passive control elements cannot be applied. In fixed-free structures like buildings and towers, a passive dynamic vibration absorber is very popular for vibration control at or near the free ends. Active control may be introduced to improve performance, but space or weight may be limited in some applications. It may not be practical to attach an actuator near the passive part. The new approach provides more flexibility to retrofit a passive dynamic vibration absorber into a high performance hybrid vibration absorber by installing the actuator at a more suitable location than collocated with the passive part. The proposed hybrid vibration absorber is based on the pole-placement control strategy. Its controller is able to deal with a possible nonminimum-phase secondary path caused by noncollocated actuator sensors. This feature does not exist in a bundled hybrid vibration absorber with collocated actuator sensors. The performance of the new hybrid vibration absorber is analyzed in this study. Experimental and simulation results are used to verify the theoretical results and demonstrate the excellent performance of the new hybrid vibration absorber for vibration control at multiple points. A bundled hybrid vibration absorber with collocated passive and active elements is compared with the proposed hybrid vibration absorber with detached control elements, using experimental and simulation results. It was found that the vibration attenuation performance of the proposed hybrid vibration absorber can be better than the traditional bundled hybrid vibration absorber. The optimal actuator location, which is not necessarily the coupling point of the passive resonator, can be selected numerically by a proposed procedure. One could miss a better solution for vibration control if he/she only uses the bundled hybrid vibration absorber without considering the detached hybrid vibration absorber as a possible alternative.
The mean square deviation (MSD) of an arch dam dynamic displacement response during a flood discharge period is an important indicator used to evaluate the vibration intensity. The whole distribution of the MSD of the dynamic displacement response reflects the whole dynamic displacement field. Inversion of the whole dynamic displacement field of the arch dam based on limited measuring points is of significance. In this study, the Ertan arch dam was used to propose an inversion algorithm for the whole prototype dynamic displacement field of the arch dam. First, inversion theory of flow-induced vibration response for the arch dam is introduced. Second, the arch dam prototype vibration test under flood discharge excitation is conducted to determine the dynamic displacement response of limited measuring points. Third, the full-scale finite element model of the Ertan arch dam is set up to conduct modal analysis, and the first nine modes are cutoff to extract the modal parameters for the inversion of equivalent excitation source load spectra. Finally, the whole dynamic displacement field of the arch dam is calculated by flow-induced vibration response positive analysis based on the equivalent excitation load spectra. Inversion results show that the whole arch dam dynamic displacement field is obtained through only seven dynamic displacement response measuring points arranged on the crest of the dam. Simultaneously, the inversion and measured values are in good agreement. This method provides a novel technique to reasonably evaluate the high arch dam during the flood discharge period.
This paper presents a method for calculating vibrational energy density from experimental data in a uniform beam. The input excitation is a point random force that induces transverse vibration along the beam. Using finite difference method and four accelerometers, both translational and rotational terms of kinetic and potential energy densities are measured. Also, an energy finite element analysis based computer program is developed. The results of the measurements achieved by developed formulation are compared with those of energy finite element analysis results. It is found that there is a fair agreement between them at relatively lower frequencies. But, in high frequencies, the difference between analytical and experimental results increases which stems from occurrence of errors in calculation of potential energy density. Finally, a comparison between kinetic and potential terms of the energy density is done. It is concluded that an efficient and very simple measurement procedure can be used based on kinetic energy measurement only.
In this paper, an linear matrix inequalities (LMI)-based second-order fast terminal sliding mode control technique is investigated for the tracking problem of a class of non-linear uncertain systems with matched and mismatched uncertainties. Using the offered approach, a robust chattering-free control scheme is presented to prove the presence of the switching around the sliding surface in the finite time. Based on the Lyapunov stability theorem, the LMI conditions are presented to make the state errors into predictable bounds and the parameters of the controller are obtained in the form of LMI. The control structure is independent of the order of the model. Then, the proposed method is fairly simple and there is no difficulty in the use of this scheme. Simulations on the well-known Genesio's chaotic system and Chua's circuit system are employed to emphasize the success of the suggested scheme. The simulation results on the Genesio's system demonstrate that the offered technique leads to the superior improvement on the control effort and tracking performance.
This paper presents a new hybrid controller which is a combination of three control schemes: fuzzy neural control, PI control and sliding mode control. The interval type 2 fuzzy model featuring updated rules via online is used in this study and in order to support the fuzzy model, a granular clustering method is applied to find groups of data related to the initial fuzzy rule. Then the output for fuzzy model is used for the PI-sliding mode controller. The combination of PI and sliding mode controls is carried out by H-infinity technique method which is rely on the modified Riccati-like equation. After developing the mathematical model, the proposed controller is applied to vibration control of a vehicle seat suspension featuring magneto-rheological (MR) damper. In order to demonstrate the effectiveness of the proposed controller, two different excitations of bump and random signals are adopted and corresponding vibration control performances are evaluated. It is demonstrated through both simulation and experiment that the proposed controller can provide much better than vibration control performance compared with the conventional controllers showing more robust stability.
Vibration control, especially in cracked rotors, is an important factor that can prevent the occurrence of disastrous failures. In this paper, vibrational control of a cracked rotor with an electromagnetic actuator has been studied with a continuous model of flexural vibration of cracked rotors. The governing equation of motion for the rotor under the external excitation of the electromagnetic actuator, gravity, and unbalanced forces is presented. A control law for the optimal control method to minimize the vibration of the rotor or stress at the crack section was obtained. To this aim, two cost functions have been introduced, based on the overall vibration of the rotor and the maximum stress at the crack section. The results of these two strategies are compared with each other and their performances are discussed.
This paper proposes a new leader–follower-based consensus vibration controller to actively suppress unwanted oscillations in distributed-parameter flexible structures. Actuation and sensing is performed via piezoelectric layers in a collocated sense. The actuator/sensor patches for the vibration control system are considered to collaborate in a network, and follow a virtual leader which is accessible to all agents. Hence, a vibration controller law is defined, to remove disagreement between agents and force the agents to follow the virtual leader. The proposed approach is an observer-based design, in which an optimal consensus state estimator is initially designed. Stability of the closed-loop system is investigated and the optimality conditions of the system are derived. Although the designed vibration controller could be implemented for suppression tasks in different distributed-parameter systems, a flexible clamped-clamped beam is used here for equation derivation and numerical performance verification. According to the results, the optimal observer estimates the system states in a finite time, as expected, and the vibration controller suppresses unwanted oscillations, either in resonant or arbitrary form, to a much lower level; while the disagreement between agents converges to zero. Additionally, suppression performance and robustness of the controller to failure in control system elements is investigated in comparison with a conventional positive position feedback controller, and its superiority is illustrated and discussed.
In this paper, an H controller with actuator saturation consideration is proposed to attenuate the vibration of periodic piecewise vibration systems. Based on a continuous Lyapunov function with a time-varying Lyapunov matrix, the H performance index of periodic piecewise vibration systems is studied first. On the basis of the obtained H criterion, the conditions of designing a state-feedback active vibration controller are proposed in matrix inequality form with actuator saturation taken into account. Because of the nonconvexity of the conditions, a corresponding algorithm to compute the controller gain is developed as well. A representative numerical example is used to verify the effectiveness of the proposed method.
The purpose of this study is to illustrate the propagation of the torsional surface waves in an intermediate inhomogeneous initially stressed vertical elastic layer sandwiched between two heterogeneous half-spaces. It is considered that the mass density and the rigidity of upper and lower half-spaces are space dependent. The proposed model is solved to obtain the different dispersion relations for the torsional surface wave in the elastic medium of different properties. The effects of compressive and tensile stresses along with the heterogeneity on the dispersion of torsional surface wave in the intermediate layer are shown numerically. The wave analysis further indicates that the inhomogeneity, the initial stress of the layer and the heterogeneity of both the half spaces affect the wave velocity remarkably. The results may be useful to understand the nature of seismic wave propagation in geophysical applications and in the field of earthquake engineering.
This paper presents the results of a computational and experimental validation exercise performed towards damage identification of a sagged rod with known damage by using the coupled axial–flexural wave interaction mechanics. Towards simulating the damage scenario in a sagged conductor made of steel wire rope, a prismatic steel rod is taken up for study. An initial axial wave, tangential to the curve of the arc, manifests as both axial and flexural waves as it propagates alongside the length of the rod. This interaction effect between axial and flexure wave propagation is studied in this paper. Impedance mismatch is made in the rod by changing its cross-sectional area along its length. Numerical simulations are implemented using the spectral finite element method with a combined axial and flexure effect. The concept of obtaining the exact spectral element dynamic stiffness matrix for a wave propagation analysis sagged rod is discussed. Computation is implemented in the Fourier domain using Fast Fourier Transform (FFT). In the time domain, post processing of the response is done, which is applicable in structural diagnostics in addition to the wave propagation problem. The predominant single-frequency-based amplitude-modulated, narrow-banded, burst wave propagation is found to be better matched if the elemental rod theory is replaced with a modified rod theory called the Love theory. The differences in the propagating waves allow identification of the damage location in a very clear-cut way. The methodology of the moving correlation coefficient is also successfully employed to detect the damage precisely. This fact is very encouraging for future work on structural health monitoring.
This paper presents an analytical model for computing the force-displacement loops of the passive hydraulic dampers filled with shear thinning fluid when the damper is subjected to a sinusoidal excitation. The analytical model is developed on the basis of Navier-Stokes equations by considering the rheological behavior of silicone oil. The obtained computational results agree well with those by experimental measurements, and both of them suggests that viscous friction, fluid compressibility, and friction loss are the three major damping mechanisms of a hydraulic damper with shear thinning fluid. The damper in a low-frequency and large-amplitude vibration may have bigger viscous damping coefficient than that when it is in a high-frequency and small-amplitude vibration, which suggests that a hydraulic damper filled with shear thinning fluid can satisfy the requirement of the isolation system better.
Brushed DC motors are essential components in a wide range of applications in which their unique benefits are explored. However, their being inherently nonlinear and sensitive to system based uncertainties such as load variation and process noise has made improving the precision control of brushed DC motors a challenging task. To mitigate such negative effects that invariably undermine motor stability and controllability, a novel wavelet-based nonlinear time-frequency control scheme viable for the concurrent speed and position tracking of brushed DC motors is presented. The control approach has its basis in discrete wavelet transformation and adaptive control. Considering system response in the wavelet domain allows the true dynamics of the system as delineated by both the time and frequency information of the response to be faithfully resolved without being distorted or misinterpreted. By employing adaptive theory, the undesirable features typical of nonlinear brushed DC motor systems such as being highly unstable and energy inefficient are also properly addressed. The validity of the controller design are demonstrated by evaluating its performance and the power requirement against PID control and fuzzy logic control in mitigating the speed, position, and armature voltage responses of a permanent magnet brushed DC motor under severe system uncertainties. The proposed nonlinear controller is shown to be accurate, robust, energy efficient, low in power requirement, and easy to switch between speed and position control.
This study investigates the small-scale effect on the flapwise bending vibrations of a rotating nanoplate that can be the basis of nano-turbine design. The nanoplate is modeled as classical plate theory (CPT) with boundary conditions as the cantilever and propped cantilever. The axial forces are also included in the model as the true spatial variation due to the rotation. Hamilton’s principle is used to derive the governing equation and boundary conditions for the classic plate based on Eringen’s nonlocal elasticity theory and the differential quadrature method is employed to solve the governing equations. The effect of the small-scale parameter, nondimensional angular velocity, nondimensional hub radius, setting angle and different boundary conditions in the first four nondimensional frequencies is discussed. Due to considering rotating effects, results of this study are applicable in nanomachines such as nanomotors and nano-turbines and other nanostructures.
This paper explores the idea of using heat as an actuator to simultaneously control vibration and temperature of a thermoelastic beam. We first model the beam as a slender, uniform cantilever beam of rectangular cross-section subject to heat through heat patches on the lower and upper surfaces at some discrete spanwise locations. The governing equations of the model are two coupled partial differential equations: one governing the elastic bending displacement and one governing the two-dimensional heat conduction of the beam. Through a discretization, the partial differential equations are replaced by a set of ordinary differential equations in a compact state-space form. We show that the coupling is actually between elastic displacement and those components of temperature contributing to the thickness-wise gradient at the midplane. The linear quadratic regulator in conjunction with the Kalman–Bucy filter is used for the control design to simultaneously damp out the displacement and the gradient. In a numerical example, we show the presence of thermoelastic damping due to the coupling. We also show that the displacement and gradient can simultaneously be controlled by using displacement measurements only, and that for less control effort it is also necessary to include some temperature measurements in the feedback.
A higher-order mechanical model of axially moving nanoscale beams with time-dependent velocity was developed in the framework of nonlocal stress gradient theory. Based on the correlation between effective and common nonlocal bending moments, a sixth-order partial differential equation of motion with respect to the transverse displacement was derived. Unlike some previous work which assumed the velocity of axially moving nanoscale beam to be a constant, a time-dependent axial velocity was considered for the nanoscale beams. The resonance vibration frequencies were obtained according to the governing equation of motion and corresponding boundary conditions. It was concluded a nonlocal nanoscale strengthening effect that the vibration frequencies of such axially moving nanostructure increase with stronger nonlocal effects, or a larger dimensionless nonlocal nanoscale parameter causes a higher vibration frequency. A jumping phenomenon in frequency field was observed, and the vibration frequency may decrease or increase with an increase in the axial average velocity. Critical speeds of the axially non-uniformly moving nanoscale beams were defined and determined, and the critical speed versus nonlocal nanoscale revealed step and strengthening effects. The theoretical results obtained were compared with some experimental data and good agreement was achieved. Subsequently, the steady-state and stability of such moving nanostructures including the principal parametric and combination resonances were analyzed using a multiple-scale method. Some beneficial analytical procedures and theoretical formulations at nanoscale were provided. Based on specific boundary conditions, the stability boundaries of the axially accelerating nanoscale beams were determined and the unstable regions were influenced by nonlocal nanoscale significantly.
The present study aims to provide some new information for the design of micro systems. It deals with free vibrations of Bernoulli–Euler micro beams with nonrigid supports. The study is based on the formulation of the modified couple stress theory. This theory is a nonclassical continuum theory that allows one to capture the small-scale size effects in the vibrational behavior of micro structures. More realistic boundary conditions are represented with elastic edge conditions. The effect of Poisson’s ratio on the micro beam characteristics is also analyzed. The present results revealed that the characterization of real boundary conditions is much more important for micro beams than for macro beams, and this is an assessment that cannot be ignored.
An efficient methodology is proposed for simulation of roll dynamics of a tank vehicle system coupled with transient hydrodynamic forces due to fluid slosh. The transient fluid slosh in a horizontal cylindrical tank is analytically modeled considering simultaneous lateral, vertical and roll excitations assuming potential flows and a linearized free-surface boundary condition. For this purpose, the fluid domain in the Cartesian coordinate system is transformed to the bipolar coordinates, where the Laplace equation could be solved using separation of variables. The resulting hydrodynamic pressure, free-surface elevation and slosh force and roll moment are formulated in the tank-fixed coordinate system. The transient fluid slosh model is subsequently integrated to a dynamic roll plane model of a tank vehicle combination to investigate the effect of transient liquid slosh on the roll stability of the vehicle during steady-turning as well as path-change maneuvers. The analyses are performed for different fluid fill heights considering both variable and constant cargo load conditions. The results suggest that the roll stability of tank vehicles can be efficiently analyzed using the coupled linear slosh and multi-body vehicle models with significantly lower computational effort than the methods employing computational fluid dynamic fluid slosh models.
In order to predict the characteristics of the vibration–acoustic coupling of an aircraft model, the finite element method–boundary element method of dynamic model (FEM-BEM dynamic model) is established. The numerical calculations and experiments of the structural vibration acceleration responses and the sound pressure levels in the model cabin under the strong noise excitations are carried out in the low and middle frequency area. By comparing the results of experiments and simulations, it’s found that the structural vibration responses and the sound pressure responses mainly distribute in the range of low and medium frequency, in which the simulated and experimental results also match each other well. This indicates the established finite element/boundary element vibration–acoustic coupled dynamic model and the calculation method proposed in this study are feasible.
A robust hybrid hidden Markov model-based fault detection method is proposed to perform multi-state fault classification of rotating components. The approach presented in this paper enhances the performance of the standard hidden Markov model (HMM) for fault detection by performing a series of pre-processing steps. First, the de-noised time-scale signatures are extracted using wavelet packet decomposition of the vibration data. Subsequently, the Teager Kaiser energy operator is employed to demodulate the time-scale components of the raw vibration signatures, following which the condition indicators are calculated. Out of several possible condition indicators, only relevant features are selected using a decision tree. This pre-processing improves the sensitivity of condition indicators under multiple faults. A Gaussian mixing model-based hidden Markov model (HMM) is then employed for fault detection. The proposed hybrid HMM is an improvement over traditional HMM in that it achieves better separation of the feature space leading to more robust state estimation under multiple fault states and measurement noise scenarios. A simulation employing modulated signals and two experimental validation studies are presented to demonstrate the performance of the proposed method.
In this paper, boundary control is designed to suppress the vibration of a nonlinear three-dimensional Euler–Bernoulli beam. Considering the coupling effect between the axial deformation and the transverse displacement, the dynamics of the beam are modeled as a distributed parameter system described by three partial differential equations (PDEs) and 12 ordinary differential equations (ODEs). Firstly, model-based boundary control is designed based on a mathematical model of the system. Subsequently, adaptive control is proposed when there are parameter uncertainties in the model. The uniform boundedness and uniform ultimate boundedness are proved under the proposed control laws. Finally, numerical simulations illustrate the effectiveness of the results.
This paper presents a new algorithm to determine the occurrence, location, and severity of damage in structures subjected to earthquakes. The algorithm is based on the analysis of the time series associated with displacement or acceleration, and provided by a limited number of sensors. The algorithm is formulated in terms of an optimization problem. An objective function is defined based on the moment generating function for a segment of the time histories and an evolutionary optimization strategy, based on the competitive optimization algorithm, is employed to detect damage. The efficiency of the proposed method is numerically validated by studying the response of some structures subjected to the 1940 El-Centro earthquake and the 1994 Northridge earthquake. In order to simulate real conditions, different levels of noise are added to the response’s signals, and then the discrete wavelet transform is used to de-noise the signals. Moreover, the robustness of the method is evaluated by considering an error in the model of the structures. Overall, we find that the proposed algorithm detects and localizes damage even in presence of noisy signals and errors in the model.
Under certain conditions, an oscillator can enter a stable regime when submitted to an external harmonic force whose frequency is far from the natural frequency of the oscillator. This may happen when the external force acts on the oscillator in a way which depends on the oscillator's spatial position. This phenomenon is called "argumental oscillation". In this paper, six argumental oscillators are described and modeled, and experimental results are given and compared to numerical simulations based on the models. A polar Van der Pol representation, with embedded time indications, is used to allow a precise comparison. The pendulums are modeled as Duffing oscillators. The six models are based on various pendulums excited by spatially localized magnetic-field sources consisting of wire coils. Each pendulum receives the excitation via a steel element, or a permanent magnet, fitted at the tip of the pendulum's rod. The spatial localization induces another nonlinearity besides the Duffing nonlinearity. A control system allowing a real-time Van der Pol representation of the motion is presented. Attractors are brought out from experimental results.
Analysis and numerical results are presented for free transverse vibrations of isotropic rectangular plates having arbitrarily varying non-homogeneity with the in-plane coordinates along the two concurrent edges on the basis of Kirchhoff plate theory. For the non-homogeneity, a general type of variation for Young’s modulus and density of the plate material has been assumed. Generalized differential quadrature method has been used to obtain the eigenvalue problem for such model of plates for four different combinations of boundary conditions at the edges namely, (i) fully clamped, (ii) two opposite edges are clamped and other two are simply supported, (iii) two opposite edges are clamped and other two are free, and (iv) two opposite edges are simply supported and other two are free. By solving these eigenvalue problems using software MATLAB, the lowest three eigenvalues have been reported as the first three natural frequencies for the first three modes of vibration. The effect of various plate parameters on the vibration characteristics has been analysed. Three dimensional mode shapes have been plotted. A comparison of results with those available in literature has been presented.
This paper presents a novel fault detection method for gearbox vibration signatures using the synchro-squeezing transform (SST). Premised upon the concept of time-frequency (TF) reassignment, the SST provides a sharp representation of signals in the TF plane compared to many popular TF methods. Additionally, it can also extract the individual components, called intrinsic mode functions or IMFs, of a nonstationary multi-component signal, akin to empirical mode decomposition. The rich mathematical structure based on the continuous wavelet transform makes synchro-squeezing a promising candidate for gearbox diagnosis, as such signals are frequently constituted out of multiple amplitude and frequency modulated signals embedded in noise. This work utilizes the decomposing power of the SST to extract the IMFs from gearbox signals, followed by the application of both condition indicators and fault detection to gearbox vibration data. For robust detection of faults in gear-motors, a fault detection technique based on time-varying auto-regressive coefficients of IMFs as features is utilized. The sequential Karhunen–Loeve transform is employed on the condition indicators to select the appropriate window sizes on which the SST can be applied. This approach promises improved fault detection capability compared to applying condition indicators directly to the raw data. Laboratory experimental data obtained from a drivetrain diagnostics simulator and seeded fault tests from a helicopter gearbox provide test beds to demonstrate the robustness of the proposed algorithm.
In the literature, typical analytical track response models are composed of beams (which represent the rail) on viscoelastic or elastic foundations. The load is usually considered as a single concentrated force (constant or varying in time) moving with constant speed. Concentrated or distributed loads or multilayer track models have rarely been considered. One can find some interesting results concerning analysis of distributed loads and multilayer track structures that include both analytical and numerical approaches. However, there is a noticeable lack of sufficient comparison between track responses under concentrated or distributed load and between one and multilayer track models. One of the unique features of the present paper is a comparison of data obtained for a series of concentrated and distributed loads, which takes into account a wide range of track parameters and train speeds. One of the fundamental questions associated with the multilayer track model is the level of coupling between the rail and the vibrations of the sleepers. In this paper, it is proved that sleepers are weakly coupled with the rail if the track is without significant imperfections, and the steady-state response is analyzed for this case. In other words, sleeper vibrations do not influence the rail vibrations significantly. Therefore the track is analyzed by means of a two-stage model. The first step of this model determines rail vibration under a moving load, and then the sleeper vibration is calculated from previously obtained kinematic excitation. The model is verified by comparison of the obtained results with experimental data. Techniques based on Fourier series are applied to the solution of the steady-state track response. Another important problem associated with track response under moving loads arises from the analysis of the effect of longitudinal forces in rails on vertical displacement. It is shown that, in the case of the steady-state response, longitudinal forces do not influence rail displacements significantly and this observation remains correct for a wide range of track parameters and train speeds. The paper also analyzes the legitimacy of the statement that additional rail deflection between sleepers, compared to the continuous rail support, can be considered as a track imperfection.
Active engine mounts significantly contribute to ensure the comfort in vehicles with emission-reducing engine technologies, e.g., cylinder-on-demand (COD), downsizing or turbochargers. To control active engine mounts, either adaptive or non-adaptive feedforward control is commonly employed. Since both approaches have previously been treated separately, this study proposes methods to connect them in terms of multiple-input-multiple-output Newton/FxLMS adaptive filters with self-trained, grid-based look-up tables. The look-up tables are incorporated as parameter-maps or parallel-maps, respectively. By combining the two feedforward control strategies, their inherent advantages, i.e., the adaptivity of adaptive filtering and the direct impact as well as the tracking behavior of map-based feedforward control, are utilized. The proposed control structures are illustrated by simulation and experimentally demonstrated in a vehicle with a V8-COD engine. While both methods significantly reduce the convergence time of the adaptive filter, the parallel implementation additionally improves the tracking behavior during fast engine run-ups.
Self-centering systems, such as base-rocking-wall systems, have been studied and demonstrated to be capable of achieving enhanced seismic-resisting performance. For these rocking-wall systems, unbonded post-tensioning strands and damage-permitted energy-dissipating fuses are usually implemented along the full height of the walls. Structural damage and residual deformation of main structures can be mitigated through deformation of the fuses which are replaceable after strong earthquakes. An innovative self-centering system referred to as a pendulum-type nontraditional tuned mass damper system is newly proposed in this paper, which can be deemed to be an inverted rocking system. Pendulum components can automatically return to their original position due to the effect of gravity, without any post-tensioning strands being required. Energy dissipators are only implemented between the bottom end of the pendulum component and the ground, and they can be easily fabricated and replaced. Both experimental and numerical studies have been carried out to examine seismic performance of the pendulum-type nontraditional tuned mass damper system, and it is found that satisfactory control of interstory drift and floor absolute acceleration can be achieved, while small movement space is required.
In a spatial K-shaped metallic frame, there exist in- and out-of-plane bending, axial, and torsional vibrations. A wave-based vibration analysis approach is applied to obtain free and forced vibration responses in a space frame. In order to validate the analytical approach, a steel K-shaped space frame was built by welding four beam elements of rectangular and square cross-section together. Bending vibrations are modeled using both the classical Euler–Bernoulli theory and the advanced Timoshenko theory. This allows the effects of rotary inertia and shear distortion, which were neglected in the classical Euler–Bernoulli theory, to be studied. In addition, the effect of torsional rigidity adjustment for structures of rotationally non-symmetric cross-section is also examined.
The vibration property of a rectangular-hollow-sectional beam with an external crack were theoretically and experimentally studied in this paper. The external part-through crack and through-thickness crack were considered. Linear elastic fracture mechanics were employed to establish the theoretical formula for computing the equivalent torsion spring stiffness of the two external cracks. Then, the experimental method of obtaining the equivalent torsion spring stiffness was developed. It is seen that the test data match fairly well with the analytical data. On this basis, the transfer matrix method was introduced to obtain the frequency equations of these cracked beams under three classic boundary conditions, and followed by the numerical method for calculating natural frequencies. Experimental tests on clamped–free beams were used to verify the accuracy. It should be noted that a part-through crack may lead to a more distinct natural frequency reduction than the through-thickness crack.
This paper presents an optimization study of sandwich plates with corrugated cores for minimizing the transmitted sound power, considering the manufacturability of the structure and constraints on the structural weight and fundamental frequency. A two-dimensional plate model is developed based on the spectral element method (SEM) for the calculation of the frequency-domain vibration response of the whole sandwich structure subject to airborne excitation, and the Rayleigh integral formula is used to calculate the transmitted sound power via its structure-born path. A genetic algorithm-based multi-parameter optimization method is employed to search for the optimal structural parameters with the objective to minimize the sound power transmitted. It is indicated that the optimization results depend highly on the properties of resonant modes in the targeted frequency band. Because of the local modes of the sandwich structure in the high frequency band, the transmitted sound power can be significantly reduced with neither increasing the structural weight nor deteriorating the bending stiffness.
Bearings are one of the most frequently used components in the rotatory machinery, so the performance degradation assessment of bearings plays an important role in the prognostics and health management of systems. Hidden Markov model (HMM) is a widely applied data-driven model used for bearing performance degradation assessment and has many successful applications. A normal HMM needs to be trained in advance, which has close relationship with the evaluation system. However, the trained HMM is quite influenced by many issues, such as the data integrity and the feature space. In this paper, an intelligent bearing performance degradation assessment method based on HMM and nuisance attribute projection (NAP) is proposed. The proposed method can combine the information from the experimental data and the real-time data effectively and assess the performance since the beginning of the monitoring. The effectiveness of the proposed method is verified through an accelerated life test of rolling element bearings.
Using an inertial part of a building structure as a tuned mass damper (TMD) has been shown to have economic advantages in terms of required materials and space for installing and operating a TMD in a building. This study suggests either designing the top story of a new asymmetric-plan building or adding a purposely designed story atop an existing asymmetric-plan building as a TMD to protect the building against earthquakes. This novel TMD, called a top-story mass damper (TSMD), is formulated using the three-degree-of-freedom modal properties of the first triplet of vibration modes of the original two-way asymmetric-plan building. The so-called first triplet of vibration modes are the first dominant modes in each of the three directions, i.e., the two horizontal translations and one vertical rotation. The proposed TSMD is intended to suppress the vibrations resulting from the first triplet of vibration modes that are generally most significant in overall seismic responses. The effectiveness of the TSMD is verified by investigating the frequency response functions and seismic responses of one single-story and one 20-story two-way asymmetric-plan buildings.
A novel numerical approach based on the weak form quadrature element method is developed to study the effect of initial stress on the attenuation zones and attenuation coefficients of periodic Timoshenko beams resting on a two-parameter elastic foundation. For some special cases, comparisons with other related investigations are conducted to validate the proposed method, and good agreement is found. The results show that the compressive initial stress enhances the maximum attenuation in the second attenuation zone while it weakens the maximum attenuation in the first attenuation zone. In addition, based on the detailed modal analysis, simplified models are proposed to determine the bound frequencies of the lowest attenuation zone. Furthermore, frequency domain analysis and transient response analysis for a beam with finite unit cells are performed to verify the theoretical analysis of the infinite-unit cell beam. The present investigation is very helpful for the design and application of periodic strip foundations and pipelines for vibration isolation in buildings and infrastructures.
In this paper, vibration suppression of shear deformable beams with hybrid material-foundation viscoelastic damping is studied. The precise behavior of viscoelastic polymeric structures is taken into consideration by Boltzmann superposition integral and utilizing dynamic mechanical analysis (DMA) results while foundation viscoelasticity is adapted by Kelvin-Voigt model. The integro-partial differential equations of motion are derived based on the Timoshenko theory via Hamilton principle. Assessment of the solution procedure is carried out by comparison with elastic Timoshenko and viscoelastic Euler-Bernoulli cases. Transient response, natural frequency and modal loss factor are attained by Fourier transform, weighted residual method and numerical iterative algorithm. Influences of hybrid viscoelastic damping, foundation properties, geometrical parameters and boundary conditions on vibration characteristics and dynamic response are investigated via comprehensive parametric study. Due to the absence of similar results in the literature, this paper is likely to fill a gap in the state of the art of this problem.
Microphone arrays have become a popular technique to identify sound sources. They can be utilized to localize the sources for various applications. The most common application is the conventional beamforming that provides the source maps with strong side lobes and poor spatial resolution at low frequencies. To overcome these problems, the focus is set on deconvolution and generalized inverse techniques such as a deconvolution approach for the mapping of acoustic sources (DAMAS) and generalized inverse beamforming (GIB). Although the source maps are clearly improved, these methods have the shortcomings of expensive computing and limited dynamic range. In this paper, we propose a source localization method called functional generalized inverse beamforming with regularization matrix (FGIBR) based on an inverse problem. Compared with GIB, the accuracy of FGIBR could be improved by introducing a new beamforming regularization matrix and a scaling parameter c0. Also the dynamic range of the source maps can be increased by applying FGIBR with an exponent parameter called order v. Several simulated examples are given to illustrate that the side lobes are suppressed and the main lobe becomes much narrow; moreover, if order v is increased, the beamforming side lobes can be sharply reduced and the actual position of the noise source can be precisely located. Then FGIBR is implemented to deal with experimental data in the free field. In the case of the experiment, the source is correctly located. The proposed FGIBR demonstrates a good performance in terms of resolution and side lobe rejection compared with other beamforming methods. Furthermore, the computation time is shown to be low if the iteration and order are reasonable.
In this article, a novel passive control system, ribbed bracing system (RBS), has been proposed to deal with the buckling problem. RBS is a bracing system with a simple mechanism that can be installed in braces as a supplemental part. The behavior of RBS is similar to that of conventional braces under tensile loading. However, under compressive force, it endures an insignificant force and prevents the braces from buckling through length reduction. In addition, seismic damage is concentrated in the bracing system of the structures equipped with RBS, decreasing the dissipated hysteretic energy in other structural members. There are two different mechanisms for RBS: 1) completely-closed RBS (CC-RBS) and 2) self-centering RBS (SC-RBS). The concept and mechanics of RBS have been verified by the results obtained from cyclic testing and numerical analysis of RBS specimens. In this research, after describing the mechanical configuration of RBS, nonlinear time history analysis has been conducted on 3-story and 6-story concentrically braced frames subjected to different seismic intensity levels, design basis earthquakes (DBE), and maximum considered earthquakes (MCE). The analyses have been performed on different types of bracing systems as follows: SC-RBS, CC-RBS, and Buckling Restrained Braces (BRB). The results show that SC-RBS frames have negligible residual story drifts, and maximum displacement in CC-RBS is slightly lower than that of BRB. Additionally, distribution of input energy into the structure was considered and showed that RBS frames demonstrate a high hysteretic energy dissipation, which results in lower demands in other structural elements.
The dynamic performance of any structure is function of existing material properties and boundary stiffness parameters which may deteriorate or become more flexible due to prolonged use. These parameters are estimated inversely through optimization of a suitable objective function. The gradient based optimization methods are preferred due to their faster convergence from a set of initial guess points, but suffers mostly from lack of reliable methodology to select appropriate step sizes. Arbitrary selection of step sizes may sometimes work well, depending upon the judgment of the user, but is case specific. The present work describes the estimation of existing material properties and boundary stiffness of isotropic and orthotropic plates from measured frequencies and mode shapes using a new gradient based step size controlled inverse eigensensitivity algorithm. The method takes a strategy that the step sizes automatically become smaller when the change in gradient of objective function is having a high value and similarly, takes larger steps when the gradient is remaining fairly constants in subsequent iterations. The results obtained from the investigations are encouraging, as some convergences could be achieved by this new adaptive step size control only, whereas methods adopting arbitrary or no step size control diverged.
A method for the non-probabilistic reliability optimization on frequency of continuum structures with uncertain-but-bounded parameters is proposed. The objective function is to maximize the non-probabilistic reliability index of frequency requirement.The corresponding bi-level optimization model is built, where the constraints are applied on the material volume in the outer loop and the limit state equation in the inner loop. The non-probabilistic reliability index of frequency requirement is derived by the analytical method for the continuum structure with the uncertain elastic module and mass density. Further, the sensitivity of the non-probabilistic reliability index with respect to the design variables is analyzed. The topology optimization in the outer loop is performed by a bi-directional evolutionary structural optimization (BESO) method, where the numerical techniques and the optimization procedure of BESO method are presented. Numerical results show that the proposed BESO method is efficient, and convergent optimal solutions can be achieved for a variety of optimization problems on frequency non-probabilistic reliability of continuum structures.
In this study, a novel dual implementation of the Kalman filter proposed by Eftekhar Azam et al. (2014, 2015) is experimentally validated for simultaneous estimation of the states and input of structural systems. By means of numerical simulations, it has been shown that the proposed method outperforms existing techniques in terms of robustness and accuracy for the estimated displacement and velocity time histories. Herein, dynamic response measurements, in the form of displacement and acceleration time histories from a small-scale laboratory building structure excited at the base by a shake table, are considered for evaluating the performance of the proposed Dual Kalman filter and in order to compare this with available alternatives, such as the augmented Kalman filter (Lourens et al., 2012b) and the Gillijn De Moore filter (GDF) (2007b). The suggested Bayesian approach requires the availability of a physical model of the system in addition to output-only measurements from limited degrees of freedom. Two categories of such physical models are herein studied to evaluate the effect of model error on the filter performances; the first, is a model that comprises identified modal parameters, i.e., natural frequencies, mode shapes, modal damping ratios and modal participation factors; the second, is a model that is extracted from a recently developed subspace identification procedure, namely the transformed stochastic subspace identification method. The results are encouraging for the further use of the dual Kalman filter and its available alternatives for addressing the important problems of full response reconstruction and fatigue estimation in the entire body of linear structures, using a limited number of output-only vibration measurements.
This paper presents a novel decentralized tracking control system of electrically driven flexible-joint robots by adaptive type-2 fuzzy estimation and compensation of uncertainties. Owing to using voltage control strategy, the proposed control approach has important advantages over the torque control approaches in terms of being free from manipulator dynamics, computationally simple and decoupled. The design includes two interior loops: the inner loop controls the motor position while the outer loop controls the joint angle of the robot. An adaptive proportional–integral–derivative controller governs the outer loop, whereas a robust nonlinear controller supported by estimation of uncertainty is employed for the inner loop. More specifically, the main contribution of the paper arises from this fact that the proposed control method uses the interval Type-2 Fuzzy Logic systems for estimation of uncertainty. This is the main difference between this paper and those published in literature. One advantage of the proposed approach is that it uses available feedbacks as an important advantage from a practical point of view. The method is verified by stability analysis and its effectiveness is demonstrated by simulations. The direct method of Lyapunov is utilized for stability analysis of the proposed approach. The case of study is the tracking control of a three-joint articulated flexible-joint robot driven by permanent magnet DC motors. Simulation results show the superior robustness of the type-2 fuzzy system to Type-1 fuzzy system.
Bridge weigh-in-motion (BWIM) technique uses an instrumented bridge as a weighing scale to estimate vehicle weights. Traditional BWIM systems use axle detectors placed on the road surface to identify vehicle axles. However, the axle detectors have poor durability due to the direct exposure to the traffic. To resolve this issue, a free-of-axle-detector (FAD) algorithm, which eliminates the use of axle detectors, was proposed. As a further improvement to simplify the BWIM systems, the concept of nothing-on-road (NOR) BWIM was recently introduced. The axle identification method proposed in this paper is an attempt to achieve the NOR BWIM, i.e., using bridge global responses to identify vehicle axles. Wavelet analysis is applied to extract the axle information from the global responses. This allows the BWIM technique to be achieved with only weighing sensors. Numerical simulations are conducted using three-dimensional vehicle and bridge models and the effect of several parameters, including sampling frequency, road surface condition and measurement noise on the identification accuracy is investigated. The results demonstrate that the proposed identification method using wavelet analysis can accurately identify vehicle axles, except for cases where the road surface condition is rough or measurement noises exceed certain levels.
An approximate integral-balance solution of the fractional subdiffusion equation by a double-integration technique has been conceived. The time-fractional linear subdiffusion equation with Dirichlet boundary condition (and zero initial condition) has been chosen as a test example. Approximations of time-fractional Riemann-Liouville and Caputo derivatives when the distribution is assumed as a parabolic profile with unspecified exponent have been developed. Problems pertinent to determination of the optimal exponent of the parabolic profile and approximations of the time-fractional derivative of by different approaches have been formulated. Solved and unresolved problems in determination of the optimal exponents have been demonstrated. Examples with predetermined quadratic and cubic assumed profiles are analyzed, too. Comparative numerical studies with exact solutions expressed by the Mainardi function in terms of a similarity variable have been performed.
In this paper, a comparison between two different machine tool columns is presented. The two columns are realized with a different technology: classic metalworking versus metal foam sandwiches. The aim of the experimental tests is the evaluation of their different mechanical performances and characteristics, with a particular focus on the dynamic response and on the convenience to consider system damping as a key parameter. This kind of comparison is generally believed as difficult, because the foam-filled structures usually show not-linear behavior, which makes not applicable the usual experimental modal procedures. The comparison is carried out in terms of both modal analysis and wide frequency range excitation, as described in the paper. A new method is introduced by the authors to deem which technology is the more suitable, based on overall dynamic response in a wide range of frequency, rather than on modal damping.
In order to study the vibration characteristics of flow-induced open cavity structures, the dynamic model of stiffened multi-plate is established. The first-order shear deformable plate theory and the Timoshenko beam theory are used to model the displacement fields of isotropic plates and stiffeners, respectively. A modified variational principle combined with a multi-segment partitioning procedure is employed to formulate the discretized equations of motion. The stiffeners are considered as discrete elements, and the energy contributions are included into the system energy functional by using the displacement compatibility conditions. The displacement and rotation components of each plate segment are expanded by a duplicate series of Chebyshev orthogonal polynomials of first kind. The convergence and accuracy of the present results for isotropic stiffened plates with different boundary conditions have been validated using comparisons with the published data and those obtained from the finite element analyses. Free vibration and dynamic responses of stiffened multi-plates with either longitudinal or orthogonally oriented stiffeners are discussed. The mathematical model and methodology presented in this paper may be used as an appropriate numerical tool in the analysis and design of stiffened multi-plate structures.
Scissor seat suspension is used widely for attenuating the cab vibration of commercial vehicles, and obtaining its dynamics characteristics accurately is the basis of scissor seat suspension optimization, control and development. As a result, this paper focuses on the scissor seat suspension dynamics modeling and characteristics analysis. Firstly, the scissor seat suspension constraint dynamics equations are derived according to the detailed physical structure. Then, a numerical algorithm with the Baumgarte is proposed to solve the derived multi-body dynamics model which considers the correlation between generalized velocity
The work presented here covers the detailed modelling and trajectory control for an elastic bladed quadrotor vehicle. The benefits of using VehicleSim modelling software are also discussed. The authors present a full elastic structural and dynamical model as well as two different aerodynamic models. These two aerodynamic models differ from each other on their level of complexity and therefore, accuracy. The control methodology employed to stabilize and guide the vehicle is Proportional-Velocity-Acceleration (PVA), derived and implemented by using Simulink. As it will be shown, it stabilises and provides satisfactory quadrotor trajectory tracking. Since the control methodology feeds back the acceleration of the vehicle, and this acceleration has an oscillating nature, an adaptive process has been designed and introduced into the vehicle’s model in order to avoid the oscillations’ transmission to the control system, showing how it reduces the amplitude of the control actions oscillations. Results of simulations and discussion on them are also provided at the end of this article.
This survey presents the broad range of research on using wavelets in the analysis and design of dynamic systems. Though wavelets have been used with all types of systems, the major focus of this survey is mechanical and electromechanical systems in addition to their controls. However, the techniques presented can be applied to any category of dynamic systems such as economic, biological, and social systems. Wavelets can be classified into three different types: orthogonal, biorthogonal, and pseudo, all of which are employed in dynamic systems engineering. Wavelets-based methods for dynamic systems applications can be divided into vibrations analysis and systems and control analysis. Wavelets applications in vibrations extend to oscillatory response solutions and vibrations-based systems identification. Also, their applications in systems and control extend to time–frequency representation and modeling, nonlinear systems linearization and model reduction, and control design and control law computation. There are serious efforts within systems and control theory to establish time–frequency and wavelets-based Frequency Response Functions (FRFs) parallel to the Fourier-based FRFs, which will pave the road for time-varying FRFs. Moreover, the natural similarity of wavelets to the representation of neural networks allows them to slip into neural-networks-based and fuzzy-neural-networks-based controllers. Additionally, wavelets have been considered for applications in feedforward and feedback control loops for computation, analysis, and synthesis of control laws.
A large amplitude vibration analysis is presented for nanocomposite doubly curved panels resting on elastic foundations in thermal environments. The doubly curved nanocomposite panels are studied with the consideration of different types of distributions of uniaxial aligned single-walled carbon nanotubes (SWCNTs). The material properties of the functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to be graded in the thickness direction according to linear distributions of the volume fraction of CNTs and are estimated through a micromechanical model. The motion equations are based on a higher order shear deformation theory and von Kármán strain-displacement relationships. The thermal effects are also included and the material properties of CNTRCs are assumed to be temperature-dependent. The motion equations are solved by a two-step perturbation approach to determine the nonlinear frequencies of the CNTRC doubly curved panel. The numerical illustrations cover small- and large-amplitude vibration characteristics of CNTRC doubly curved panels resting on Pasternak elastic foundations. The present solutions also highlight the effects of CNT volume fraction, temperature variation, foundation stiffness, panel curvature ratio as well as in-plane boundary conditions on the nonlinear free vibration behaviors of CNTRC doubly curved panels.
The Duffing oscillator under time-delayed displacement feedback is investigated to study the effect of intentional time-delay on the global dynamics of the oscillator. From the free vibration study performed by employing the describing function method it is observed that for the undamped oscillator, an infinite number of limit cycles is present for all possible values of gain and delay. The number of stable and unstable limit cycles in the gain versus delay plane is studied region wise with the help of limit cycle stability lines. Secondly, in a damped system, the number of limit cycles is finite and depends upon the values of gain, delay and damping coefficient from which the maximum number of limit cycles, their frequencies and amplitudes are obtained. When the system is excited by harmonic forcing, these limit cycles exhibit the phenomena of multiple entrainments and their frequency response curves become very complex and most often results in the very high amplitude oscillations. The study of the forced damped oscillator is therefore carried out by applying the method of slowly varying parameter and the frequency response curves for period-1 responses are analyzed. Further, with the a priori knowledge of possible stable and unstable limit cycles obtained by the application of semi-analytical methods, the various instability phenomena due to subharmonic and quasiperiodic responses have also been investigated by numerical simulation using Simulink in the different parametric ranges.
Pressure pulsations in volumetric compressor manifolds have a high impact on compression power requirement and the reliability of manifold operation. These pulsations induce vibrations, noise, and in some cases, mechanical failure of piping or compressor valves. For pressure pulsation attenuation, different types of mufflers are applied using a design based upon the Helmholtz resonator approach. This design is particularly effective for constant revolution speed compressors. For contemporary applications of variable revolution speed compressors, other pressure pulsation attenuation methods are needed. It is known that different shapes of nozzles can attenuate pressure pulsations, however, they unfortunately increase the compressor power at the same time. The main criterion for nozzle selection is achieving pressure pulsation attenuation that is as high as possible whilst having the lowest possible effect on compressor power. In this paper, innovative computational fluid dynamics (CFD) simulation methodology is applied for the optimisation of nozzle shape and size. The steady flow simulation results correspond with compressor power consumption and impulse flow simulation results are related to pressure pulsation attenuation. This method has been validated on the basis of the experimental results for three different nozzle geometries. For experimental validation, nozzles have been mounted in the variable speed screw compressor discharge manifold.
This paper deals with the problem of elastic constant identification in thin plates made of orthotropic composite materials. The approach is based on the analysis of Lamb wave propagation and the related dispersion curves to find the underlying material elastic constants. In the proposed implementation a scanning laser Doppler vibrometer is used to measure Lamb wave dispersion curves. The Local Interaction Simulation Approach is used simultaneously to find a solution to a high-frequency wave propagation problem. The experimental and simulated data are combined in a Bayesian framework for parameter identification which is robust in condition of parameter, modeling and measurement uncertainty. The results are discussed and compared with the results from a deterministic optimization.
In this paper, the recently developed analytical mode decomposition with a constant or time-varying cutoff frequency is extended into the decomposition of a non-stationary discrete time sequence. The discretization of the signal and the selection of the cutoff frequency may cause the failure of low frequency component extraction. In this study, to eliminate the effects of the signal discretization, the one-step, two-step, and four-step low-pass filters with cutoff frequencies are proposed. Based on the theoretical derivation, the previous one-step low-pass filter is effective only when the cutoff frequency is not greater than a quarter of the sampling frequency and the maximum frequency of the signal not greater than a half of the sampling frequency. In this study, if the cutoff frequency is less than or equal to a quarter of the sampling frequency, a two-step low-pass filter is proposed to extract the low frequency component. If the cutoff frequency is greater than a quarter of the sampling frequency, a four-step low-pass filter with frequency shifting process is proposed. When the time-varying cutoff frequency is not always larger than or less than a quarter of the sampling frequency, a sufficient condition, which is the sampling frequency is greater than four times of the maximum frequency of the signal component, is provided in this study. Two numerical examples are used to validate the effectiveness of the proposed low-pass filters. Both the theoretic derivation and numerical simulations show that the proposed filters can analytical extract the discrete low frequency component with an appropriate cutoff frequency.
There exist multiple disturbances resulting from the structural vibrations of flexible appendages, unknown external and internal disturbances, and parameter uncertainties, which affect the attitude control performance seriously. To enhance the disturbance attenuation performance and vibration suppression ability, a composite anti-disturbance control scheme (CADCS) based on disturbance observer is proposed for attitude stabilization and vibration reduction of flexible spacecraft. The CADCS combines a composite disturbance observer (CDO) and a PD controller with feedforward. The multiple disturbances are equivalent to slowly varying disturbance and harmonic disturbance. The CDO can estimate two types of disturbance and compensate for them through feedforward. The PD controller realizes the asymptotic convergence by compensating the disturbance from CDO. The CADCS based on CDO and PD controller is not only simple and easy to realize, but also yields better vibration suppression and anti-disturbance performance. Simulation results of a certain spacecraft demonstrate the effectiveness of the proposed CADCS.
The dynamical behavior of a non-linear mechanical system with two degrees of freedom (DOFs) during free and forced excitations is studied analytically and numerically. The non-linearity of the system is represented intentionally by a smooth non-linear simple function with periodically varying stiffness around a constant value for the sake of practical investigations. Analysis of the system leads to a method that could be used to design the non-linear energy sink (NES) so that the behavior of the system during relaxation and its strongly modulated response (SMR) could be improved versus the constant stiffness configuration.
A methodology is proposed for classification of type of defect in a bearing using vibration data. Hilbert-Huang Transform (HHT) is used to obtain Instantaneous energy density (IE) values corresponding to interaction of rolling elements and the defect. IE values are treated as a time series and autocorrelation coefficients (ACs) with varying lags are calculated. Based on the ACs, a Defect Occurrence Index (DOI) is proposed to rank the possibility of a type of bearing damage. Based on the DOI, an adaptive filtering process is used to filter the maximum IE corresponding to the peaks generated during the defect interaction. The main feature of the present approach involves capturing the phenomenon of amplitude modulation (using the approach of autocorrelation) for an inner race defect and uses its absence in the case of outer race defect to distinguish between the inner and outer race defects. Statistical techniques (Chi-square test and Coefficient of variation (CV)) on the filtered IE are used for damage type identification. A new parameter, Defect Severity Value (DSV), is proposed for assessment of the severity of the bearing defect. The proposed methodology is validated on simulated outer/inner race defect, and on two different vibration datasets obtained from seeded defect experiments. The proposed methodology helps uniquely identify the bearing damage.
In this analytical study, free vibration analyses of a 3d mixed formulation beam element are performed by adopting force-based consistent mass matrix that incorporates shear and rotary inertia effects. The force-based approach takes into account the actual distribution of mass of an element in the derivation of the mass matrix. Moreover, the force-based approach enables accurate determination of free vibration frequencies of members with varying geometry and material distribution without any need for specification of different displacement shape functions for each individual case. This phenomenon is justified by comparing free vibration frequencies of cantilever beams that have circular and rectangular cross-sections and various mass distribution configurations. Vibration frequencies of the mixed formulation element are compared with the frequencies obtained from closed-form solutions and finite element analyses. Fundamental frequency is computed with only one element per member span and higher order frequencies are determined with two or four elements with considerable accuracy by employing 3d mixed element and force-based consistent mass matrix.
In this paper, a hybrid empirical mode decomposition (EMD) method is proposed to undertake ambient modal identification of civil structures. Unlike univariate EMD that uses single channel measurement independently, multivariate EMD (MEMD) is employed to estimate the joint information of multichannel vibration measurements of structural systems. The mode mixing in the resulting modal responses from MEMD is then circumvented using ensemble EMD (EEMD). The proposed hybrid MEMD method is validated using a suite of numerical models and experimental studies including the presence of low energy modes, closely-spaced frequencies, measurement noise and reduced sensor densities. The results show the improved performance of the proposed method over the traditional EMD method and reveal the potential of MEMD as a possible candidate for the ambient modal identification method.
In this manuscript, the dynamic stability and bifurcation occurrence for three famous types of plates including orthotropic sigmoid, power-law and exponential functionally graded plates under lateral stochastic loads are studied. Due to randomness, the behavior and analysis are not conventional deterministic investigation. So, the dynamic stability zone and border curves of bifurcation are evaluated using probability density function of the response. The latter is computed from a completely exact solution of the Fokker Planck Kolmogorov equation. The three dimensional dynamic stable zone and the border surfaces of bifurcation are obtained as a function of material parameter, in-plane forces and the mean value of lateral load. To generalize the results, all the parameters are transformed to some proper non-dimensional variables and then the effects of all prescribed parameters on the dynamic stability are completely discussed and compared. The comparison is done between the plates with themselves and also the corresponding homogenous plate. Finally the results are validated by the bifurcation diagrams of non dimensional deflection of plates that are obtained directly and numerically from the governing equations of plates.
The use of a multilayer piezoelectric cantilever beam for vibration-based energy harvesting applications has been investigated as an effective technique to increase the harvested electrical power. It has been shown that the multilayered energy harvester performance is very sensitive to the number of layers and their electrical connection due to impedance variations. The objective of this work is to suggest a comprehensive mathematical model of multilayered unimorph piezoelectric energy harvester allowing analytical solution for the harvested voltage and electrical power. The model is used to deeply investigate the influence of different parameters on the harvested power. A distributed-parameter model of the harvester using the Euler–Bernoulli beam theory and Hamilton's principle is derived. Gauss's law is used to derive the electrical equations for parallel and series connections. A closed-form solution is proposed based on the Galerkin procedure and the obtained results are validated with a finite element 3D model. A parametric study is performed to ascertain the influence of the load resistance, the thickness ratio, the number of piezoelectric layers on the tip displacement and the electrical harvested power. It is shown that this model can be easily used to adjust the geometrical and electrical parameters of the energy harvester in order to improve the system's performances. In addition, it is proven that if one of the system's parameter is not correctly tuned, the harvested power can decrease by several orders of magnitude.
A novel nonsingular fast terminal sliding mode (NNFTSM) control strategy based on the extended state observer (ESO) and the tracking differentiator (TD) is developed for the stabilization and tracking of the uncertain perturbed permanent magnet synchronous motor (PMSM) chaotic system. The proposed NNFTSM surface not only makes the system state rapidly converge to the equilibrium point in finite time with high steady-state precision, but also avoids the singular phenomenon. Furthermore, the ESO which does not rely on the mathematical model of the system is used for estimating uncertainties and disturbances to decrease the chattering caused by the big switching gain through compensating controller. Meanwhile, the TD is introduced to arrange the transition process for the reference input signal to realize the coordinated control between the rapidity and overshoot, and to decrease the initial impulse of the manipulative variable. The simulation results demonstrate that the proposed control scheme can flexibly restrain chaos which provides good dynamic and static performances, and has strong robustness to parameter variations and external load disturbances with low chattering.
The design of high performance instruments often involves the attenuation of poorly damped resonant modes. Current design practices typically rely on informed trial and error based modifications to improve dynamic performance. In this article, a multi-material topology optimization approach is presented as a systematic methodology to develop structures with optimal damping characteristics. The proposed method applies a multi-material, parametric, level set-based topology optimization to simultaneously distribute structural and viscoelastic material to optimize damping characteristics. The viscoelastic behavior is represented by a complex-valued material modulus resulting in a complex-valued eigenvalue problem. The structural loss factor is used as objective function during the optimization and is calculated using the complex-valued eigenmodes. An adjoint sensitivity analysis is presented that provides an analytical expression for the corresponding sensitivities. Multiple numerical examples are treated to illustrate the effectiveness of the approach and the influence of different viscoelastic material models on the optimized designs is studied. The optimization routine is able to generate designs for a number of eigenmodes and to attenuate a resonant mode of an existing structure.
A new de-noising method combining Wavelet threshold and empirical mode decomposition (EMD) (WTEMD for short) is proposed to improve the precision of de-noising performance for vibration signal of flood discharge structure in low signal to noise ratio (SNR). White noise is partially filtered out by decomposing the vibration signal with wavelet. Then conducting the further EMD on wavelet reconstructed signal to obtain Intrinsic Mode Function (IMF), through analyzing spectrum diagram of every IMF component, low-frequency waterflow noise and the rest of high-frequency white noise are filtered out, regarding SNR and root mean square error (RMSE) as evaluation index for noise reduction effect. The novelty of this method is that it can reduce the endpoint effect of EMD. By comparing the filtering effect of WTEMD with other methods on simulation signals, study shows that, WTEMD has a higher precision and a better de-noising effect. The dominant vibration information of dam structure is achieved by using WTEMD in Laxiwa arch dam hydro-elastic model and Three Gorges Dam, which can provide the basis for safe operation and on-line monitoring of the dam structure. This method can effectively solve the problem of dominant information extraction for large flood discharge structure.
In this paper, combination of cubic nonlinearity and time delay is designed to improve the performance of a viscoelastic isolation system with a power-form restoring force. By the method of multiple scales, the amplitude-frequency response, stability, backbone curve and energy transmissibility are considered. More specifically, three nonlinear cubic delayed feedback control methodologies are examined: position, velocity and acceleration delayed feedback. It is found that the viscoelastic damping coefficient can induce multi-valued response, especially frequency island phenomenon. In this regard, the isolation system indicates the softening behavior for under-linear restoring force and hardening behavior for over-linear restoring force. And equivalent damping and jump avoidance condition are first proposed to interpret the effect of feedback control loop on dynamical behaviors. Furthermore, with the purpose of improving the stability and reducing the vibration, suitable feedback parameter pairs are determined by the frequency response together with stability conditions. Finally, the vibration isolation property is predicted based on energy transmissibility in different cases. Results show that the strategy proposed in this paper is practicable and feedback control parameters are significant factors to alter dynamical behaviors, and more importantly, to improve the isolation effectiveness for the viscoelastic isolation system.
This article presents the experimental validation of a new control technique for reducing vibration in flexible structures: Dependent modal space control. While the classic independent modal space control allows only the frequency and the damping of the controlled modes to be changed, dependent modal space control can also impose the controlled mode shapes. Depending on the kind and number of sensors and actuators available for control, the mode shape can be imposed in both a direct and an indirect way. Owing to the need for modal sensors and actuators for direct mode shape imposition, the second methodology is often preferred in many engineering applications. In the indirect method, the optimal closed loop mode shapes set is computed with an optimization algorithm in order to minimize an Input-Output Performance Index. The worsening spillover effects due to errors in the estimates of the system state variables are considered when computing the gain matrix and play an important role in the entire control logic. Experimental validation on a cantilevered beam shows the effectiveness of the dependent modal space control and a good match between the numerical and the experimental results.
The levitation phenomenon of permanent magnets immersed in ferrofluid is the foundation of ferrofluid dampers. According to the model built using bipolar coordinates, the analytical equation describing the force exerted on the cylindrical magnets in ferrofluid dampers is obtained, which is different from that of the previous results. The analysis of the equation indicates that the magnetic levitation force increases with the eccentricity of the magnet, the radius of the magnet and the permeability of ferrofluid, respectively, when other factors are definite. As a result, we can increase the permeability of ferrofluid and decrease the radius ratio of the magnet and the tube to enhance the levitation stability.
This paper focuses on suppression of free vibration of single degree-of-freedom systems that possess time delay. The switchable stiffness (SS) control strategy is reviewed. The implication of time delay is examined. It shows that the system delay can cause malfunction of the direct SS control. To overcome this problem, the two time-delay control strategies are proposed. The first strategy named as half period delay SS control introduces an intentional delay such that the switch action takes place in a half of oscillation period later. The second strategy named as quarter period delay SS control is to add an intentional delay such that the switch action occurs in a quarter of oscillation period later. In this case, the SS control law is inverted. An apparatus consisting of an electromagnetic (EM) spring is developed to validate the proposed strategies. The stiffness models of the system are established. In computer simulation, three cases have been examined. In case A, the system is simplified as linear and the dynamics of the EMs is neglected. In case B, the stiffness models are used and the dynamics of the EMs is neglected. In case C, the stiffness models are used and the dynamics of the EMs is considered. An experimental study is conducted in real time. The results have validated the observations obtained from the computer simulations.
This paper presents an investigation into the dynamic behavior of an embedded rail track coupled with a tram vehicle in time domain. A new designed embedded rail track structure firstly introduced into the Chinese tramways is described and the results of vibration tests of the embedded rail track (ERT) and another fastened slab track (FST) are discussed. A three-dimensional (3D) dynamic model of a tram vehicle coupled with an embedded rail track was developed on the basis of the multi-body dynamics approach and the finite element method. In the model, the tram vehicle was modeled as a multi-body system. The embedded rail track was modeled as a two layer system consisting of two rails, filling material, slabs, and adjustment layer beneath slabs. The rails were treated as Timoshenko beams with continuous elastic supports, in which the modal superposition method was used to reduce the order of the partial differential equations of beams. Continuous viscoelastic elements were used to represent the filling material and rail pad that connecting the rails and the slabs. The concrete slabs were modelled using the 3D finite element method, while the modal superposition method was adopted to improve the computational efficiency. Uniformly viscoelastic elements were introduced to model the elastic layer beneath the concrete slabs. The proposed model was then applied to compare the dynamic response of the innovative embedded rail track with respect to a conventional fastened slab track. The numerical results indicate that the innovative embedded rail track has advantages over the fastened slab track for its potentialities to reduce the dynamic wheel/rail force, the vibration level and deformation of the track parts, and the track defects and damages.
In this paper, the active control of sound transmission through a simply supported soft-core sandwich panel is analytically studied. Since, the sound transmission through soft-core sandwich panels in the low-frequency region mainly occurs due to flexural and dilatational modes, and therefore to control these structural modes, volume velocity and weighted sum of spatial gradients (WSSG) are used to drive a piezoceramic actuator (PZT) attached on the exterior side of the bottom face plate. Sound power level and voltage required to drive the PZT are compared for different values of isotropic core loss factor. Numerical studies indicate that both control metrics are capable of attenuating the flexural and the dilatational modes of the sandwich panel, and hence, reduce significant amount of sound power in a wider frequency range. By carefully selecting the modes to calculate the scaling factors, WSSG provides comparable control to volume velocity. However, the necessary voltage required to drive the PZT to minimize the WSSG is less as compared to minimize the volume velocity.
Global vibrational behaviour of a single degree-of-freedom (SDOF) oscillator subjected to Coulomb type of dry frictional constraint and harmonic excitation is investigated in this paper. To obtain a numerical solution to the non-smooth dynamical problem, the equation of motion is discretized in the time domain by means of the implicit Bozzak-Newmark scheme. An algebraic equation governing the current state of the system is obtained in terms of its velocity. Utilizing the fact that the frictional constraint can be completely characterized by two scenarios - (i) forward sliding or stiction with a tendency to move forward, and (ii) backward sliding or stiction with a tendency to move backward, two coupled linear complementary equations are deduced. With the reduction of the non-smooth dynamical problem to a linear complementarity problem (LCP) in terms of supremum velocities and slack forces, the rapid and endless switches from sliding to stiction, and vice versa, in a vibration problem, are automatically detected and handled effectively. This is superior to the event-based methods and analytical methods available in the literature. Numerical results obtained using the proposed method are compared with the analytical solutions for harmonically excited dry-friction oscillator with ordinary behaviour; excellent agreement is observed. The proposed method is then employed for determining the global chaotic and deterministic behaviour of a harmonically excited dry-friction oscillator with system and excitation parameters varying in wide ranges.
Since the local stiffness or damping variation happens when damage occurs in engineer structures, it is useful to detect the local variation as a way for structural damage inspection. As a vibration based approach, transmissibility has attracted considerable interest because of its convenience and effectiveness in damage detection. However, using the traditional Fourier transform, it should be very careful to select the frequency bands in transmissibility calculation. Inappropriate choice of frequency band could cause a complete inaccurate result. For unknown damage detection, it is difficult to select the frequency band which eigen-frequency should be included. This paper proposes a novel method using wavelet based transmissibility for local variation detection. Benefiting from the ability in subtle information acquisition of wavelet transform, it is useful in reducing the influence of frequency bands to the indicators. Analytical derivation using wavelet balance method and numerical studies of a multiple degree of freedom (MDOF) system are carried out to verify the effectiveness of the proposed method. In the last section, the method is applied for detecting crack position in cantilever beam with analysis of its sensitivity to frequency bands and measurement inaccuracies.
A new electro-hydraulic vibrator with rotary valve and the vibration wave influence caused by different structures of the rotary valve are presented. By establishing flow open area models of different valve cores, the models are analyzed using Matlab/simulink and structure characteristics are studied. Then, the relationship between the vibrator and the valve core is established, taking into account the effect of orifice pressure drop. Numerical analysis and experimental verification of waveform are carried out. The results show that the rectangular zero valve can obtain linear flow gain and the zero flow gain is comparatively big. In view of meeting higher flow, pressure and linear flow control requirements, windows in the sleeve and grooves in the spool can be designed to be rectangular with an according annular recess.
A technique aimed at neutralizing the presence of free-play effects in a control surface actuation chain is presented. It is based on an adaptive inversion of a function approximating such a nonlinearity. A simple, yet robust, on-line adaptive algorithm is proposed to identify the free-play parameters, i.e. free-play width, the equivalent control stiffness and friction. The procedure is then coupled to an immersion and invariance control law to drastically reduce possible residual closed-loop limit cycle oscillations due to the free-play nonlinearity. Within such a framework, the so chosen compensation technique can be interpreted as a control augmentation, easily extendable to multiple control surfaces. The methodology is then verified on a four-degree-of-freedom airfoil in a transonic regime, characterized by highly nonlinear unsteady aerodynamic loads, producing significant shock motions and large limit cycles, at a relatively high frequency. The presence of both aerodynamic and structural nonlinearities makes such a system bistable, leading to complex responses dependent on the initial conditions and the input used to excite the system. The effective suppression of these auto-induced vibrations becomes even more challenging because the limit cycle oscillations generated by different sources are characterized by differing amplitudes and frequencies.
Rolling bearings as vital components are present ubiquitously in manufacturing machines and systems, timely fault diagnosis is of great importance in avoiding serious catastrophe, and a variety of methods have been developed to detect faults of rolling bearings. In this study, we introduce labels to adjust the distance of classes and propose a method called supervised kernel entropy component analysis for fault diagnosis of rolling bearings. The method is developed based on kernel entropy component analysis which attempts to preserve the Renyi entropy of the data set after dimension reduction and presents a good performance for nonlinear feature extraction. Simulation and experiments are carried out to verify the method. The intrinsic geometric features derived from original vibration signals are extracted, and then classified by support vector machine. The results prove the feasibility and effectivity of the supervised kernel entropy component analysis in comparison with other similar methods, demonstrating its potentiality for fault diagnosis of rolling bearings.
The aim of the study is to maintain the desired period-1 rotation of the parametric pendulum over a wide range of the excitation parameters. Here the Time-Delayed Feedback control method is employed to suppress those bifurcations, which lead to loss of stability of the desired rotational motion. First, the nonlinear dynamic analysis is carried out numerically for the system without control. Specifically, bifurcation diagrams and basins of attractions are computed showing co-existence of oscillatory and rotary attractors. Then numerical bifurcation diagrams are experimentally validated for a typical set of the system parameters giving undesired bifurcations. Finally, the control has been implemented and investigated both numerically and experimentally showing a good qualitative agreement.
This paper considers a vibration control problem for a multi-span beam under moving masses by using boundary control method. The vibration of the multi-span beam under active control is governed by both a partial differential equation (PDE) and several ordinary differential equations (ODEs) which are derived from Hamilton’s principle. In order to suppress its vibration, boundary control strategy is proposed based on Lyapunov’s direct method. The closed-loop system stability of the multi-span beam with the proposed boundary control is proved. It can avoid spill-over effects which may occur in those popular methods that discretise the system model through modal expansion, as it directly acts on the PDE-ODEs of the system model in control design. Moreover, the sensors and actuators in the proposed boundary control strategy can be easily placed, as they are installed at the boundary of the system. The external excitations applied in simulation are a rectangular impulse, a moving mass and two moving masses, respectively. Numerical results demonstrate the effectiveness of the proposed method and good control performance in suppressing vibration of moving mass problems. This investigation has wide applications in engineering, notably, train-bridge dynamic interaction in high-speed railways.
In this paper, the effect of damage on the effective dynamic Young's and shear moduli of a viscoelastic adhesive is investigated, in both linear and nonlinear regions of adhesive behavior. The investigation method is based on the measurement of the nonlinear Frequency Response Function (FRF) of adhesive bonded structure and inverse eigen sensitivity identification technique. Several single-lap joint specimens are manufactured in healthy and damaged configurations and their linear and nonlinear FRFs are then measured, using the Optimum Equivalent Linear FRF (OELF) concept. The measured FRFs are then used to extract linear and nonlinear bending and shear modes of the bonded structure. The modes of healthy and damaged structures are further used for identifying of Young's and shear moduli at different frequencies. The results show that, for both linear and nonlinear regions, damages as small as 5% in the adhesive joint can be detected by the proposed technique, through their effects on the identified effective mechanical properties.
In this work, a model that accounts for the extensional, chordwise, flapwise and torsional vibrations of a flexible rotating blade was developed. The model also takes into consideration the offset between the elastic and inertial axes of the blade. In order to account for the centrifugal stiffening effect, expression for the strain energy was obtained based on an ordering scheme that retains terms up to 2nd order. Hence, a set of four nonlinear coupled partial differential equations governing the deformations of the blade was derived. The linearized equations were non-dimensionalized and then spatially discretized by the FEM (Finite Element Method). State space techniques were used to obtain the blade's natural modes and response to initial excitation. Effect of the mass and shear center offset on the coupling between the modes and veering regions at different rotor speeds were investigated.
According to the actual working condition of the gear, the supporting gear shaft is treated as an elastic support. Its impact on the gear body vibration is considered and investigated and the dynamic response of elastic teeth and gear body is analyzed. On this basis, the gear body is considered as a three-dimensional elastic disc and the gear teeth are treated as an elastic cantilever beam. Under the conditions of the elastic boundary (support shaft), combining to the elastic disk and elastic teeth, the influence of three-dimensional elastic discs on the meshing tooth response under an elastic boundary condition is also included. A dynamic model of the gear support system and calculated model of the gear tooth response are then established. The inherent characteristics of the gear support system and dynamics response of the meshing tooth are presented and simulated. It was shown by the results that it is correct to use the elastic support condition to analyze the gear support system. Based on the above three-dimensional elastic dynamics analysis, this paper set up a dynamics coupling model of a cracked gear structure support system that considered the influence of a three-dimensional elastic disc on a cracked meshing tooth under elastic conditions. It discusses the dynamic characteristic of the cracked gear structure system and coupling dynamic response of the meshing tooth, offering a three-dimensional elastic body model of the tooth root crack and pitch circle crack with different sizes, conducting the three-dimensional elastic dynamic analysis to the faulty crack. ANSYS was employed to carry out dynamic responses, as well as to simulate the acoustic field radiation orientation of a three-dimensional elastic crack body at the tooth root crack and pitch circle with different sizes.
The governing equations of motion, together with the associated boundary conditions, are derived for the second strain gradient Timoshenko micro- and nano-beams. The second strain gradient theory is a highly powerful nonclassical continuum theory, capable of capturing the size effects in micro- and nano-scale structures. In case studies, the static and free-vibration behaviors of a hinged–hinged beam are investigated utilizing the presented second strain gradient theory-based Timoshenko beam model. The obtained results are compared with those of the available models in the literature, which are based on the (first) strain gradient theory, the modified couple stress theory, and the classical continuum theory.
This paper describes a novel manoeuvre planning method to attenuate disturbances acting on occupants of autonomous cars as a result of driving behaviour. New research findings suggested that the passengers in autonomous cars might be more prone to motion sickness and thus overall discomfort. The proposed approach is based on a recently developed novel continuous B-spline path smoothing algorithm for car-like steered robots. Two algorithms are designed for urban driving scenarios and steering between two predefined poses. The resulting paths avoid abrupt changes in steering and longitudinal velocity, by maintaining curvature and its high order continuity. We show that this lead to reduced high frequency disturbances in steering and resulting load disturbances on passengers. The presented novel B-spline manoeuvres outperform other planning methods by reducing lateral acceleration and yaw disturbances. New approach was verified by rigorous simulations, numerical and field experimentation. Tests were repeated for a number of different paths and velocities. The reported results are the first spline based parameterisation methods practically applied for autonomous cars planning and re-planning, then validated using both noisy actuation simulations and field experiments.
Rotating shafts are prone to vibration and it is necessary to mitigate these vibrations to ensure proper operation of the machine. Such mitigation can be performed by active control. Among the available control strategies, one can apply the methodology proposed by Udwadia and Kalaba for trajectory control of nonlinear systems. In this work, such methodology is analyzed for controlling the lateral vibrations of a rotating shaft. First, this control technique is evaluated by placing the sensor–actuator pair in the point of interest for control (disc position of the shaft). Results show that the kinematic constraints applied by the control strategy are exactly tracked and lateral vibration of the shaft is significantly reduced. Second, the control technique is evaluated by placing the sensor–actuator pair at the bearing position of the shaft, thus far from the point of interest for control (disc position). In this case, vibration is reduced at the point of actuation, but not at the point of interest for control. However, the application of the methodology in an on/off strategy resulted in a successful reduction of the lateral vibrations of the shaft at the point of interest for control when crossing the first critical speeds.
This paper proposes part by part usage of Timoshenko and Euler–Bernoulli beam theories for obtaining natural frequencies of the non-uniform beam that has partially thick and thin beam vibration characteristics. The paper also presents convergence tests to determine proper function among the simple admissible shape functions taken into consideration. By doing so, closer approximation of the Rayleigh–Ritz method is achieved. The method is applied using a simple computation technique. In the analyses of the Timoshenko beams, an additional function is employed to identify shear deformation and rotational inertia effects. Modified angular displacement functions are defined to improve convergence capability of the method. Furthermore, optimal numbers of lateral and angular displacement terms are investigated for suggested function couple of the Timoshenko beams. Efficiencies of part by part modelling and advantages of novel approaches suggested for the Rayleigh–Ritz approximation are introduced by the comparative studies performed on tapered, stepped and continuously segmented beams under some classical end conditions. All of the computational outcomes for the beams with rectangular cross-section are validated by the results given in current literature and also those obtained by the finite element analyses.
Analysis and numerical results for the axisymmetric vibrations of two-directional functionally graded circular plates under the action of an in-plane force have been presented on the basis of classical theory of plates. The mechanical properties of the plate material are assumed to vary in both radial and transverse directions. Generalized differential quadrature method has been employed to obtain the frequency equations from the differential equation governing the motion of such simply supported and clamped plates. The lowest three roots of these frequency equations have been reported as the first three modes of vibration. The effect of volume fraction index, in-plane force parameter, heterogeneity parameter and density parameter has been studied on the natural frequencies of vibration. By allowing the frequencies to approach zero, the critical buckling loads for both the plates have been computed. Three-dimensional (3D) mode shapes for specified plate have been plotted. A comparison of results has been presented.
Particle damping is one of the promising damping techniques in effectively suppressing chatter in boring process. In earlier studies, granular particles are packed with the single particle type used to suppress chatter. This paper attempts at a novel hybrid approach in particle damping to increase the effectiveness of chatter suppression and enhance the machining stability. In this hybrid approach, Copper and Zinc particles are used together in equal proportion for packing inside the boring bar. The study finds this combined packing significantly improves the damping characteristic compared to the unmodified boring bar and also bar packed with single (Cu or Zn) particle type. The assessment benchmarks were the dynamic characteristics, modal analysis, damping ratio, logarithmic decrement and resonance gap of the machining system, as well as the displacement amplitude of the boring bar and the surface roughness of the work piece. The displacement amplitude of the boring bar and the surface roughness of the work piece in the combined packing case are reduced by 55% and 80% respectively when it is compared to the unmodified case.
Squeeze film dampers are widely used to reduce the vibration of rotating systems. Using magnetorheological fluid in these dampers can lead to a variable-damping damper called Magnetorheological Squeeze Film Damper (MRSFD). Magnetorheological fluid viscosity alter under different values of magnetic field. The previous research have widely used long bearing approximation to derive the equations governing the hydrodynamic behavior of MRSFDs. In this paper, the behavior of MRSFDs has been studied using short bearing approximation. Next, the effects of MRSFDs on the dynamic behavior of a flexible rotor have been studied, using finite element method (FEM). Synchronous whirl motion has not been imposed on the system behavior, as an external assumption. Damper pressure distribution and forces, dynamic trajectories, eccentricity and the frequency response of the rotor are tools used to analyze the dynamic behavior of MRSFDs and rotor system. As the results show, it seems to be more precise to use short bearing approximation to analyze dampers with aspect ratios lower than a limit (especially L/D < 1). Furthermore, by controlling electrical current one can control the dynamic behavior of a rotor, to avoid failure and damage. Finally, the whirl motion of the rotor was observed to remain synchronous, even when fluid forces are present.
This paper studies the optimal control of vibration of a beam excited by a moving mass. One important background of this work is vehicle-bridge interaction. As this is a time-varying system, some methods suitable for time-invariant systems are not always effective and will lead to suboptimal solutions when applied. In this particular vibration problem, the terminal time instant when the moving mass leaves the beam and the moving mass as the source of excitation are known. This particularity allows this problem to be expressed in a very simple way as a fixed terminal-time optimal control problem. In this paper the limitations of the practical implementation of the control solution are discussed in relation to different performance indices and actuation strategies. Numerical results obtained by using several control methods (time-invariant, time-variant with or without bounds on the control force) are analyzed and compared. It is shown that for particular actuator locations the use of time-varying control strategy instead of a time invariant strategy is necessary. The approach of formulating the system equation in an augmented form put forward in this paper is shown to yield accurate results at lower cost than the conventional time-dependent Riccati equation method. This approach is expected to be applicable to optimal control of vibration of other more complicated time-variant systems.
The two main sources of internal friction in a rotor-shaft system are the shaft structural hysteresis and the possible shrink-fit release of the assembly. The internal friction tends to destabilize the over-critical rotor running, but a remedy against this effect may be provided by a proper combination of some external damping in the supports and an anisotropic arrangement of the support stiffness, or at most by the support damping alone, depending on the system geometry. The present analysis reported here considers a general asymmetric rotor-shaft system, where the rotor is perfectly rigid and is constrained by viscous–flexible supports having different stiffnesses on two orthogonal planes. The internal friction is modelled by nonlinear Coulombian forces, which counteract the translational motion of the rotor relative to a frame rotating with the shaft ends. The nonlinear equations of motion are dealt with using an averaging approach based on the Krylov-Bogoliubov method with some adaptation to address the multi-degree-of-freedom nature of the problem. Stable limit cycles may be attained by the overcritical whirling motions, whose amplitudes are inversely proportional to the external dissipation applied by the supports. A noteworthy result is that the stiffness anisotropy of the supports is recognized as beneficial in reducing the natural whirl amplitudes, albeit mainly in the symmetric configuration of the rotor at the mid span and, to a rather lesser extent, in the asymmetric configuration, which then requires a stronger damping action in the supports.
Active magnetic bearing systems (AMBs) have many potential industrial applications where extremely fast and accurate operations are required. However, AMBs are often subject to disturbances in the form of synchronous vibrations due to unmodeled dynamics such as the rotor mass-imbalance and centrifugal forces while the rotor is in rotation. Several methods such as variable notch filters, gain scheduling controllers, and linear parameter varying controllers have been proposed recently to reject the disturbances while the system is operating at high rotational speeds. These methods are practical only if the frequencies of these sinusoidal-like disturbances are directly measurable or accurately known in advance. In this paper, a hybrid control scheme comprised of a feedback H controller and an inner-loop disturbance observer-based control is proposed. The effectiveness of this control scheme is verified by simulation and real-time experiments on an AMB system. Both constant and sinusoidal disturbances are taken into consideration while the rotor is stationary as well as while it is rotating at different speeds. The results demonstrate that the proposed hybrid control scheme exhibits significantly improved performance in comparison to single-loop controllers in the presence of unknown but bounded disturbances.
This paper targets the frequency domain identification of current structural modal properties under earthquake excitation. A new refined Frequency Domain Decomposition (rFDD) algorithm is implemented towards the output-only modal dynamic identification of heavy-damped frame structures, which are subjected to a wide set of strong ground motions. In fact, both seismic excitation and/or high damping values shall not fulfil traditional FDD assumptions. Despite that, with the present rFDD implementation quite limited errors in the modal parameter estimates have been achieved, including for the modal damping ratios (ranging from 1% to 10%). At first, the identification technique is formulated and explored analytically, by proving its potential effectiveness with seismic response input. Then, all strong motion modal parameters are consistently identified. As a fundamental necessary condition, synthetic response signals are adopted. These have been generated prior to dynamic identification from computed numerical seismic responses of a set of shear-type frames. The efficiency of the present original implementation is highlighted, by proving that consistent rFDD modal dynamic identification of structures at seismic input and simultaneous heavy damping looks feasible. Thus, the paper delivers a robust method for inspecting current structural modal properties of frame buildings under earthquake excitation and for observing their possible variation along experienced seismic histories.
The nonlinear free vibration behaviour of laminated composite single/doubly curved shell panel embedded with the piezoelectric layer is investigated numerically in this article. For the analysis purpose, a general nonlinear mathematical model has been developed using higher-order shear deformation theory and Green-Lagrange nonlinearity including the quadratic variation of the electric potential across the thickness due to the piezoelectric layer. In order to capture the exact flexure of the shear deformable panel, all the nonlinear higher order terms are included in the present model. The nonlinear governing equation of free vibrated shell panel is derived using Hamilton’s principle and discretised through suitable finite element steps. The desired nonlinear responses are computed numerically using the direct iterative method. The developed nonlinear numerical model has been validated by comparing the responses with that to available published literature. Finally, the efficacy and applicability of the present nonlinear model has been checked by solving few numerical examples for different geometrical parameters (stacking sequence, thickness ratio, aspect ratio, curvature ratio, different support constraints and amplitude ratio) and number of piezo layers and discussed in details.
To protect the engineering structures from natural hazards, especially for large-scale structures, a novel fast model predictive control (NFMPC) method is presented in this paper. Based on the second-order dynamic equation, a novel explicit expression form of Newmark-β method is first derived, from which the future states can be easily predicted without computing matrix exponential. By applying this explicit expression form into the standard model predictive control (MPC) method, the NFMPC method is developed. Based on the explicit expression form, the optimal control input can be computed by two off-line transient analyses and one on-line transient analysis at every sampling instant on the structure. For no computation of matrix exponential, the off-line computation efficiency of NFMPC is several orders of magnitude higher than that of MPC. And the small amount of on-line computation guarantees the on-line computation efficiency. Furthermore, the use of the Newmark-β method also guarantees the computation accuracy. At last, several typical numerical examples are carried out to verify the validity and high efficiency of NFMPC by the comparison with MPC.
This paper presents a theoretical analysis of free vibration and forced vibration of nanowires with surface effects. Using the Timoshenko beam theory incorporated with the surface effects, exact frequency equations are derived for various end supports. Natural frequencies and mode shapes are determined for simply supported, clamped-clamped, and clamped-free ends. Forced vibration of nanowires is also treated by superposing vibration modes of free vibration. An inverse problem is further investigated to determine the size-dependent effective Young's modulus of nanowires. Obtained results for a nanowire with residual stress and surface elasticity are confirmed by comparing them with the results using the finite element method. Theoretical natural frequencies and finite element method simulation have good agreement with the results from experimental data and molecular dynamics simulation. The effect of surface stress on forced vibration is analyzed. Residual surface tension has a more significant influence on the frequencies and a somewhat effect on the mode shapes.
A novel loading control system is proposed to accurately simulate the five-degree-of-freedom loads experienced by a real wind turbine. For this system, the real wind rotor and blades are replaced by an equivalent rotating disc and driven by an electric motor. A set of loading actuators are uniformly placed around this disc and are regulated to accurately create these turbine loads. In this paper, the five-degree-of-freedom turbine loads are defined in blade and hub reference frames. A load-decomposition based loading control strategy is presented to decompose such loads into reference loading forces for each actuator. An axial loading actuator is used for system modeling and analysis. Experimental results have validated that the proposed loading system and control strategy can accurately simulate the representative turbine loads with a good confidence level.
In this study, a two-link manipulator with flexible members is considered. The end point vibration signals are simulated by developing a MatLAB code based on the finite element theory and Newmark solution. Experimental results are also presented and compared with simulation results. The mass and stiffness matrices are time dependent because the angular positions of the links change during the motion. Trapezoidal velocity profiles for the actuating motors are used. The time dependent inertia forces are calculated by using the rigid body dynamics. The inertia forces are due to the motors, end point payload mass and distributed masses of the links. The acceleration, constant velocity and deceleration time intervals of the trapezoidal velocity profile are selected by considering the lowest natural frequency of the manipulator structure at the stopping position. Various starting and stopping positions are considered. The root mean square (RMS) acceleration values of the vibration signals after stopping are calculated. It is observed that the residual vibration is sensitive to the deceleration time. The RMS values are lowest if the inverse of the deceleration time equals to the first natural frequency. It is highest if the inverse of the deceleration time equals to the half of the first natural frequency. It is observed that simulation and experimental results are in good agreement.
In this paper, the bending waves propagating along the edge of a semi-infinite Kirchhoff plate resting on a two-parameter Pasternak elastic foundation are studied. Two geometries of the foundation are considered: either it is infinite or it is semi-infinite with the edges of the plate and of the foundation coinciding. Dispersion relations along with phase and group velocity expressions are obtained. It is shown that the semi-infinite foundation setup exhibits a cut-off frequency which is the same as for a Winkler foundation. The phase velocity possesses a minimum which corresponds to the critical velocity of a moving load. The infinite foundation exhibits a cut-off frequency which depends on its relative stiffness and occurs at a nonzero wavenumber, which is in fact hardly observed in elastodynamics. As a result, the associated phase velocity minimum is admissible only up to a limiting value of the stiffness. In the case of a foundation with small stiffness, asymptotic expansions are derived and beam-like one-dimensional equivalent models are deduced accordingly. It is demonstrated that for the infinite foundation the related nonclassical beam-like model comprises a pseudo-differential operator.
The fault diagnosis of electrical machines is significant to reduce the costs of maintenance through early detection of faults, which could be expensive to service. The idea of the research is that the advanced signal processing techniques called wavelet transform is exercised to haul out the faults from the vibration and current signal and a spectral component is being received to diagnose the condition of the machine. The existing system used wavelet transforms for the analysis of the stator faults and rotor faults are taken as a case study to prove the wavelet techniques for fault diagnosis. The proposed investigation of vibration analysis for the induction machines is done through frequency pattern using the decomposition of wavelet packet. The wavelet coefficients for the vibration have been extracted over a wide range of signals and the analysis could be percolated on the frequency domain through HAAR wavelet. In this paper, healthy and unhealthy motor with two broken ball bearings are used to estimate the vibration and current spectrum. Experimentally observed vibration and current signals are transformed into power spectral density through approximate and detailed coefficients with the help of MATLAB tools and the steady state rotor frequency was used to introduce a new frequency pattern for fault diagnosis.
In this study, the problem of vibration control of structures involving parameter uncertainties and actuator saturation using hedge-algebras-based fuzzy controller (HAC) is presented. When structural damping and stiffness cannot always be measured easily and precisely, their uncertainties are assumed to be norm-bounded. The proposed controller is designed based on hedge algebras theory, where inherent order relationships between linguistic values of each linguistic variable, determined by isomorphisms mapping called semantically quantifying mapping based on few fuzziness parameters of each linguistic variable instead of using any fuzzy sets, are always ensured. The performance of the proposed controller is investigated by numerical simulations on active control of a benchmark three-storey building structure with active bracing system subjected to excitation of typical earthquakes. A conventional fuzzy controller, designed based on parameters similar to those of HAC, is also considered for the purpose of comparing effectiveness between controllers in order to shown advantages of the proposed method.
In this paper, we consider the problem of modal-space control for the hydraulically driven fully parallel mechanism with actuation redundancy. Firstly, the mechanical-hydraulic interaction system is transformed into modal-space model. Then, independent modal decoupled systems for the redundant mechanism are obtained. According to the eigenvalue frequency characteristics, two types of modal systems – zero eigenvalue modal systems and nonzero ones – naturally result and these systems can be treated separately. For the nonzero eigenvalue modal systems, it is convenient to employ dynamic pressure feedback control to regulate damping. For the zero eigenvalue modal systems, we give a proof to show that they just lie in the null space of the Jacobian of the mechanism, then it is more appropriate to implement force control for this type of modal system. Some simulation results further explain the proposed modal-space control method.
During the process of deep rock mass excavations by drill and blast, transient release of in-situ stress (TRIS) induced vibrations have a negative effect on the safety and stability of nearby structures. However, little attention has been focused on the prediction of peak particle velocity (PPV) of TRIS induced vibrations. To forecast the PPV of TRIS induced vibrations, a new model was set up by dimensional analysis method based on an analysis of PPV influencing factors. To train and test the prediction model proposed in this paper, firstly, TRIS induced vibrations were identified and separated from the recorded vibrations during a blasting excavation of deep rock masses in the Jinping II hydropower station by the methods of amplitude spectrum analysis and finite impulse response digital filter, and then, unknown coefficients in the proposed model were calculated via multivariate regression analysis from the collected data of upper part excavation. Finally, for the lower part excavation, the separated and predicted PPV of TRIS induced vibrations were compared. In addition, the correlation coefficient and root mean square error (RMSE) were compared between the proposed model and the other commonly used model. Results seem to indicate that the proposed model with a higher correlation coefficient and a smaller RMSE is the better option for predicting the PPV of TRIS induced vibrations.
The vibration signals of hydropower units are nonstationary when serious vortex occurs in the draft tube of the hydraulic turbine. The traditional signal analysis method based on Fourier transform is not suitable for the nonstationary signals. In the face of the nonstationarity of such signals and the limitation of the empirical mode decomposition method, a new nonstationary and nonlinear signal analyzing method based on variational mode decomposition (VMD) is introduced into hydropower unit vibration signals analysis. Firstly, VMD is used to decompose the signal into an ensemble of band-limited intrinsic mode functions components. Then, frequency spectrum analysis of these components is conducted to obtain the characteristic frequencies of the signal caused by the serious vortex of hydraulic turbine. Analysis of real test data shows that this proposed method can effectively suppress mode mixing. It can realize accurate analysis of nonstationary vibration signals. This provides a new way for analyzing hydropower unit vibration signals.
Slurry pumps are widely used to transport abrasive slurry that contains oil and sands. Because of the abrasive nature, the impellers inside the pumps wear easily. Severe impeller wear may cause unexpected pump failure that leads to substantial oil production loss. To assess the impeller performance degradation and then estimate its remaining useful life (RUL), an efficient prognostic method has been designed. For assessing the impeller performance degradation, statistical features were extracted from vibration signals collected from on-site operating slurry pumps. Their corresponding frequency spectra were generated after the vibration signals were processed by a low-pass filter. Here, the low-pass filter aims to retain impeller-related vibration components, such as the pump vane-passing frequency and its harmonics. Principal component analysis was then applied to reduce the dimensionality of the extracted statistical features to one dimensionality, which was used to construct a health indicator to reflect the health evolution of the impeller over time. For estimating the impeller's RUL, a nonlinear state space model was designed to track its temporal health indicator. An efficient unscented transform method was employed to iteratively estimate the joint posterior probability density function of the parameters of the nonlinear state space model. After the proper nonlinear state space model had been determined, extrapolations of the nonlinear state space model to a specified alert threshold were used to estimate the impeller's RUL. Vibration signals captured from on-site operating slurry pumps were used to verify the effectiveness of the proposed prognostic method. The results show that prediction accuracy of the estimated RULs have been improved as compared to those generated by other recently developed slurry pump prognostic methods. Moreover, the more the temporal vibration data is available, the better the performance of the state space model; hence, the higher the accuracy in predicting the impeller's RUL.
In this paper, a novel formulation for modeling the vibration of spatial flexible mechanisms and robots is introduced. The formulation is based on the concepts of equivalent rigid-link system (ERLS) that allows kinematic equations of motion for the ERLS decoupled from the compatibility equations of the displacement at the joint to be written. With respect to the available literature, in which the ERLS concept has been proposed together with a finite element method (FEM) approach (ERLS-FEM), the formulation is extended in this paper through a modal approach and, in particular, a component mode synthesis technique which allows a reduced-order system of dynamic equations to be maintained even when a fine discretization is needed. The model is validated numerically by comparing it with the results obtained from the Adams-Flex™ software, which implements the well-known floating frame of reference approach for a benchmark L-shaped mechanism. A good agreement between the two models is shown.
The application of smart control technology to both aging and new infrastructure is essential to extending service life, increasing life safety, and decreasing repair and replacement costs. One area of control technology research for civil engineering structures that has received little attention historically is that of high-impact loads, such as collision events. The dissipation of impact energy using smart control devices, such as magnetorheological (MR) dampers, leads to less plastic deformation and damage, and a lower likelihood of collapse in civil engineering structures. Due to the short duration and high variability in magnitude of potential impact loads, the issue of sub-optimal controller performance arises. In order to boost controller performance and improve the effectiveness of the control system, a radar-based impact load identifier is proposed. This radar-based impact load identifier will be used to estimate impact loads from imminent impacting objects, for example vessels and trucks, thus providing input information to the control system before the impact actually occurs. This paper presents the characterization and validation, through laboratory tests, of one part of the radar-based impact load identifier, the range and velocity estimation of the incoming moving objects. The range and velocity information are then used to direct structural control based on laboratory impact tests. An ultrawideband monostatic pulsed radar is used for range and velocity measurements of a laboratory-scale impacting vehicle. The range and velocity measurements obtained from the radar scans are verified using physical measurements and control testing. The tests showed great accuracy for both range and velocity with less than 3% error for each measurement and demonstrated structural control based on these measurements. It is shown from control system testing that the proposed approach is effective in reducing the structural impact responses by 11–30%, depending on the performance index, for pre-impact structural stiffening with passive control of MR dampers.
The forced vibration of the system consisting of a pre-stressed elastic plate, barotropic compressible Newtonian viscous fluid and rigid wall is considered. The space between the plate and rigid wall is filled by the fluid. It is assumed that the forced vibration is caused by the lineally-located time-harmonic force acting on the free face plane of the plate. The motion of the plate is written by utilizing the exact equations of elastodynamics, but the motion of the compressible viscous fluid is described by the linearized Navier-Stokes equations. Moreover, it is assumed that the velocities and stresses of the constituents are continuous on the contact plane between the plate and fluid, and that the impermeability conditions on the rigid wall are satisfied. The dimensionless parameters which characterize the compressibility and viscosity of the fluid as well as the elasticity constants of the plate are introduced. Plane strain state in the plate and two-dimensional plane flow of the fluid are considered. Numerical results on the interface normal stress and velocities are presented. The influence of the problem parameters is also discussed, including the fluid viscosity and compressibility, thickness of the plate and fluid depth as well as the excitation frequency. In this discussion the focus is on the influence of the fluid depth on the studied quantities. This is the parameter through which the main difference arises between the present and previous works by the authors.
Transverse vibration of viscoelastic Timoshenko beam-columns is investigated. The normal and the shear stress-strains are constituted by the Kelvin model with different viscosity parameters. The governing equations and the boundary conditions are derived from the generalized Hamilton principle. The exact frequency equations and the modal functions are proposed. The orthogonality conditions are established in the state space. The transverse response to arbitrary external excitation and initial conditions is determined via decoupling the governing equations based on the orthogonality. The natural frequencies and the decrement coefficients of various beam and beam-column models are numerically contrasted. The effects of the length-to-depth ratio, the axial tension, and the viscosity coefficients on the natural frequencies and the decrement coefficients are numerically demonstrated.
Due to the limitation of the machining accuracy, there exist mass imbalance and sensor runout in magnetically suspended rotor system, which will result in harmonic current in the rotor system. Harmonic current can not only increase the power consumption but also induce harmonic vibration which will be transmitted to spacecraft by magnetic bearings and affect the attitude stability of spacecraft. In order to analyze and reduce harmonic current, the model of magnetically suspended rotor system is built and analyzed. Variable-step-size FBLMS algorithm is proposed in this paper to suppress harmonic current simultaneously. According to the proposed algorithm, step size variation depending on harmonic current and individual step size is figured out for each weight vector so that each frequency component in the block can be adjusted. As a result, convergence performances are further improved by adjusting the weight vectors adaptively. The validity of the proposed method is testified by simulation. Simulation results show that variable-step-size FBLMS algorithm can reduce the harmonic current further and increase the convergence rate.
In this paper the problem of the response evaluation of nonlinear systems under multiplicative impulsive input is treated. Such systems exhibit a jump at each impulse occurrence, whose value cannot be predicted through the classical differential calculus. In this context here the correct jump evaluation of nonlinear systems is obtained in closed form for two general classes of nonlinear multiplicative functions. Analysis has been performed to show the different typical behaviors of the response, which in some cases could diverge or converge to zero instantaneously, depending on the amplitude of the Dirac's delta.
Theoretical analysis is conducted to investigate the nonlinear vibration response in a double-helical gear set under the influence of staggering, single pitch error and cumulative pitch error. A dynamic model of the double-helical gear set is established considering the axial deflection of shaft and gyroscopic effect, and the natural frequencies, mode shapes and critical speeds for the gear set with axial degree and gyroscopic effect are calculated. Moreover, several cases are numerically simulated after consideration of time varying mesh stiffness and gear backlash, and then some general results are deduced about the influences of staggering, single pitch error and cumulative pitch error on vibration intensity and gear teeth impact. Although the pitch error is modeled as a lower frequency excitation, high natural frequencies and modes are excited, especially when the double-helical gear pair operates under high speed condition. Comparisons are listed which are useful for understanding the high speed performance of a high speed gear set.
This paper investigates the nonlinear vibration and stability analysis of a doubly clamped piezoelectric nanobeam, as a nano resonator actuated by a combined alternating current and direct current loadings, including surface effects and intermolecular van der Waals forces. The governing equation of motion is obtained using the extended Hamilton principle. The multiple scales method is used to solve nonlinear equations of motion. The influence of van der Waals forces, piezoelectric voltages and surface effects are investigated on the static equilibria, pull-in voltages and dynamic primary resonances of the nano resonator. It is shown that for accurate and exact investigation of the system response, it is necessary to consider the surface effects. To validate the analytical results, numerical simulation is performed. It is seen that the perturbation results are in accordance with numerical results.
The present article deals with the vibration and damping analysis of functionally graded carbon nanotubes reinforced hybrid composite (FG-CNTRHC) shell structure which consists of conventional carbon fiber as reinforcing phase and single-walled carbon nanotubes based polymer as matrix phase. The Eshelby–Mori–Tanaka approach in conjunction with strength of material approach is implemented to obtain the material properties of FG-CNTRHC structures. The material properties of FG-CNTRHCs are assumed to be graded through the thickness direction according to power law distributions of the volume fraction of carbon fibers and fiber orientations. An eight node shell element considering transverse shear effect according to Mindlin’s hypothesis has been formulated for finite element modelling and analysis of such functionally graded hybrid composite shell structures. The formulation of shell midsurface in an arbitrary curvilinear coordinate system based on the tensorial notation also presented. The Rayleigh damping model has been implemented in order to study the effects of carbon nanotubes (CNTs) on damping capacity of such hybrid shell structures. Different types of spherical shell panels have been analyzed in order to study the time and frequency responses. The influences of CNTs, carbon fiber, geometry of the shell, power law index and material distributions on the vibration damping characteristics of FG-CNTRHC shell structures have also been presented and discussed. Various types of FG-CNTRHC shell structures (such as spherical, ellipsoidal, doubly curved and cylindrical) have been analyzed and discussed in order to comparative studies in terms of settling time, first resonant frequency and absolute amplitude corresponding to first resonant frequency and the effects of CNTs on vibrations responses of such shell structures are also presented.
This paper presents a novel design methodology for discrete-time internal model control (IMC) used to compute a disturbance filter. The proposed method employs a generalized algorithm for disturbance rejection and for process dynamics compensation. In IMC, the controller is designed based on a model of the process, while ensuring a desired closed loop performance trajectory (for setpoint tracking). However, in some situations, for example poorly damped systems, the open loop poles of the process affect the closed loop disturbance rejection dynamics. The novel design methodology presented is able to compensate both process dynamics and input disturbances. The method is validated both in simulations and in experimental tests on a poorly damped mass–spring–damper testbench.
Hilbert-Huang Transform (HHT) has been renowned for its capacity to reveal fault indicating information issue from vibration signals. It uses Empirical Mode Decomposition (EMD) to decompose a signal accordingly to its contained information into a set of Intrinsic Mode Functions (IMFs). Then, the instantaneous frequencies are performed of each IMF using Hilbert Transform (HT). However, the HHT has some disadvantages which are caused by the EMD technique. The EMD has the mode mixing problem that may occur between IMFs, it causes the End Effect phenomenon, which leads to a wrong instantaneous values at both sides of the signal. Furthermore, its lack of mathematical basis. To overcome the HHT inherent problems, we propose the use of the Empirical Wavelet Transform (EWT) which designs an appropriate wavelet filter bank fully depends on the processed signal with HT in the early detection and condition monitoring of tooth crack fault. In this paper, we develop a dynamic model describing a single stage spur gear in normal and abnormal functioning. Results of analyzing the pinion’s vibration displacement show that the proposed approach denoted (HEWT) successfully detect the tooth crack at a much earlier stage of damage development even though in noisy environment. Performance evaluation and comparison between HEWT and HHT methods show that the HEWT is better sensitive to tooth crack fault detection in gearbox systems.
Energy dissipating damping devices such as fluid viscous dampers (FVDs) often have applications in shock vibration control of structural and mechanical systems. Nonlinear FVDs are more suitable compared to the linear FVDs for applications where large force and velocities are exerted, such as in structures subjected to shock excitations. This paper discusses the influence of shock impulse characteristics on vibration control of a single-degree-of-freedom system with linear and nonlinear fluid viscous dampers for three types of shock excitation profile, viz. half-cycle sine, initial-peak saw tooth and rectangular. The following response parameters have been considered: (1) maximum acceleration of the structure, (2) maximum displacement of the structure, and (3) time required for attenuation of response below a specified threshold. An approximation based on the concept of equal energy dissipation to determine the response of the structure with nonlinear fluid viscous dampers subjected to shock excitation has been proposed. The paper also presents non-dimensional design charts for above shock pulses for linear and nonlinear fluid viscous dampers, which can be used for preliminary decision on damper parameters to be used in design.
The design of vibration controllers for flexible structures requires special attention due to the size of structural models, generally with a high number of degrees of freedom. The implementation of full order controllers for structures with high numbers of degrees of freedom often requires a high computational processing effort and advanced hardware. To avoid this, it is desirable to use reduced order controllers. The design of reduced order
To realize a vibration suppression of flexible structures like a membrane, our research focuses on introducing smart structures technology into the membrane structure. In this study, the membrane structure is composed of a vibration control system using a flexible Polyvinylidene fluoride (PVDF) film as an actuator. A non-contact vibration test system, which uses a high power Nd: YAG pulse laser for producing an ideal impulse excitation and laser Doppler vibrometers for measuring the response on the membrane, is employed to evaluate the vibration characteristics of the smart membrane structure. To confirm the effectiveness of the proposed method, using a flexible PVDF actuator installed on the membrane structure, control experiments with H control for reducing single mode and multiple modes vibration are conducted. In the results of the control experiments for single mode vibration suppression, a corresponding resonance peak is reduced by around 20 dB. In case of multiple modes vibration suppression, the first and second resonance peaks are reduced by 14 dB and 24 dB, respectively. This study demonstrates that the present control method using a flexible piezoelectric element and a non-contact vibration test system effectively suppress and evaluate the vibration responses of smart membrane structures.
The present paper attempts to study the propagation of torsional surface waves in a pre-stressed dry sandy layer sandwiched by a pre-stressed non-homogeneous semi-infinite medium and an anisotropic porous half-space under gravity. The non-homogeneity in the non-homogeneous layer is caused by the quadratic variation in rigidity, density and initial stress. The inhomogeneity has been assumed as hyperbolic variation in the dry sandy layer. The dispersion equation of motion has been derived under suitable boundary conditions in a close form, which shows the variation of phase velocity of the corresponding wave number. The velocities of torsional waves are calculated numerically as a function of kH and presented in a number of graphs where k is the wave number and H is the thickness of the sandy layer. The effect of inhomogeneity in the elastic modulus of rigidity, pre-stress, density, gravity and porosity depicted by means of graph, using MATLAB software. The study reveals that the torsional waves propagate in the pre-stress dry sandy layer sandwiched between the considered media. This work may be useful to understand the nature of seismic wave propagation during earthquakes.
Metamaterials have been the subject of significant interest over the past decade due to their ability to produce novel acoustic behaviour beyond that seen in naturally occurring media. As well as their potential in acoustic cloaks and lenses, of particular interest is the appearance of band gaps which lead to very high levels of attenuation across the material within narrow frequency ranges. Unlike traditional periodic materials which have been employed at high frequencies, the resonant elements within metamaterials allow band gaps to form within the long wavelength limit; at low frequencies where it is most difficult to design satisfactory passive isolation solutions. Hence, metamaterials may provide a path to high-performance isolation at low frequencies. Passively these band gaps occur over a narrow bandwidth, however the inclusion of active elements provide a method for enhancing this behaviour and producing attenuation over a broad band. A new type of active viscoelastic metamaterial is presented that achieves double negativity and could be employed as a high-performance vibration isolator at low frequencies. A mathematical method for manipulating the band gap profile is developed and a prototype is produced. The passive band gap is confirmed in the laboratory, and then by applying active control using optimised feedback filters it is shown that the region at which attenuation occurs around the band gap could be greatly enhanced whilst retaining the peak passive band gap performance. The active metamaterial demonstrates that a unified design philosophy matching the best features of active and passive functionality can achieve high levels of attenuation over wide frequency bands.
One important issue in the investigation of axially moving systems is the viscoelastic constitutive relation. In the present paper, the effects of viscosity on the natural frequency of transverse vibration of an axially moving viscoelastic beam are studied. The viscoelastic material of the moving Euler-Bernoulli beam obeys the Kelvin model. For the first time, the qualitative difference between the natural frequencies with the material time derivative and the partial time derivative in the constitutive relation is investigated. The method of multiple scales with three terms is directly applied to obtain the approximate analytical solutions of the natural frequency. An interesting phenomenon is found in this study. Specifically, for an axially moving viscoelastic beam constituted by the material time derivative, the natural frequencies of transverse vibration may increase with the axial speed. Furthermore, the validity of the analytical results is examined by comparing with two numerical approaches, the differential quadrature methods (DQM) via separating variables and DQM combined with the fast Fourier transforms. There is qualitative difference between the results based on the constitutive relations with the material time derivative and the partial time derivative. Therefore, the results of this work provide an possible approach to determine which kind of the constitutive relation should be adopted to describe the viscoelastic property of axially moving materials.
To realize a broadened band gap as a potential application of vibration control in the electric vehicle powertrain system requires, a novel configuration of locally resonant (LR) beam with multi-oscillators attached is proposed, in which two types of oscillators are periodically and alternately attached at identical intervals. An analytical model is proposed based on transfer matrix method, which is validated by a finite element simulation. The band gaps in flexural vibration generated by this novel structure are investigated by the analytical model. The band gap coupling effect is observed and the influence of the intervals and oscillator parameters are discussed. The novel configuration effectively enlarges the range of band gaps in flexural vibrations.
Inverted pendulum systems, because of highly nonlinear, coupled, and unstable dynamic behaviour, are excellent experimental platforms for testing new developed control algorithms. This study explores nonlinear modelling, simulation and sliding mode stabilizing control of a real rotary inverted pendulum in detail. For simulation purposes only, the system was modelled in a nonlinear state space form including the servomotor dynamics. In the light of the simulation results, a rotary inverted pendulum system was designed and manufactured. For a certain quality level of desired output, benefits of the sliding mode control of the system without using an equivalent control signal by selecting a proper smoothing function were shown. This model free approach can be used to satisfy a need especially for practical control applications in industry to a certain level, encouraging practical control engineers to use sliding mode control, who have no ability to model a system or no sufficient time for this, or encounter very complex nonlinear system models in many cases. Comparisons of the theoretical and experimental results demonstrate that the state equations describe the dynamics of the system satisfactorily, and that robust and accurate balancing of the pendulum can be achieved by using model free sliding mode control with sigmoid smoothing function.
Quasi-periodic vibrations in a delayed van der Pol oscillator with time-periodic delay amplitude is investigated in this paper. The case where the delay amplitude in the position is modulated with a certain amplitude and a resonant frequency is considered. Application of the double perturbation method enables approximation of the amplitudes of quasi-periodic vibrations of the oscillator near a parametric resonance for which the frequency of the delay amplitude modulation is near twice the natural frequency of the oscillator. Analytical approximations supported by numerical simulations provide the regions in parameter space where quasi-periodic vibrations exist. Results show that the modulation of the delay amplitude in the position not only gives birth to quasi-periodic vibrations in a large range of parameters, but also with broadband large-amplitude covering a wide range of excitation frequency.
A hybrid foil-magnetic bearing (HFMB) was successfully studied as a vibration isolator by introducing a sudden imbalance or an unexpected disturbance during turbine/rotor operation. This HFMB is used to achieve stability during transient vibration behavior. The HFMB consists of two oil-free bearing technologies: an active magnetic bearing (AMB) and air foil bearing (AFB). Using both technologies takes advantage of the strengths of each bearing while compensating for their inherent weaknesses. In addition, the HFMB has good dynamic characteristics, and the damping can be adjusted using the appropriate gain selection for the AMB controller. Based on these unique features, dynamic stability can be enhanced, even if a sudden imbalance occurs while the rotor is operating. In this study, a rigid rotor was operated at up to 12,000 rpm and tested using a control algorithm to reduce the sudden imbalance vibration amplitudes. The experiment was conducted under the situation that the mass dropped out at 6,000 rpm. In order to validate the stability performance of the HFMB with a sudden mass loss, the vibration response results for the AFB and HFMB were compared. When applying the HFMB, the asynchronous vibration was suppressed, and the 1x vibration results showed reductions of almost 30%. When the sudden mass loss occurred, the magnetic control force was remarkably effective at reducing the asynchronous vibration of the rotor supported by the HFMB. In conclusion, it was experimentally verified that using the HFMB made sudden imbalance vibration control possible during rotor operation with an air foil bearing. In this respect, the HFMB has the characteristics of high stiffness/damping, which prevent rubbing and suppress excessive vibration due to a sudden imbalance event.
This paper describes the dither control system used for suppressing drum brake squeal. The dither force is generated by a piezoceramic actuator installed on the back plate of a drum brake system and successfully quenches the drum brake squeal to background noise level above the critical dither actuation level. The dither is represented as a forcing function in sine waveform in a bi-axial two degrees of freedom mathematical model of drum brake squeal. The model parameters are based on the complex eigenvalue obtained from the mobility measurement and verified with the measured frequency response function. The numerical results show that dither control is more efficient at low sliding speed where lower dither force is needed to quench the brake squeal. Both measured and simulated results show that dither tends to excite the sidebands of the squeal peak with equal frequency spacing at both sides, and these sidebands shift closer to the squeal peak with increase in the dither actuation force.
In this study, the use of acoustic absorbent materials specifically felt to mitigate tire cavity resonance noise is presented. The inclusion of a trim in the tire cavity is represented by the addition of the acoustic damping loss factor into the sound pressure response function. In addition, the possible solution of using multilayer trim materials to mitigate the cavity mode effect is presented using the sound absorption coefficient values from the impedance tube experiments and by adopting other empirical models. Moreover, the sound absorption coefficient calculated from the method of electrical-analogy is compared with that from the experimental data and found to be reasonable. Experimental modal analysis was performed to show the effect of inserting an absorbent material (polyfelt) onto the inside surface of the tire where reduction in both the inside cavity sound pressure level and the wheel hub acceleration was observed. A Taguchi analysis is also done to rank the effectiveness of varying trim thickness and mass density as well as adding air gap to suppress tire cavity resonance noise.
In this paper, a fully adaptive control design is considered for a four-degree-of-freedom aeroelastic system that has structural nonlinearities and operates in an unsteady aerodynamic incompressible flowfield. By using the flap hinge torque of a trailing-edge flap surface in combination with a leading-edge active flap, a closed-loop controller that adapts for uncertainties in the system parameters is designed. An implicit observer is implemented in the control design to compensate for lack of measurements of the lag states that model the unsteady flow. The innovative Lyapunov-based control design procedure results in a partial-state feedback adaptive controller that is globally asymptotically stable. Numerical simulation results show the effectiveness of the control strategy; comparative simulations are run to illustrate the benefit of using twin flaps as opposed to the conventional single flap control design.
Due to frictional slippage between the joint components, clamp band joints may generate nonlinear stiffness and friction damping, which will affect the dynamics of the joint structures. Accurate modeling of the frictional behavior in clamp band joints is crucial for reliable estimation of the joint structure dynamics. While the finite element (FE) method is a powerful tool to analyze structures assembled with joints, it is computationally expensive and inefficient to perform transient analyses with three-dimensional (3D) FE models involving contact nonlinearity. In this paper, a two-dimensional (2D) FE model of much more efficiency is applied to investigate the dynamics of a clamp band jointed structure subjected to longitudinal base excitations. Prior to dynamic analyses, the sources of the model inaccuracy are determined, upon which a two-step model updating technique is proposed to improve the accuracy of the 2D model in accordance with the quasi-static test data. Then, based on the updated 2D model, the nonlinear influence of the clamp band joint on the dynamic response of the joint structure is investigated. Sine-sweep tests are carried out to validate the updated 2D FE model. The FE modeling and updating techniques proposed here can be applied to other types of structures of cyclic symmetry to develop accurate model with high computational efficiency.
In this research, the effects of rotational components of earthquakes on seismic responses of Triple Concave Friction Pendulum (TCFP) base-isolated structures are investigated elaborately. Although it is common to ignore the influence of rotational components of earthquakes on structural analysis, this investigation demonstrates the significant effects of these components on seismic responses of isolated structures mounted on TCFP bearings. Extensive base-isolated structures models with different superstructure specifications such as slenderness and aspect ratios as well as isolation properties such as effective period and damping are investigated. Essential seismic responses such as base shear, roof acceleration, isolator displacement and base slab rotation are studied while isolated structures subjected to the translational components of earthquakes as well as the rotational and translational components of earthquakes simultaneously. The results demonstrate the sensitivity of seismic responses to the superstructure properties such as the slenderness ratio and plan aspect ratio in presence of rotational components; whereas it does not show such sensitivity to isolation properties. Generally, the roof acceleration and the base shear can be affected by the rotational components, tremendously. For instance the roof acceleration can be raised 220% in a structure when its plan length is three times more than its plan width and the base shear can be increased 33% for a 9-story building in presence of rotational components.
This paper investigates asymmetric vibrations of non-homogeneous circular plates of parabolically varying thickness on the basis of classical plate theory. The non-homogeneity of the plate material is assumed to arise due to exponential variation in Young’s modulus as well as density along radial direction in distinct manner. First three natural frequencies of clamped, simply supported and free plates have been obtained using Ritz method. The basis functions have been chosen as polynomial co-ordinate functions satisfying the essential boundary conditions. Thereafter, the effects of taper parameter, non-homogeneity parameter, density parameter and nodal diameter have been analysed for first three modes of vibration. The results obtained are compared with those available in literature for homogeneous and non-homogeneous plates.
These days fibre-reinforced materials are frequently used in construction sector for example in dams, bridges etc. Also the earth structure and artificial structure made by human may contain irregularity or corrugation, therefore, propagation of waves and vibrations through these structures gets affected by them. Motivated by these facts the present problem aims to study the propagation of torsional surface wave in a fibre-reinforced layer with corrugated boundary surface overlying an initially stressed transversely isotropic half-space. The closed form of the dispersion equation has been deduced and the notable effect of reinforcement, undulatory parameter of corrugated boundary surfaces of the layer, corrugation parameter of upper and lower boundary surfaces of the layer, initial stress acting in half-space and wave number on the phase velocity of torsional surface wave has been exhibited. The numerical computation along with graphical illustration has been carried out for fibre-reinforced layer of carbon fibre-epoxy resin and T300/5208 graphite/epoxy material for the transversely isotropic half-space. As a special case of the problem, deduced dispersion equation is found in well-agreement with the classical Love wave equation. Comparative study for reinforced and reinforced free layer has been performed and also depicted graphically. Moreover some analysis is made to highlight the important peculiarities of the problem.
In the present paper, viscously damped free vibrations of sectorial and annular sectorial membranes are investigated. Instead of undamped natural frequencies which are typically computed and applied in the free vibrations, viscously damped natural frequencies are done. The viscously damped natural frequency equation and the critical viscous damping equation are exactly derived. In the viscously damped free vibration, effects of viscous damping on natural frequencies are also studied.
We present a probabilistic methodology for designing tuned mass dampers for flutter suppression in long-span bridges. The procedure is computationally efficient and computes the probability of flutter occurrence based on a modified first-order method of reliability analysis, a reduced-order representation of the structure and a time domain formulation of aeroelastic loads. Results of a parametric investigation show that the proposed methodology is preferable to a deterministic design procedure, which relies on nominal values of mechanical and aerodynamic parameters and does not guarantee the maximum safety. Furthermore, the reliability-based approach can be effectively used in the design of multiple tuned mass damper configurations by enhancing robustness against frequency mistuning and by reducing costs associated with supplemental damping for a given safety performance level.
The present paper deals with the free vibration modal analysis of hybrid laminates using a finite element model based on the third order shear deformation theory (TSDT) and the first order shear deformation theory (FSDT). A computer code has been developed using MATLAB, 2013. The experimental investigation on the free vibration of hybrid laminates made of carbon and glass fibres has been conducted. The hybrid laminate is prepared by placing carbon fibres in the outermost laminae and glass fibres in the rest of the laminate. The bi-directional glass and carbon fabrics and the epoxy resin are used for the preparation of laminates in the laboratory. The experimental models of laminates have been prepared by the resin infusion process using vacuum bagging technique. The natural frequencies of hybrid laminates for different modes are determined and the mode shapes are plotted for the corresponding frequencies by experiment and numerical procedure. The finite element formulations based on TSDT and FSDT for the composite laminates predict the natural frequencies and are validated by comparing with the experimental results.
This paper focuses on building a controller for active suspension system of train cars in the case that the sprung mass and model error are uncertainty parameters. The sprung mass is always varied due to many reasons such as changing of the passengers and load or impacting of wind on the operating train while an unknown difference between the suspension model used for survey and the real suspension system also always exists. The controller is built based on an adaptive neuro-fuzzy inference system (ANFIS), sliding mode control, uncertainty observer (NFSmUoC) and a magnetorheological damper (MRD) which can be seen as an actuator for applying active force. A nonlinear uncertainty observer (NUO), a sliding mode controller (SMC) together with an inverse model of the MRD are designed in order to calculate the current value by which the MRD creates the required active control force u(t). An ANFIS and measured MR-damper-dynamic-response data sets are used to identify the MRD as an inverse MRD model (ANFIS-I-MRD). Based on dynamic response of the suspension, firstly the active control force u(t) is calculated by NUO and SMC, in which the impact of the uncertainty load on the system is estimated by the NUO. The ANFIS-I-MRD is then used to estimate applied current for the MRD in order to create the calculated active control force to control vertical vibration status of the train cars. Simulation surveys are carried out to evaluate the effectiveness of the proposed method.
The nonlinear and time-varying characteristics of the V-belt continuously variable transmission system driven by a permanent magnet synchronous motor (PMSM) are unknown, therefore, improving the control performance of the linear control design is time-consuming. To overcome difficulties in the design of a linear controller for the PMSM servo-driven V-belt continuously variable transmission system with the lumped nonlinear load disturbances, a composite recurrent Laguerre orthogonal polynomial neural network (NN) control system which has online learning capability to respond the nonlinear time-varying system, was developed. The composite recurrent Laguerre orthogonal polynomial NN control system can perform inspector control, recurrent Laguerre orthogonal polynomial NN control which involves an adaptation law, and recouped control which involves an estimation law. Moreover, the adaptation law of online weight parameters in the recurrent Laguerre orthogonal polynomial NN is based on Lyapunov stability theorem. The use of modified particle swarm optimization yielded two optimal learning rates for the weight parameters which helped improve convergence. Finally, comparison of the experimental results of the present study with those of previous studies demonstrated the high control performance of the proposed control scheme.
Heavy lathe-mill and turn-mill machine tools with both turning and milling operations are usually equipped with a frictional brake system to mitigate the effect of the mechanical backlash on the gear driven rotary table. In this paper the simultaneous effects of the coupled nonlinear frictions and backlashes on the positioning of the rotary axis have been investigated theoretically and empirically. Using the describing function method, it is shown that the undesired oscillations of the system are due to the existence of a limit cycle in the nonlinear closed-loop trajectory pattern of the rotary axis. Some simple practical rules are proposed for parameters adjustment of the rotary table, to assure that limit cycle is not created, and the multi-function machine does not oscillate improperly. The proposed rules can be used both at the designing stage and also during the maintenance of the machine. In order to verify the simulation results, a complete set of experimental data in a heavy lathe-mill machine has been utilized. It is shown that the deviation between the simulation results and the real experimental data at different operating conditions are quite small.
The present paper investigates the effect of initial stress, irregularity depth, irregularity factor and magneto-elastic coupling parameter on the dynamic response due to a normal moving load with constant velocity on the free surface of an irregular magneto-elastic transversely isotropic half-space under the state of hydrostatic initial stress. The expressions for normal stress and shear stress are obtained in closed form analytically. The considerable effect of initial stress, irregularity depth, irregularity factor and magneto-elastic coupling parameter on normal stress and shear stress are computed numerically and depicted by means of graphs. Moreover, comparative study highlighting the effect of various types of irregularity viz. rectangular irregularity, parabolic irregularity and no irregularity on the normal stress and shear stress is a key feature of the study.
Researchers worldwide have developed various semi-active control devices for seismic protection of structures. Most of these devices are electromechanical in nature and thus require a power source for their operation. In this paper, a newly developed rotation-based mechanical adaptive passive device is presented. These unique devices are able to mechanically change stiffness, either by adding positive or negative stiffness, by using different types of rotational elements. The devices are compact due to their use of rotational elements, facilitating their implementation in structures. The conceptual development of these devices is presented herein along with analytical models and numerical simulation results that demonstrate their potential for providing seismic protection. In addition, an extension of the stiffness modulation concept is introduced wherein damping is modulated.
This paper proposes a robust observer for a flexible single-link manipulator based on the partial differential equation (PDE) dynamic model. Unlike observers for the PDE model introduced by previous researchers, this observer is designed to estimate the distributed spatiotemporally varying states with unknown boundary disturbance and spatially distributed disturbance. The asymptotic stability of the proposed observer is proved by theoretical analysis and demonstrated by simulation results.
This paper describes an adaptive system for controlling the tonal vibration of a single-degree-of-freedom system with nonlinear damping. The adaptive control system consists of a force actuator in parallel with the suspension, which includes the nonlinear damper, and a velocity sensor mounted on the mass. The adaptation of the controller is done once every period of the excitation. Because the response of the nonlinear system changes with excitation level, conventional adaptive algorithms, with a linear model of the plant, can be slow to converge and may not achieve the desired performance. An on-line observer is used to obtain a describing function model of the plant, which can vary with the excitation level. This allows the adaptive control algorithm to converge more quickly than using a fixed plant model, although care has to be taken to ensure that the dynamics of the observer do not interfere with the dynamics of the adaptive controller.
The purpose behind this work is to discuss dynamic stability when self-excited vibration occurs on tire tread. First of all, a suspension-tire-tread model has been built for simulation, and the result shows the existence of self-excited vibration on tire tread under particular conditions. A six-component test of the wheel indicates that self-excited vibration often takes place on tire tread when the vehicle travels straightaway at high speed. Then, through bifurcation analysis of tire tread, we found that the speed of the vehicle and slip angle of the wheel play significant roles in vibration generation. Within the lateral speed component caused by the tiny slip angle, equivalent damping of system turns to negative and thus provides enough energy to be consumed by obstructions. In order to investigate the influence of this self-excited vibration on the system, the system model has been simulated with different parameters, such as vehicle speed, vertical load, and tire pressure. The result explains different wear characteristics from the driven wheel to the driving wheel, which provides the basis of polygonal wear calculation.
Dynamic engraving processes upon a projectile under five charge cases were studied using numerical simulations. A finite element model of the rotating band engraving into the forcing cone of the barrel was constructed, and the deformation process of the rotating band, the projectile motions, the dynamic engraving resistance, the average work pressure and the engraving pressure were obtained. The simulation results show that the interior ballistic parameters, including the engraving speed, the projectile motion, the maximum engraving resistance and the engraving pressure are different for different charge cases. This work provides an approach to investigating the interior ballistics processes considering the dynamic engraving of rotating bands.
Particle damping is one of the recent passive damping methods and its relevance in space structural applications is increasing. This paper presents the novel application of a radial basis function (RBF) neural network to accurately predict the modal damping ratio of a particle damping system using system input parameters such as particle size, particle density, packing ratio, and their effect at different modes of vibration. The prediction of particle damping using the RBF neural network is studied in comparison with the back propagation neural (BPN) network on an aluminum alloy beam structure with extensive experimental tests. The prediction accuracy of the RBF neural network is significant with 9.83% error compared to 12.22% obtained by the BPN network for a best case. Limited experiments were also carried out on a mild steel beam to study and compare the trends predicted in earlier studies. The relationships obtained by the proposed method readily provide useful guidelines in the design of particle dampers for space applications. The RBF neural network provides superior accuracy with reduced computational effort.
Tensile instability in beam-like structures has been highlighted in very few papers; the studies reported in the specific literature are limited to beam-columns characterised either by high shear deformation or by the presence of a single structural junction allowing a transversal displacement discontinuity. Moreover, to the authors’ knowledge, the flutter instability associated to tensile axial load has not yet been disclosed. This work aims to offer further contribution to the knowledge of tensile instability of beam-columns by considering the dynamic instability of an Euler Bernoulli beam in presence of an arbitrary number of internal sliders endowed with translational elastic springs. The use of the generalised functions allows an exact evaluation of the eigensolution, provided in closed form, both for conservative and nonconservative axial load. In particular, the following relevant question is posed: Can a beam-column undergo tensile flutter instability? A comprehensive parametric analysis conducted in this work gives an affirmative answer to the asked question.
The vibration behavior was investigated of thin-to-moderately thick functionally graded carbon nanotube (FG-CNT) reinforced composite quadrilateral plates resting on elastic foundations. In the study, transverse shear and rotatory inertia were incorporated through first-order shear deformation theory. The improved moving least-squares-Ritz method was employed to derive the eigenvalue equation of the plate vibration. The study examined the effects of the elastic Winkler medium, CNT ratios, distributions of CNTs, boundary conditions, side angles, thickness-to-width ratios, and the relative plate aspect ratios on the vibration response of the FG-CNT reinforced composite plates. A set of vibration frequencies and mode shapes for the FG-CNT reinforced composite quadrilateral plates is presented. Additionally, a comprehensive parametric study and vivid mode shape plots demonstrate details of the vibration spectrum of the FG-CNT reinforced composite plates.
The new perturbation iteration method developed by Pakdemirli and co-workers for regular problems is extended to cover problems with blow up secularities for sufficiently long time intervals. The Duffing equation, the quintic Duffing equation, systems with quadratic and cubic nonlinearities and systems with odd nonlinearities are treated using the new approach. In all cases, the perturbation parameter and/or the nonlinearity coefficients are selected to be large so that the system is strongly nonlinear. Approximate analytical solutions are presented and contrasted with the numerical solutions. It is concluded that the method outlined is reliable for strongly nonlinear equations having constant-amplitude type solutions.
Autonomous unmanned aerial vehicles (UAVs) often carry video cameras as part of their payload. Outdoor video captured by such cameras can be used to estimate the attitude and altitude of the UAV by detecting the location of the horizon in the video frames. This paper presents a video frame processing algorithm for estimating the pitch and roll of a UAV, as well as its altitude. The frames are obtained from a downward pointing video camera equipped with a fisheye lens. These open-loop estimates can serve as redundant data used to implement graceful-degradation in the event that the main closed-loop control sensors fail, or for fault-tolerance purposes to augment inertial sensors for increased accuracy. The estimated values had a mean error of ±0.7 angular degrees for roll and ±0.9 angular degrees for pitch, while the altitude estimation from the video had a mean error of ±0.9 meters. The results are presented and compared to actual attitude and altitude values obtained from a traditional inertial measurement unit and, in the case of altitude comparison, an absolute air pressure sensor. The algorithm was developed on a personal computer to work at 10 frames per second and uses only simple image processing functions that can be deployed using open source libraries on lightweight computing boards capable of image processing.
Air vortex flow can induce small amplitude vibration of aerostatic bearings on the order of nanometers, which is known to be harmful to positioning accuracy of aerostatically supported devices in ultra-precision applications. In this paper, in order to suppress the vortex flow and reduce vibration of aerostatic bearings, a novel design of arrayed microhole restrictor (AMR) is proposed, and its effects are numerically and experimentally investigated. By computational fluid dynamics analysis, the transient flow features are studied for aerostatic bearings with AMR and conventional restrictors, and static performances of the bearings are also compared. Vibration strength of the bearing is measured experimentally to validate the effectiveness of AMR. The results show that vortex shedding in the recess is suppressed and the vibration can be effectively reduced by AMR, while load capacity and stiffness of the bearing remain unchanged.
This paper investigates the behavior of a rotor-bearing system with a breathing crack, under the action of active magnetic bearings, implemented to suppress the vibration induced by the presence of the crack and the unbalance. In such a case, identification of the crack with help of vibration signals may be difficult; other observables such as the controller current may be utilized for the purpose. Linear system equations of motion together with the switching crack excitation function are used to develop the identification algorithm. The use of full spectrum analysis is made to determine the crack force coefficients of the harmonics exciting the rotor in the same and the reverse direction of the rotor spin. Usage of these coefficients in the identification algorithm estimates the viscous damping, disc unbalance and additive crack stiffness. The algorithm has been tested for measurement noise and bias errors in system parameters, for robustness. In practical terms, the situation analyzed in this paper relates to identification of crack and other parameters in a rotor integrated with an active magnetic bearing.
This paper presents a new approach for intelligent fuzzy logic (IFL) controller tuning via firefly algorithm (FA) and particle swarm optimization (PSO) for a semi-active (SA) suspension system using a magneto-rheological (MR) damper. The SA suspension system’s mathematical model is established based on quarter vehicles. The MR damper is used to change a conventional damper system to an intelligent damper. It contains a magnetic polarizable particle suspended in a liquid form. The Bouc–Wen model of a MR damper is used to determine the required damping force based on force–displacement and force–velocity characteristics. The performance of the IFL controller optimized by FA and PSO is investigated for control of a MR damper system. The gain scaling of the IFL controller is optimized using FA and PSO techniques in order to achieve the lowest mean square error (MSE) of the system response. The performance of the proposed controllers is then compared with an uncontrolled system in terms of body displacement, body acceleration, suspension deflection, and tire deflection. Two bump disturbance signals and sinusoidal signals are implemented into the system. The simulation results demonstrate that the PSO-tuned IFL exhibits an improvement in ride comfort and has the smallest MSE for acceleration analysis. In addition, the FA-tuned IFL has been proven better than IFL–PSO and uncontrolled systems for both road profile conditions in terms of displacement analysis.
An analytical study is presented for vibration and acoustic radiation of a finite thin orthotropic composite cylindrical shell excited by a harmonic concentrated force in a hygroscopic environment. The modal analysis method is used to solve the governing equations. Theoretical results are presented in natural vibration, radial quadratic velocity, sound power and radiation efficiency, with uniform incremental moisture content. Furthermore, different stiffness, length and thickness are set respectively to research the effects of the material and structure parameters variation of the orthotropic cylindrical shell on the vibration and acoustic radiation characteristics. It is found that the natural frequencies decrease with an increase of moisture content. The modal indices associated with the lowest frequency mode reaches the modal indices corresponding to the lowest buckling mode near the critical buckling moisture content with moisture content. The radial quadratic velocity and sound radiation power decrease with the incremental moisture content in the lower frequency band. The vibration and acoustic response decrease with the enhanced stiffness. The increasing length has little impact on the sound radiation and the thickened cylindrical shell weakens the sound radiation response.
The aim of this paper is to investigate synchronization of fractional-order complex dynamic networks. To ensure synchronization of two dynamic networks, an adaptive feedback control method is proposed. With the stability analysis of the fractional-order differential system, we rigorously prove that the controller can make trajectory errors between the drive and response networks synchronized. The simple but practical method can be applied to a class of fractional-order networks without any prior analytical knowledge of the systems. Three illustrative examples are given to show the effectiveness of the proposed method.
Recently, fractional-order proportional–integral–derivative (FOPID) controllers are demonstrated as a general form of the classical proportional–integral–derivative (PID) using fractional calculus. In FOPID controller, the orders of the derivative and integral portions are not integers which offer more flexibility in succeeding control objectives. This paper proposes a multi-objective genetic algorithm (MOGA) to optimize the FOPID controller gains to enhance the ride comfort of heavy vehicles. The usage of magnetorheological (MR) damper in seat suspension system provides considerable benefits in this area. The proposed semi-active control algorithm consists of a system controller that determines the desired damping force using a FOPID controller tuned using a MOGA, and a continuous state damper controller that calculates the input voltage to the damper coil. A mathematical model of a six degrees–of–freedom seat suspension system incorporating human body model using an MR damper is derived and simulated using Matlab/Simulink software. The proposed semi–active MR seat suspension is compared to the classical PID, optimum PID tuned using genetic algorithm (GA) and passive seat suspension systems for predetermined chassis displacement. System performance criteria are examined in both time and frequency domains, in order to verify the success of the proposed FOPID algorithm. The simulation results prove that the proposed FOPID controller of MR seat suspension offers a superior performance of the ride comfort over the integer controllers.
This paper presents a new method which can identify the structure parameters (such as the bearing parameters, the nonlinear rub-impact parameters, and so on) of a nonlinear rotor-bearing system. Based on an improved kriging surrogate model and evolutionary algorithm (IKSMEA), the new method can provide more accurate results with less computation time. The initial kriging surrogate model (KSM) is constructed by the samples of varying structure parameters and their response values. According to the identified process, a multi-point addition criterion is proposed and more appropriate predicted points are added to update the KSM. Numerical studies and experimental validation of a nonlinear rotor-bearing system are performed. Comparing to the previous method (KSM and evolutionary algorithm), the new method satisfies the condition of convergence with less updating steps and increased robustness to noise. The identified results indicate that the IKSMEA can identify the nonlinear rotor system more effectively and accurately.
This paper presents a novel global sliding mode control technique for the stabilization of a class of uncertain and nonlinear dynamic systems with perturbation. Using the Lyapunov stability theory and linear matrix inequality, some sufficient conditions are deduced to guarantee the asymptotic stabilization of the system states and to modify the robustness of the system. To improve the robust performance, an innovative reaching control law is designed to guarantee a chattering-free finite time performance under the uncertainty and nonlinearities and is optimally tuned using a modified random search algorithm. Simulation results are provided to show the effectiveness of the suggested technique.
A dynamic model is developed to incorporate a curved beam periodic structure in the transfer path of an internal isolation system to reduce the resultant vibro-acoustic of the receiving cylindrical shell structure in a passive broadband way. The vibration transmission from the multi-connected internal isolation system with/without the curved beam periodic structure is built by the matrix method. The analytical representation of the curved beam is employed to establish the transfer matrix dynamic model of the proposed multi-layer curved beam periodic structure. Both numerical simulations and experimental investigations are carried out. The numerical simulations demonstrate that the resonances of the internal isolation system will magnify the vibro-acoustic responses notably and the designed curved beam periodic structure is an effective band-stop mechanical filter to minimize the vibration transmission and acoustic radiation responses at resonances in the band gap. The experimental results confirm that the normal acceleration responses on both the bases and the surface of the cylindrical shell are reduced in the band gap of the curved beam periodic structure. An average reduction amount of 9~12 dB on the bases and 2~3 dB on the shell is obtained. The vibration transmission in the curved beam periodic structure is tested and found to be influenced by the boundary conditions at the input and output ends, which is different from that under the free boundary conditions.
The paper presents a new nonlinear control design methodology for inducing modal, self-excited oscillation in a class of multi degrees-of-freedom mechanical systems. The system is assumed to be fully actuated and the controller operates in a centralized fashion based on the direct nonlinear velocity feedback. The linear part of the controller is designed to assign negative modal damping in the mode to be excited and positive modal damping in other modes. The nonlinear modal interaction is investigated using averaging analysis and different excitation regimes are delineated in the control parameter space. The nonlinear part of the controller is optimized to minimize the control cost. Numerical simulations of the control system are performed to substantiate the analytical results and validate the accuracy of the design. The control method is also shown to have some degree of robustness against parametric variations over the nominal values.
A simplified three-degree-of-freedom dynamic model with nonlinear friction torque and engine torque excitation, capable of identifying the effect of the engine excitation on clutch judder, is presented. The analysis of harmonic order is performed and a sinusoidal contact pressure between friction surfaces is considered, along with an analytical solution for the relative angular velocity of the clutch plates. The average fluctuation amplitude of the clutch relative angular velocity is used to evaluate the judder. Numerical calculations indicate that the clutch judder increases significantly when the angular velocity of the crankshaft, corresponding to the harmonic orders of the engine, is equal or close to the natural frequency of the driveline. An identical frequency of the engine excitation and the oil pressure fluctuation contributes little to the clutch judder, unless the excitation is at or near the resonance frequency. The amplitudes of oscillations due to the engine excitation grow when the pulsating torque of the engine increases. The mean torque of the engine has little influence on the judder, although it governs the clutch engagement time. The results further show that clutch judder attenuates as the torsional stiffness of the system increases.
In this paper a nonlinear observer for a class of partial differential equations known as the advection equation is designed. The observer, that uses only boundary measurements, is developed based on the sliding mode method. The convergence of states of the observer to the actual system, in spite of possible mismatches between the model and the system, is proven through the Lyapunov stability techniques. In addition, a sliding mode method is employed to design an anomaly detection system that is able to identify parameters of the disturbance in the system such as intensity and location. The Lyapunov stability theorem has been used in order to guarantee the convergence of the anomaly detection system. The applications of observer and anomaly detector are illustrated through simulation.
Wind turbine tower dynamic load is related to the fatigue and reliability of the structure. This paper deals with the problem of tower vibration control using specially designed and built numerical and laboratory model. The regarded wind turbine tower-nacelle model consists of vertically arranged stiff rod (representing the tower), and a stiff body fixed at its top representing nacelle assembly that is equipped with horizontally aligned tuned vibration absorber (TVA) with magnetorheological (MR) damper. To model tower-nacelle dynamics, Comsol Multiphysics finite element method environment was used. For time and frequency domain numerical analyses (including first and second bending modes of vibration) of system with TVA and MR damper models, MATLAB/Simulink environment was used with Comsol Multiphysics tower-nacelle model embedded. Force excitation sources applied horizontally to the nacelle, and to the tower itself were both considered. The MR damper real-time control algorithms, including ground hook control and its modification, sliding mode control, linear and nonlinear (cubic and square root) damping, and adaptive solutions are compared to the open-loop case with various constant MR damper input current values and system without MRTVA (i.e. MRTVA in ‘locked’ state). Comprehensive numerical analyses results are presented along with Vensys 82 full-scale tower-nacelle model validation. Finally, preliminary results of laboratory tests are included.
This paper reports work on the optimization and performance evaluation of a hybrid electromagnetic suspension system equipped with a hybrid electromagnetic damper. The hybrid damper is configured to operate with hydraulic and electromagnetic components. The hydraulic component produces a large fail-safe baseline damping force, while the electromagnetic component adds energy regeneration and adaptability to the suspension. For analyzing the system, the electromagnetic component was modeled and integrated into a 2DOF quarter-car model. Three criteria were considered for evaluating the performance of the suspension system: ride comfort, road holding and regenerated power. Using the genetic algorithm multi-objective optimization (NSGA-II), the suspension design was optimized to improve the performance of the vehicle with respect to the selected criteria. The multi-objective optimization method provided a set of solutions called Pareto front in which all solutions are equally good and the selection of each one depends on conditions and needs. Among the given solutions in the Pareto front, a small number of cases, with different design purposes, were selected. The performances of the selected designs were compared with two reference systems: a conventional and a nonoptimized hybrid suspension system. The results show that the ride comfort and road holding qualities of the optimized hybrid system are improved, and the regenerated power is considerably increased.
This paper considers the calculation of the sensitivity of modal assurance criteria (MAC) values of viscously damped systems. A direct method is proposed by constructing a Lagrange function whose Lagrange multiplier only needs to be calculated once for different design parameters. It is efficient in computational time and storage capacity. An extensive numerical analysis is used to show the effectiveness of the derived results. Several applications concerning the sensitivity of MAC values are discussed on the basis of the experimental data and the numerical analysis of a long beam structure with bolted joints.
In this paper, a nonlinear active control scheme is applied to suppress the flutter vibration of a wing/store. The system is considered as a two dimensional airfoil with attached store. The nonlinear aero-servo-elastic model of the system is obtained based on the Lagrange's formulation. The proposed active pylon involves the piezoelectric wafer strut as the actuator. The aero loads are modeled using Theodorsen function. A gust disturbance model is also added to the system governing equations of motion. An adaptive-robust control scheme is used to suppress the flutter vibration of the wing/store system. The proposed adaptive-robust controller is a composition of the adaptive and robust controllers and so can be considered as a useful controller in presence of unknown parameter uncertainty and disturbances. Finally, the system is simulated and the controller is applied to the system to control the flutter vibrations. The results illustrate the high performance and effectiveness of the controller.
In this paper, the finite-state helicopter rotor inflow modes have been studied based on eigenanalysis. The inflow velocity mode shapes with node lines have been displayed with various skew angles. The eigenvalues are highly coupled especially for higher skew angles, and the mode shapes change significantly for different angles. The changing of eigenvalues with different harmonic numbers is also exhibited in the tables for axial flow of both the Peters–He and Morillo dynamic inflow models. An easy way to estimate the eigenvalues of the Peters–He inflow model is also established.
In many engineering systems there is a common requirement to isolate the supporting foundation from low frequency periodic machinery vibration sources. In such cases the vibration is mainly transmitted at the fundamental excitation frequency and its multiple harmonics. It is well known that passive approaches have poor performance at low frequencies and for this reason a number of active control technologies have been developed. For discrete frequencies disturbance rejection Harmonic Control (HC) techniques provide excellent performance. In the general case of variable speed engines or motors, the disturbance frequency changes with time, following the rotational speed of the engine or motor. For such applications, an important requirement for the control system is to converge to the optimal solution as rapidly as possible for all variations without altering the system's stability. For a variety of applications this may be difficult to achieve, especially when the disturbance frequency is close to a resonance peak and a small value of convergence gain is usually preferred to ensure closed-loop stability. This can lead to poor vibration isolation performance and long convergence times. In this paper, the performance of two recently developed HC algorithms are compared (in terms of both closed-loop stability and speed of convergence) in a vibration control application and for the case when the disturbance frequency is close to a resonant frequency. In earlier work it has been shown that both frequency domain HC algorithms can be represented by Linear Time Invariant (LTI) feedback compensators each designed to operate at the disturbance frequency. As a result, the convergence and stability analysis can be performed using the LTI representations with any suitable method from the LTI framework. For the example mentioned above, the speed of convergence provided by each algorithm is compared by determining the locations of the dominant closed-loop poles and stability analysis is performed using the open-loop frequency responses and the Nyquist criterion. The theoretical findings are validated through simulations and experimental analysis.
A finite elastic plate, partially covered by piezoelectric patches on two sides to periodically charge or recharge electronic devices operating in a sealed armor, is considered to study the effects of a viscoelastic interface on the resonant frequency, transformation ratio, efficiency, displacement and stress distributions of the structure. Based on the shear-slip model, we apply the Fourier series method to analyze the symmetric thickness-twist modes of the system containing an imperfect viscoelastic interface. An examination of the numerical results confirms the good convergence and high precision of the Fourier series method. If an appropriate thickness ratio is chosen, the energy-trapping phenomenon is well presented. The numerical results also reveal that the transformation ratio, efficiency and displacement of the system decrease for weaker interfaces, whereas the resonant frequency is not sensitive to interface damping parameters. This result could provide a theoretical guide to design high-performance piezoelectric plate transformers.
Classical input shaping is based on convolving a general input signal with a sequence of timed impulses. These impulses are chosen to match certain modal parameters of the system under control to eliminate residual vibrations in rest-to-rest maneuvers. This type of input shaping is strongly dependent on the system period. In this work, an adjustable maneuvering time wave form command shaper is presented. The equation of motion of a simple pendulum model of a crane is derived and solved in order to eliminate residual vibrations at the end of motion. Several cases are simulated numerically and validated experimentally on an experimental model of an overhead crane. Results show that the proposed command shaper is capable of eliminating residual vibrations effectively with a single continuous wave form command. The work is extended to include the effect of hoisting on the shaper performance. Several functions are used to simulate hoisting. To overcome the added complexity of hoisting on the system, an approximation technique is used to determine initial shaped command parameters, which are later used in a genetic algorithm optimization scheme. Numerical and experimental results prove that the proposed command shaper can effectively eliminate residual vibrations in rest-to-rest maneuvers.
Shaft alignment is a key factor for the safe and reliable operation of a turbine unit. This paper presents an approach to estimate the turbo-generator shaft alignment using strain gauge technique with two measuring sections nearby each coupling. The change of shaft bending moment is linearly proportional to the change of bearing elevation and reaction force. So the bearing load distribution can be identified from the strain values and bending moments which are measured using strain gauge. The transfer matrix method is used to calculate the detailed shaft alignment data including deflection, slopes, bearing reaction forces, influence coefficients, sag/gap values. Experiments were carried out on a test rig with 3 rotors, 2 couplings and 6 bearings. It was shown that the strain gauge identification results agree well with the results using the jack-up method. The maximum relative error of each bearing loads is almost 8.7%. The sag/gap values using the strain gauge method are close to those using the laser alignment method. The maximum relative error is less than 7.5%. Results also show that the strain gauge method is sensitive to possible disturbances in the bearing elevation. In the end, strain gauge alignment technique with two measuring sections nearby each coupling was applied on the shaft alignment estimation of a 600 MW turbine unit successfully. The bearing loads and shaft deflection were obtained accurately.
The main emphasis of the paper is put on the experimental verification and comparison of classical modal analysis techniques and recurrence plots sensitivity to damage size. Identification experiments were carried out for the laboratory object subjected to random and chirp excitations, respectively. In the course of carried out experiments, the process of damage propagation was simulated by the successive drilling into one of the object elements. Measured time histories of system responses were analyzed with the application of the classical modal analysis, recurrence plots (RP), cross recurrence plots (CRP) and joint recurrence plots (JRP) methods. Obtained results proved that the RP, CRP and JRP methods are much more sensitive to changes in dynamical system properties resulting from damage initialization and propagation than classical modal analysis methods and can be successfully applied to damage detection and tracking changes in the system natural frequencies.
Surface waviness is one important source of vibrations in a roller bearing. When the surface waviness occurs on the surface of the inner or outer race of a roller bearing, a time-varying deflection excitation and a time-varying contact stiffness excitation can be generated due to the changes in the curvature radii of the race with surface waviness at the contact position between the roller and the race of the roller bearing. In this paper, a new dynamic model (TDCE model) considering both the time-varying deflection excitation, the time-varying contact stiffness excitation, and the lubricating oil film is proposed to investigate vibration responses of a lubricated roller bearing with a uniform and a nonuniform surface waviness on its races, which cannot be accurately modelled by the previous time-varying deflection excitation (PTDE) model in the literature. Effects of the number, the maximum amplitude, and the nonuniform distribution of the surface waviness on the contact stiffness between one roller and the race with surface waviness are investigated, as well as the vibration responses of a lubricated roller bearing. Numerical results from the proposed model are compared with those from the PTDE model in the literature, which shows that the proposed TDCE model can provide more accurate impulses generated by the surface waviness on the races of the roller bearing. Moreover, the results show that the proposed method can provide a new vibration modelling method for a lubricated roller bearing with the uniform and nonuniform surface waviness on its races.
For the first time in this research, a feedback control system is used to study the free vibration response of rectangular plate made of magnetostrictive material. In this regard, magnetostrictive plate (MsP) is analyzed by trigonometric higher order shear deformation theory that involved six unknown displacement functions and does not require shear correction factor. The MsP is supported by elastic medium as Pasternak foundation which considers both normal and shears modules. Also the MsP undergoes in-plane forces in x and y directions. Considering simply supported boundary condition, six equations of motion are derived using Hamilton’s principle and solved by differential quadrature method. Results indicate the effect of aspect ratio, thickness ratio, elastic medium, compression and tension loads on vibration behavior of MsP. Also, findings show the controller effect of velocity feedback gain to minimize the frequency as far as other parameters become ineffective. These findings can be used to active noise and vibration cancellation systems in many structures.
The hypersonic waverider using the morphing configuration can improve the overall performance and broaden the flight range. On the other hand, the hypersonic waverider belongs to the lightweight construction, leading to the presence of the intrinsic elasticity. As a result, the integrated consideration of the active deformation and elastic action is important for the morphing waverider to realize global optimization. In this paper, the contro-integrated design methods are proposed for the morphing waverider to implement the trade-off analysis between the active deformation and intrinsic elasticity. First, the parametric model is built to describe the hypersonic flight characteristics. Then, the elastic dynamics is introduced to quantify the coupling responses associated with the angle of attack and elevon deflection. Furthermore, the integrated design is considered for the active deformation and inherent elastic action, and also the control law is designed to suppress the active and passive morphing disturbances. Finally, the simulation is conducted to test the effectiveness of the presented methods for the morphing waverider.
A damage identification method named virtual vibration deflection (VVD) was developed, the principle of which was formulated based on the "weak" modality of the pseudo-excitation (PE) approach previously established. In essence, VVD is based on locating structural damage within a series of "sub-regions" divided from the entire structure under inspection, and each sub-region was considered as a "virtual" structure undergoing independent vibration. The corresponding vibration deflection of the "virtual" structure was then used to derive the damage index of VVD. Besides various advantages inheriting from the PE approach, for example, capability of detecting damage without baseline signals and pre-developed benchmark structures, VVD exhibits improved detection accuracy and particularly enhanced noise immunity compared with the PE approach, attributed to a hybrid use of multi-types of vibration signatures (MTVS). As a proof-of-concept investigation, a beam model was used in a numerical study to examine the philosophy of VVD. And the influences from different factors (i.e., level of measurement noise and measurement density) on the detection accuracy of VVD were discussed based on the numerical model. An experiment was carried out subsequently to identify the locations of multiple defects contained in an aluminum beam-like structure. Identification results constructed by the PE approach, VVD using single-type of vibration signatures, and VVD using MTVS, were presented, respectively, for the purpose of comparison.
This study is concerned with the problem of harmonic disturbance rejection in active magnetic bearing systems. A modified notch filter is presented to identify both constant and harmonic disturbances caused by sensor runout and mass unbalance. The proposed method can attenuate harmonic displacement and currents at the synchronous frequency and its integer multiples. The reduction of stability is a common problem in adaptive techniques because they alter the original closed-loop system. The main advantage of the proposed method is that it is possible to determine the stability margins of the system by few parameters. The negative phase shift of the modified notch filter can be tuned to achieve a desired phase margin, while the gain margin can also be adjusted separately. It is shown that the modified notch filter can be designed to suppress multiple harmonics at the same time. It is implemented on a three-pole magnetic bearing test rig to evaluate its performance. Simulation and experimental results indicate that the presented method can be successfully applied to compensate the periodic disturbances such as sensor runout and mass unbalance in active magnetic bearing systems.
Active suspension can effectively resolve the contradictions between vehicle ride comfort and stability. However, a new contradiction between the active suspension performance and efficiency is aroused. Active suspension with excellent performance requires high actuation power and force in an aggressive condition, which is usually an excess capacity for normal conditions. To improve the efficiency and capacity utilization rate, this paper conducted an investigation on the efficiency and utilization rate of vehicle active suspension based on a seven degrees-of-freedom full vehicle mode with a linear quadratic Gaussian active suspension controller. The multiple objectives of active suspension performance and efficiency are integrally optimized via genetic algorithm with an elaborately designed penalty function. The proposed integration of multiple objectives is proved effective according to the comprehensive comparison analysis. The overall performance of the optimized suspension achieved the Pareto optimality. Not only a better balance between the ride comfort and stability is accomplished, but also the active suspension utilization rate is improved. By this method, the obtained Pareto optimality set can greatly improve the parameters matching and design of the active suspension.
In this study, fluid conveying continuous media was considered as micro beam. Unlike the classical beam theory, the effects of shear stress on micro-structure's dynamic behavior not negligible. Therefore, modified couple stress theory (MCST) were used to see the effects of being micro-sized. By using Hamilton's principle, the nonlinear equations of motion for the fluid conveying micro beam were obtained. Micro beam was considered as resting on an elastic foundation. The obtained equations of motion were became independence from material and geometric structure by nondimensionalization. Approximate solutions of the system were achieved with using the multiple time scales method (a perturbation method). The effects of micro-structure, spring constant, the occupancy rate of micro beam, the fluid velocity on natural frequency and solutions were researched. MCST compared with classical beam theory and showed that beam models that based on classical beam theory are not capable of describing the size effects. Comparisons of classical beam theory and MCST were showed in graphics and these graphics also proved that obtained mathematical model suitable for describe the behavior of normal sized beams.
In this paper, the performance of a smooth nonlinear energy sink (NES) to mitigate vibration of a rotating beam under an external force is investigated. The rotating beam is modeled using the Euler-Bernoulli beam theory, and the centrifugal stiffening effect is considered. It is assumed that the nonlinear energy sink has a linear damping and an essentially nonlinear (nonlinearizable or cubic) stiffness. Required conditions for occurring Hopf bifurcation, saddle-node bifurcation and strongly modulated responses (SMR) in the system are investigated. The most important parameter to study NES performance is SMR occurrence range in the detuning parameter span. Effects of position and damping of the NES and magnitude of the external force on the vibration mitigation of the rotating beam are studied. The Complexification-Averaging and the Runge Kutta methods are employed for analytical and numerical investigations, respectively. Finally, the efficiency of an optimal linear absorber and an optimal NES in the vibration mitigation of the rotating beam are compared. It is shown that the best range for the parameters of the NES is the one in which SMR and weak modulated response occur simultaneously. Furthermore, the best position for connecting the NES to a rotating beam is at the beam tip.
Recently, for fractional order model, a distinction has emerged between real state and pseudo state. Pseudo state is a vector of finite dimension but does not have the property of a state (it does not allow to determine future behavior of the system for instance). The real state is of infinite dimension as it is distributed, but is distributed on an infinite domain. A fractional model can thus be viewed as a doubly infinite model (distributed model on an infinite domain). It is shown in the paper, that this last feature induces the real state ability to store an infinite amount of energy using an electrical interpretation of fractional models. Thus, fractional models do not reflect the reality of macroscopic physical systems in terms of energy storage ability. As a consequence, even if fractional models permit to capture accurately the input-output dynamical behavior of many physical systems, such a property highlights a physical inconsistence of fractional models. They do not reflect the internal behavior of the modelled system. This analysis is made for explicit and implicit differentiation based fractional order models.
The present paper investigates the effect of gravity and initial stress on the propagation of torsional surface waves in heterogeneous medium. The dispersion equation has been obtained for rigid and traction free boundaries in terms of Whittaker function. The present study reveals that torsional surface waves can propagate in both the cases. In this paper, we assume the expansion of Whittaker function up to linear term. It is observed that, in presence of initial stress and gravity for both rigid and traction free boundary, the phase velocity of torsional surface waves increases with the growth of rigidity. In both the cases, it has also been noticed that as the gravity increases, the phase velocity of the torsional surface waves decreases in presence of heterogeneity and initial stress. It is concluded that in presence of traction free boundary, the phase velocity of the torsional surface waves is more than the rigid boundary.
This paper presents a novel approach to the design of an active suspended handle by identifying the effective frequency range, based on the saturation effects of the piezo stack actuator, in terms of the force-displacement-voltage relationship as a function of the excitation frequency. The effective range allows for proper matching between the operating speed of the machine and the suspended handle. A model of the active suspended handle was developed, which took into account the non-linear saturation effect of the piezo stack actuator. A proportional-integral-derivative controller generated the counter voltage for the piezo stack actuator, using a proportional feedback gain (P) step up method, in order to attenuate the vibration transmitted to the handle. By including the saturation effect, the Pearson’s correlation coefficient (R 2) of the model improved to 0.97, within the frequency range of 50 ~ 500 Hz. Using this approach, we identified that the effective frequency range of isolation with transmissibility less than unity is between 250 ~ 450 Hz. The active suspended handle was attached to a die grinder with a nominal operating speed of 25000 rpm and the vibration transmitted from the die grinder to the handle was reduced by 91%.
A novel model of general purpose operational amplifiers is made to approximate, at best, the equivalent circuit for real model at high-frequency. With this new model, it appears that certain oscillators, usually studied under ideal considerations or using many existing real models of operational amplifiers, have hidden subtle and attractive chaotic dynamics that have previously been unknown. These can now be revealed. With the new considerations, a "two-component" circuit, consisting simply of a capacitor in parallel with a nonmodified (and usually presented as a linear, negative) resistance, tends to exhibit chaotic signals. P-Spice and laboratory experimental results are in good agreement with the theoretical predictions.
A modified numerical technique was developed to solve a wide class of variable order fractional optimal control problems in the sense of Riemann Liouville or Caputo derivatives. The modified algorithm is based on the non-standard finite difference method of solving fractional differential equations of variable order. Important property of a reflection operator is used to simplify the variable order right Riemann Liouville or Caputo derivatives to the variable order left Riemann Liouville or Caputo derivatives. Necessary and sufficient conditions that guarantee the existence and the uniqueness of the solution of the resulting systems are given. Illustrative examples are included to demonstrate the validity and the effectiveness of the established approach.
In this paper, the vibration characteristics of axially moving plates with viscous damping are analyzed. A partial differential linear equation of motion with four simply supported edges is presented. The effects of two different viscous damping models are highlighted, while both of them have been introduced in previous studies. The investigation into the two different viscous damping models is interesting in itself. It is noteworthy that which model is closer to the fact, for which there are no systematic techniques of investigation to deal with this problem. In order to give a reference for possible verification in experiment, the difference of the two different viscous damping models in theory was proposed. The complex frequencies and its corresponding complex modes are studied by the complex mode approach. As other parameters are fixed, the effect of some parameters, such as viscous damping coefficients, axial speeds, aspect ratios, stiffness ratios, and support stiffness parameters, on the frequencies and critical speeds are examined. The complex modes illustrated in the 3-demensional figures are neither symmetric nor anti-symmetric to the midpoint of the plate owing to the plate motion. The differential quadrature scheme is used to verify the modes for the first time. The numerical calculations confirm the analytical results.
Joints are the main source of nonlinearity and energy dissipation in large assembled structures which could be otherwise considered as linear. Consequently, modeling and parameter identification of joints play a significant role in any successful design and finite element (FE) modeling of structures. In the present research, an identification procedure is proposed for the modeling of the nonlinear behavior of a bolted joint. The main emphasis are placed on the simplicity of the experimental procedures involved as well as ease of incorporation of the identified model in the FE model of the structure. Using the concept of the optimum equivalent linear frequency response function, structure was excited by two levels of random force, at two bolt preload levels, and then the eigen values of the nonlinear structure and the inverse eigen-sensitivity identification technique are used, in order to identify the nonlinear properties of bolted joints. The results of implementing the method are promising and indicative of the fact that, in contrast to static Iwan’s model of a bolted joint, the equivalent dynamic characteristics of a bolted joint may be frequency dependent, as the different modes will affect the interface zone of the jointed structures in a different manner.
The aim of this study is to provide an approach to predicting human influence on a compliant mechanical structure using a substructuring technique. Substructuring techniques allow us to obtain detailed information on the vibrational behaviour of an assembly of structures by characterization of each structure separately. In this manuscript, a hand-arm system is coupled with a vibrating structure using a substructuring technique. A lightweight and compliant vibrating beam is used to demonstrate the concept. To demonstrate the feasibility of accurately predicting the hand-arm systems’ influence on the beam, we selected one position and tested it using four push forces. The characteristics of the hand-arm system for each configuration were coupled with the dynamic characteristics of the beam only over a frequency range of [5; 300] Hz. For each of the four configurations, the coupling predicts the influence of the hand on the vibrational behaviour of the beam. Reliable predictions were obtained for the vibrational behaviour of the assembly. The results indicate that the substructuring approach predicted the vibrational behaviour of the hand-arm-beam assembly with less than 3% error.
Frequent variation in the wind flow affects the Wind Turbine (WT) to generate fluctuating output power and this can negatively impact the entire power network. This paper aims at modelling an Enhanced-Elman Neural Network (EENN) based pitch angle controller to mitigate the output power fluctuation in a grid connected Wind Energy Conversion System. The outstanding aspect of the proposed controller is that, they can smoothen the output power fluctuation, when the wind speed is above or below rated speed of the WT. The proposed EENN pitch controller is trained online using Gradient Descent (GD) algorithm and the network learning is carried out using Customized-Particle swarm optimization (C-PSO) algorithm. The C-PSO is adopted, in order to increase the learning capability of the training process by adjusting the networks learning rate. Further, the node connecting weights of the EENN is updated by means of GD algorithm using back-propagation methodology. The performance of the proposed controller is analysed using the simulation studies carried out in MATLAB /Simulink environment.
A modified Galerkin approach is employed to calculate the dynamic characteristics of a complex non-uniform fluid-conveying pipe assembled by a uniform and a conical segment. The effects of two geometric parameters (length ratio of the uniform part and conical truncation factor) on the dynamic stability are studied. Results prove that for the assembled fluid-conveying pipe 1) when fluid enters the pipe from the thinner end, the natural frequencies are higher than those when it enters from the wider end; 2) the critical flow velocity increases linearly with the increase of the uniform part ratio, while it decreases squarely with the increase of the conical truncation factor in a limited range and 3) the clamp-pined non-uniform pipe has a higher dimensionless critical velocity than the pin-clamped pipe when fluid enters from the wider end.
A unified solution for coupled cylindrical shell and annular plate systems with general boundary and coupling conditions is presented in the study by using a modified Fourier-Ritz method. Under the framework, regardless of the boundary and continuity conditions, each displacement for the cylindrical shell and the annular plate is invariantly expressed as the modified Fourier series composed of the standard Fourier series and auxiliary functions. The introduction of the auxiliary functions can not only remove the potential discontinuities at the junction and the extremes of the combination but also accelerate the convergence of the series expansion. All the expansion coefficients are determined by the Rayleigh-Ritz method as the generalized coordinates. The arbitrary axial position of the annular plate coupling with the cylindrical shell considered in the theoretical formulation makes the present method more general. The theoretical model established by present method can be conveniently applied to cylindrical shell-circular plate combinations just by varying the inner radius of the annular plate. The convergence and accuracy of present method are tested and validated by a number of numerical examples for coupled annular plate-cylindrical shell structures with various boundary restraints and general elastic coupling conditions. The effects of the axial position of the annular plate and elastic coupling conditions on the vibration behavior of the coupled system are also investigated. The power of present method compared to conventional finite element method is demonstrated with less computation cost. Some new results are presented to provide useful information for future researchers.
The output of an accelerometer often has coupled components of displacement and acceleration, and is rarely used individually for balancing tasks. In order to balance a wheeled inverted pendulum like the Segway, the conventional control usually requires gyroscopes or a combination of accelerometers and gyroscopes. In this paper, we prove that even in the presence of time delay, a wheeled inverted pendulum can be well stabilized with only one accelerometer as the sensor when the mechanical structure is slightly modified. The key idea is the introduction of an additional damper that does not have a physical connection with the wheels. Moreover, we show that balancing can be achieved with an appropriately selected accelerometer position over a range of time delays.
Vibration characteristics are one of the most important criteria to assess performances of agricultural tractors. Since vibration excitation primarily arise from short wavelength ground unevenness, tire enveloping behaviour plays significant role in determining effective excitation transmitted to the tractor and human operator. In order to be able to influence tractor vibration behaviour in early stage of computer simulation based development, appropriate tire model is needed that is able to account for this phenomenon, characterized at the same time by high computational speed. In this work, two quasistatic enveloping models of the tractor tire were developed and compared to each other. Main purpose of quasistatic enveloping model is to pass effective excitation to the dynamic model of tire viscoelastic structure. For one of the models, novel approach that makes use of artificial neural network for empirical modelling is introduced. In the second case modelling approach is of physical nature, based on analytical description of the simplified tire structure represented by radially distributed springs. It was concluded that neural network based model fulfils requirements for use in vehicle dynamics simulations, due to high computational speed and satisfactory accuracy. Physically based model, due to low computational speed, is not appropriate for vehicle dynamics but can serve as auxiliary model to obtain broader set of empirical data for neural network model development, hence reducing laboratory work needed.
A model is introduced for analyzing the influence of tooth shape deviations and assembly errors on the helical gear mesh stiffness, loaded transmission error, tooth contact stress and tooth root stress. The helical gear is approximated as a series of independent spur gear slices along axial direction whose face-width is relatively small. The relative position relationships among those sliced teeth in mesh are developed with tooth profile errors and the stiffness of the sliced tooth is calculated by the potential energy method. From the equilibriums of the forces, gear mesh stiffness, loaded transmission error, tooth contact stress and tooth root stress are calculated. Then two cases are presented for validation of the model. It is demonstrated that the model is effective for calculating the stiffness of helical gear pairs. Finally, the effects of the tooth tip reliefs, lead crown reliefs and misalignments on the gear mesh stiffness, transmission error, tooth contact stress and tooth root stress are analyzed. The results show that mesh stiffness decreases, loaded transmission error, the maximum tooth contact stress and the maximum tooth root stress grow with the increasing tooth tip relief, lead crown relief and misalignment. And tooth edge has concentrated tooth contact stresses with a gear misalignment.
A tracking controller is proposed for a crane attached to a mobile harbor (MH) equipped with a dual-stage trolley system, to dynamically position a container from the MH to the container ship or vice versa. Wave-induced motions of the MH and container ship occur during loading and unloading operations owing to external disturbances such as waves. However, a challenging task is to move a payload with unwanted swing motions accurately to the loading and unloading positions on a moving target vessel. To solve this problem, a dynamic MH crane model is derived in three-dimensional space, with roll, pitch, and heave motions caused by sea-wave disturbances. The MH crane model is then linearized to design a tracking controller and the parameters of the linearized model are obtained by carrying out the system identification process. A preview tracking control method that includes feedback and feed-forward control with the predicted target position in the x-y plane in the near future is utilized. Through numerical simulations and experiments with a scaled model, the tracking performance of the proposed dynamic positioning control system is considered when sinusoidal roll and pitch motions of the MH are generated to mimic the wavy sea environment.
This article investigates the limit cycle (LC) prediction of systems with backlash by means of the describing function (DF) when using discrete fractional-order (FO) algorithms. The DF is an approximate method that gives good estimates of LCs. The implementation of FO controllers requires the use of rational approximations, but such realizations produce distinct dynamic types of behavior. This study analyzes the accuracy in the prediction of LCs, namely their amplitude and frequency, when using several different algorithms. To illustrate this problem we use FO-PID algorithms in the control of systems with backlash.
Effective attenuation of the noise level is an important problem in acoustic systems. In this paper, we propose a robust adaptive output feedback control scheme that can considerably attenuate narrow-band noises made up of periodic signals mixed with random noise in the presence of modeling uncertainties. The amplitude, phase and frequencies as well as the number of periodic terms are unknown and could vary with time. The performance and robustness of the proposed scheme with respect to unstructured modeling uncertainties are analyzed for continuous-time single-input, single-output systems; the results, however, are extendable to multi-channel systems. The successful attenuation of the unknown periodic components of the disturbance despite the time variations, modeling errors, and random noise is demonstrated using simulations. In addition, guidelines how to choose certain design parameters for performance improvement have been presented.
The chattering phenomenon and a system with both matched and mismatched disturbances are the major difficulties in sliding mode control design. This paper presents an effective design procedure to alleviate these two difficulties for a class of second-order under-actuated mechanical systems. In the proposed design, new hierarchical sliding surfaces are designed and a modified disturbance observer is utilized to estimate the lumped disturbance which is a linear combination of the matched and mismatched disturbances. The chatter in control input is filtered out by an integrator, which acts as a low-pass filter. The asymptotic stabilities of the entire sliding surfaces are guaranteed. A design study considering lateral control of a vehicle with matched and mismatched disturbances demonstrates the effectiveness of the proposed design.
Accurate determination of natural frequencies and mode shapes of the rotating tapered Timoshenko beam is important in engineering practice. This paper re-examines the free vibration of rotating tapered Timoshenko beams using the technique of variational iteration, which is relatively new and is capable of providing accurate solutions for eigenvalue problems in a quite easy way. Natural frequencies and mode shapes for rotating tapered Timoshenko beams with linearly varying height as well as linearly varying height and width are investigated via two numerical examples, and solutions are compared with results published in literature where available. Since the method constitutes a numerical procedure, the convergence of solutions which is important for practical implementation is evaluated as well, where efficiency and accuracy of variational iteration method in solving high order eigenvalue problems are demonstrated.
The optimal location of Flexible AC Transmission Systems (FACTS) controllers in a multi-machine power system using proposed differential gravitational search algorithm (DGSA) optimization method is proposed in this paper. The main objective of this paper is to employ DGSA optimization technique to solve optimal power flow problem in the presence of Unified Power Flow controller for improving voltage profile by reducing losses along with the installation cost thereby enhancing the power system stability. A differential operator is incorporated into the gravitational search algorithm for effective search of the better solution. Due to this, the convergence and accuracy will be faster. The IEEE-6 bus, IEEE-14 bus and IEEE-30 bus systems are tested along with three other optimization techniques to validate the effectiveness of this proposed method. This proposed algorithm presents an optimal location of FACTS devices in transmission lines.
A computationally efficient method for automatic synthesis of quantitative feedback theory (QFT)-based robust controllers is proposed. The synthesis problem consists of obtaining a fixed structure QFT controller that ensures stability and achieves the performance specifications in the presence of disturbances and parametric uncertainty. The proposed method uses an interval consistency technique (hull consistency HC4) and hybrid optimization. The HC4 method is used to remove inconsistent values, which are not part of the solution in the controller parameter regions. The hybrid part incorporates interval global optimization and nonlinear local optimization methods. The proposed algorithm is illustrated by means of two examples. The first one concerns the longitudinal motion control of an aircraft system (flexible), while the second one describes the experimental study of the position control of the industrial plant emulator setup. The robustness of the designed control system for emulator setup is validated by adding extra weights on the load disk in the presence of disturbances. The experimental results show that the designed controller satisfies the robust performance specifications.
A thorough understanding of the dynamic behavior of one-dimensional structural members such as beams plays a crucial role in specialized disciplines including ocean, bridge and railway engineering. The vibratory response of an in-service beam-like component may deviate from that expected from the intact structure when defects are present. In this work, we present a semi-analytical approach to predict the forced response of a multi-cracked Timoshenko beam traversed by a moving harmonic load with constant speed. The beam is fully or partially supported by the viscoelastic foundation, where the normal stiffness and shear modulus of the subgrade are considered. The effects of transverse open cracks are modeled by massless rotational springs with a linear moment-rotation constitutive law to account for the local flexibility induced by the damage. Based on the transfer matrix method, the defective structure is treated as an assembly of sub-beams to derive the eigenvalue solution of the system. The time response is then obtained by utilizing identical generalized coordinates for lateral and rotational displacement components when applying the modal expansion technique. The use of general elastic end constraints allows us to recover all possible boundary conditions. Numerical examples are also provided to demonstrate the robustness and accuracy of the proposed method, and also to investigate the influence of important parameters on the dynamic behavior of the damaged structure.
Quasiperiodic galloping of a wind-excited tower under unsteady wind is investigated analytically near secondary (sub/superharmonic) resonances of order 2 considering a single degree-of-freedom model. The case where the unsteady wind develops multiharmonic excitations consisting of the two first harmonic terms is examined. We perform two successive multiple scale methods to obtain analytical expressions of a quasiperiodic solution and its modulation envelope near the secondary resonances. The influence of unsteady wind on the quasiperiodic galloping and on the frequency of its modulation is examined for different cases of wind excitation. The results show that the quasiperiodic galloping onset and its modulation envelope can be influenced, depending on the activated resonance and the harmonic component induced by the unsteady wind. It is also shown that the frequency of the quasiperiodic galloping is higher near the 2-superharmonic resonance in all cases of wind excitation.
A cyclic sector corresponding to blade-disk structure with dovetail connection (1/38 blade-disk) is studied and the finite element (FE) model of this structure is established based on ANSYS software. A revised normal rubbing force model is developed and a pulse force model is established to simulate the local rubbing phenomenon between the blade and elastic casing based on the revised model. The effects of the rubbing under different rotating speeds and penetration depths on the blade vibration response and contact behaviors of dovetail interface are analyzed. The results show that the rubbing will cause amplitude amplification phenomenon when the multiple frequency components are close to the first bending and first torsion natural frequencies. The arch bending of the blade caused by blade-tip rubbing can be identified by evaluating the displacement and stress of the blade in the radial direction (y-direction). The dynamic stress in the process of rubbing gradually changes from alternation between tension and compression stress to the tension stress with the increasing rotating speed. Maximum contact sliding distance may change dramatically when the rubbing force is greater than the centrifugal force. With the increase of rotating speed, the contact pressure increases under the centrifugal force and its fluctuation under rubbing is smaller at higher rotating speeds.
Problems associated with the modeling and vibration control of rectangular plates under dynamic loads with integrated polycrystalline NiTi shape memory alloy (SMA) ribbons are developed. In order to simulate the thermo-mechanical behavior of SMA ribbons under dominant axial and transverse shear stresses, a robust macroscopic constitutive model is introduced. The model is able to accurately predict martensite transformation/orientation, shape memory effect, pseudo-elasticity and in particular reorientation of martensite variants and ferro-elasticity features. The structural model is based on the adoption of the first-order shear deformation theory and on the geometrical non-linearity in the von Kármán sense. Towards obtaining the governing equations of motion, the Hamilton principle is used. Finite element and Newmark methods along with an iterative incremental process based on the elastic-predictor inelastic-corrector return mapping algorithm are implemented to solve the non-linear governing equations in spatial and time domains. Numerical simulations highlighting the implications of pre-strain state and temperature of the SMA ribbons, as well as those related to the respective dynamic loads, are presented and discussed in detail. It is found that the modeling of ferro-elasticity in the dynamic analysis of SMA composite structures could lead to significant conclusions concerning the passive vibration control capability of low-temperature SMA ribbons.
This research is on the nonlinear dynamics of a two-sided electrostatically actuated capacitive micro-beam. The micro-resonator is composed of silicon and PZT as a piezoelectric material. PZT is functionally distributed along the height of the micro-beam according to the power law distribution. The micro-resonator is simultaneously subjected to DC piezoelectric and two-sided electrostatic actuations. The DC piezoelectric actuation leads to the generation of an axial force along the length of the micro-beam and this is used as a tuning tool to shift the primary resonance of the micro-resonator. The governing equation of the motion is derived by the minimization of the Hamiltonian and generalized to the viscously damped systems. The periodic solutions in the vicinity of the primary resonance are detected by means of the shooting method and their stability is investigated by determining the so-called Floquet exponents of the perturbed motions. The basins of attraction corresponding to three individual periodic orbits are determined. The results depict that the higher the amplitude of the periodic orbit, the smaller is the area of the attractor.
This paper proposes a novel recursive terminal sliding mode structure for tracking control of third-order chained–form nonholonomic systems in the presence of the unknown external disturbances. Finite-time convergence of the disturbance approximation error is guaranteed using the designed disturbance observer. Under the proposed terminal sliding model tracking control technique, the finite-time convergence of the states of the closed-loop system is guaranteed via Lyapunov analysis. A new reaching control law is proposed to guarantee the existence of the sliding mode around the recursive TSM surface in a finite-time. Simulation results are illustrated on a benchmark example of third-order chained-form nonholonomic systems: a wheeled mobile robot. The results demonstrate that the proposed control technique achieves promising tracking performance for nonholonomic systems.
The present paper describes the effect of surface roughness orientation pattern on the nonlinear transient response of symmetric two lobe capillary compensated hole entry hybrid journal bearing. Nonlinear equations of motion have been solved with the Runge-Kutta method. The stability of the journal bearing system has been studied by obtaining the journal center motion trajectories. The results of the study reveal that the surface roughness pattern significantly changes the stability of capillary compensated two lobe hole entry hybrid journal bearing. Hence, from the bearing stability point of view, a proper selection of the surface roughness pattern and bearing geometry is essential.
In this study, adaptive observer-based synchronization of chaotic systems is considered. The master and slaves systems have different dynamics and it is assumed that the master system parameters are unknown while its states are available. First, it is assumed that the slave system parameters are known but its states are not completely available. It is shown that an observer for the slave system can be designed and applied for the purpose of synchronization. Based on a Lyapunov function, an adaptive law for master parameters estimation and a control law for the synchronization goal are extracted. Stability of the entire system including the observer dynamics has been proved. Further, it is assumed that the parameters of both master and slave systems are unknown. For this case, an adaptive nonlinear observer is designed to estimate the slave system states and two adaptive laws for estimating the unknown parameters are proposed. In addition, a proper control law to achieve the synchronization goal has been suggested, and the stability of the closed-loop system is established. Finally, the effectiveness of the proposed synchronization method is shown via simulation results.
Chaos control of a spinning disk having transverse vibration is considered in this article by stabilizing the system on its corresponding unstable periodic orbit (UPO). At the first step, the system continuous-time dynamic equations are quantized by utilizing a proper Poincare map. Then, using the regression method a linear description from the obtained cross points is achieved around the corresponding fixed point of the target UPO. Finally, through solving the Riccati equation, an optimal controller is introduced which stabilizes the system on its unstable fixed point. At the end, the effectiveness of the proposed control method is examined through numerical simulations.
The equations of two-dimensional parametric sloshing are derived for a fluid in an arbitrary shape tank. The parametric instability of the liquid free surface is reduced to the Mathieu equation. An energy-growth exponent (EGE) and the corresponding non-dimensional energy-growth coefficient (EGC) are defined for measuring the instability intensity and determining the stability boundaries of the parametrically-excited fluid system. A stability criterion is proposed by using the EGE. On the basis of the numerical tests, the analytical expressions of EGE/EGC are developed for the fluid system that is governed by the Mathieu equation. Under the small excitations, the stability boundaries by using EGE/EGC agree well with those by the traditional theory. The unstable properties, including instability intensity, instability boundaries and competition of unstable patterns etc, of parametric sloshing are analyzed and discussed in details with EGE/EGC for the fluid system. The fluid system always selects such an unstable pattern that possesses a larger energy-growth exponent. A two-dimensional parametric sloshing experiment is respectively conducted for the fluid in the rectangular, circular and U-shaped tanks. The theoretical and experimental stability boundaries of the principal parametric sloshing are obtained and compared for the fluid in three different shape tanks. Some theoretical predictions of the unstable properties of parametric sloshing are verified through the experiment.
A globally neural-adaptive simultaneous position and torque variable structure tracking control (GNASPTVSTC) for the permanent magnet synchronous motors (PMSMs) subjected to excess uncertainties (e.g., time-varying system parameters, friction and load torques for different operating conditions, the avoidance of zero control gain, the similar convergence of position and torque) is developed. Based on Lyapunov stability criterion, the desired torque is first derived from the mechanical subsystem. A simultaneous position and torque variable structure tracking control (SPTVSTC) with the avoidance of zero control gain and the similar convergence of position and torque is first designed to obtain acceptable performance for the PMSM with mild uncertainties. To improve the PMSM in the presence of excess uncertainties, the integration of SPTVSTC and two on-line neural network models for uncertainties is employed to construct the proposed GNASPTVSTC. For approximating these non-autonomous uncertainties, they are assumed to be absolutely bounded for time variable and relatively bounded for other variables, respectively. It not only improves the steady state performance as compared with SPTVSTC, but also enhances the system stability in the face of excess uncertainties. The compared simulation results validate the global tracking ability outside of approximated set and the excess robustness for different amplitudes of uncertainties and saturated control input.
The influence of shear-spring + normal-spring type imperfect interface conditions on the dispersion of the generalized Rayleigh waves in a system consisting of a covering layer and a half-space with two-axial homogeneous initial stresses is investigated. The three-dimensional linearized theory of elastic waves in initially stressed bodies is employed and the plane-strain state is considered. The elasticity relations of the materials of the constituents are described through the Murnaghan potential and the influence of the third order elastic constants which enter the expression of this potential is taken into consideration. The corresponding dispersion equation is derived and an algorithm is developed for numerical solution to this equation. Numerical results on the action of the parameters, which enter the formulation of the imperfect contact conditions, on the wave dispersion curves are presented and discussed. The results of these investigations can be successfully used for estimation of the degree of the bonded defects between the covering layer and the half-space.
Nonlinear energy sinks (NES) are widely studied as a possible engineering solution for mitigation of steady-state, impulsive and transient broadband excitations. Current work is devoted to the applicability of common pendulum as the NES for mitigation of impulsive excitations. It turns out that the pendulum NES can overcome one of the main shortcomings of more traditional NES designs, since it is able to mitigate excitation of a primary system in a relatively wide range of initial energies. This is because the pendulum can be captured into a resonance with primary oscillator both for rotational and oscillatory responses. If parameters are chosen properly, for small energies the pendulum responds almost as a common tuned mass damper. However, at higher energies, the pendulum acts as rotational NES. Thus, relatively broad diapason of initial energies can be covered. This paper presents numeric evidence for the efficiency of this design of the NES and discusses its optimal tuning. Another important finding is that the NES’s efficiency exhibits rather broad deviations for different realizations of the initial conditions with the same energy. We present a theoretical analysis of the damped targeted energy transfer into the pendulum NES from the primary mass with an account of corrections caused by the effect of gravity.
An improved stochastic averaging method of the energy envelope is proposed, whose application sphere is extensive and whose implementation is convenient. An oscillating system with both nonlinear damping and stiffness is taken into account. Its averaged Fokker-Planck-Kolmogorov (FPK) equation in respect of the transition probability density function of the energy envelope is deduced by virtue of the method mentioned above. Under the initial and boundary conditions, the joint probability density function as to the displacement and velocity of the system is worked out in closed form after solving the averaged FPK equation by right of a technique based on the integral transformation. With the aid of the special functions, the transient solutions of the probabilistic characteristics of the system response are further derived analytically, including the probability density functions and the mean square values. A simple approach to generate the ideal white noise is drastically ameliorated in order to produce the stationary wide-band stochastic external excitation for the Monte Carlo simulating investigation of the nonlinear system. Both the theoretical solution and the numerical solution of the probabilistic properties of the system response are obtained, which are extremely coincident with each other. The numerical simulation and the theoretical computation all show that the time factor has a certain influence on the probability characteristics of the response. For example, the probabilistic distribution of the displacement tends to be scattered and the mean square displacement trends toward its steady-state value as time goes by. Of course the transient process to reach the steady-state value will obviously be shorter if the damping of the system is greater.
High-frequency transverse vibration of stepped beams has attracted increasing attention in various industrial areas. For an n-step Timoshenko beam, the governing differential equations of transverse vibration have been well established in the literature on the basis of assembling classic Timoshenko beam equations for uniform beam segments. However, solving the governing differential equation has not been resolved well to date, manifested by a computational bottleneck: only the first k modes (k ≤ 12) are solvable for i-step (i ≥ 0) Timoshenko beams. This bottleneck diminishes the completeness of stepped Timoshenko beam theory. To address this problem, this study first reveals the root cause of the bottleneck in solving the governing differential equations for high-order modes, and then creates a sophisticated method, based on local coordinate systems, that can overcome the bottleneck to accomplish high-order mode shapes of an n-step Timoshenko beam. The proposed method uses a set of local coordinate systems in place of the conventional global coordinate system to characterize the transverse vibration of an n-step Timoshenko beam. With the method, the local coordinate systems can simplify the frequency equation for the vibration of an n-step Timoshenko beam, making it possible to obtain high-order modes of the beam. The accuracy, capacity, and efficiency of the method based on local coordinate systems in acquiring high-order modes are corroborated using the well-known exact dynamic stiffness method underpinned by the Wittrick-Williams algorithm as a reference. Removal of the bottlenecks in solving the governing differential equations for high-order modes contributes usefully to the completeness of stepped Timoshenko beam theory.
This paper presents a new approach to the problem of determining the frequencies and mode shapes of Euler–Bernoulli tapered cantilever beams with a tip mass and a spring at the free end. The approach is based on the replacement of the flexible beam by a rigid multibody system. Beams with constant thickness and exponentially and linearly tapered width, as well as double-tapered cantilever beams are considered. The influence of the tip mass, stiffness of the spring, and taper on the frequencies of the free transverse vibrations of tapered cantilever beams are examined. Numerical examples with results confirming the convergence and accuracy of the approach are given.
In bridge design codes, the dynamic impact factor (IM) is a well-accepted measure of the impact effect of vehicular loads on bridges. Many previous studies focused on the evaluation of IMs based on the global responses of the main girders while little attention was paid to the local impact effect on bridge decks. As a result, the IMs specified in many design codes, which were traditionally derived from the global responses of bridges, may not be necessarily reasonable for the design of deck slabs. This study was intended to investigate the local impact effect of vehicular loads on the deck slabs of prestressed concrete box-girder bridges. A bridge-vehicle coupled model was adopted to calculate both the local and global IMs. The obtained local and global IMs were compared and the relationship between the IM and three important parameters, including the road surface condition, vehicle speed, and bridge span length, was studied. The results showed that there was no strong correlation between the global and local IMs; however, the local IMs were well correlated with the road surface condition and bridge span length. A discussion on the impact provisions in different bridge codes was also presented.
Pyroshocks are structural responses to transient excitation caused by the essential use of pyrotechnic devices in aerospace applications. In order to avoid damage in aerospace structures due to pyroshocks, tests are performed on earth prior to launching space modules. In these tests, explosive loads are often replaced by alternative excitation methods such as hammer pendulums or shakers simulating on earth the impact taking place in space. However, there does not yet exist an adequate excitation method satisfying all requirements of a fast, reliable, predictable and repeatable test setup. Whereas hammers are poorely controllable in terms of generating desired shock spectra, shakers show limitations in terms of the bandwidths of up to 10 kHz which are prescribed in the test specifications.
The authors present a novel contactless and non-destructive excitation method for pyroshock test devices based on a mechatronic coupling by applying Lorentz forces to the carrying structure. For generating the corresponding magnetic field, the capacitor of a Resistor-Inductor-Capacitor RLC resonator circuit is initially charged and then discharged leading to high currents in the coil which is placed close to the carrying structure. Latter is then inducing a counter current in the aluminum structure which reacts with high multidirectional Lorentz forces. Any adjustments are done by tuning the properties of the circuit such as initial charge, capacitance and inductance. By connecting several different coils, frequency modulation and by splitting the currents more complex signals can be generated matching the natural frequencies of the structure. Almost all disadvantages of common excitation methods are eliminated by the proposed mechanism.
A generalized hyperbolic perturbation method for heteroclinic solutions is presented for strongly nonlinear self-excited oscillators in the more general form of
One of the most important issues, which high-speed underwater vehicles (HSUV) deal with, is the so-called planing force. The dynamic of HSUV includes two separate phases called planing phase and non-planing phase. Ideally, in perfect flight, the vehicle should fly within the cavity walls. However, in practice, the vehicle impacts on the cavity boundaries due to disturbances. The magnitude of the planing force is large and has a strong effect on dynamics of HSUV. However, planing force modeling is often too simple and therefore inaccurate, due to the nonlinear interaction among the solid, liquid, and gaseous phases, which is not well understood yet. Consequently, planing force identification is of great importance and should be studied in details. The present paper discusses the identification of the planing force in HSUV. For this purpose, the equations of motion are developed for the HSUV in the planing phase while the tail and the body end impact on the cavity wall. Then, a robust hybrid switching control approach is employed to deal with the highly nonlinear behavior of the underwater vehicle as it is influenced by the liquid-gas boundary interactions. An on-line planing force identification based on Lyapunov function is considered within designing controller procedure, thus the stability of the system is guaranteed. Lateral and longitudinal planing force identification are achieved and discussed. Compared to the proportional-integral-derivative control scheme, the hybrid control scheme seems to increase the stabilization of HSUV, which is useful in avoiding unsteady changes of cavity shape.
This paper proposes a novel approach to periodic fault signal enhancement in rotating machine vibrations with a tristable mechanical vibration amplifier (TMVA) by exploiting stochastic resonance (SR). The TMVA is a nonlinear physical structure system that consists of a cantilever beam and a magnet system. Through the TMVA, the periodic weak signal can be amplified with the assistance of noise in the regime of SR. Benefitting from a wider interwell spacing and a smoother potential curve, the TMVA produces a more regular output waveform with lower noise in a wider operating bandwidth as compared to the monostable and bistable amplifiers. Different from the traditional signal enhancement approach which is based on digital signal processing (DSP) techniques, the designed physical structure can realize signal enhancement in a simple, intuitive, effective and adaptive way without too much complex operations. The effectiveness and efficiency of the proposed approach are validated by a simulated fault signal and the practical bearing and gearbox fault signals, in comparison with a traditional DSP-based SR method. The principle of the proposed approach shows potential applications on rotating machine fault diagnosis area and other areas related to weak periodic signal enhancement.
Aerodynamic loads may have effects on the hunting stability, and the factor of curved track makes it more complicated. Therefore, considering the steady aerodynamic loads generated by crosswind and airflow in the opposite advancing direction of train, the hunting stability of high-speed railway vehicle on a curved track is studied in this paper. The changes of gravitational restoring force and creep coefficients which are caused by aerodynamic loads are considered, and the change of equilibrium position due to aerodynamic loads, centrifugal force and the factor of curved track is also in consideration. A mathematical model of a high-speed railway vehicle during curve negotiation with aerodynamic loads is set up. A program based on the model is written and verified. Using this program, the linear critical speed considering the effects of aerodynamic loads is determined by the eigenvalue analysis. This paper investigates the critical speeds in three aerodynamic conditions. Considering the aerodynamic loads, the dependence of critical speed on curve radius and super-elevation is analyzed, and the impact of aerodynamic loads on instability mode is analyzed as well. In addition, this paper obtains the dominant factors affecting critical speed and the variation tendency of critical speed with primary longitudinal stiffness by orthogonal experiments. The results show that the critical speed decreases or increases while the wind is blowing to outer rail or inner rail respectively. The aerodynamic loads produce obvious effects on the instability mode. The variation tendency of critical speed dependence on curve radius in the conditions with aerodynamic loads keeps consistent with the case without aerodynamic loads. It is seen from the orthogonal experiments that, aerodynamic loads and curve radius are the dominant factors affecting linear critical speed of vehicle on a curved track, and the linear critical speed decreases with the increasing of primary longitudinal stiffness.
Cable-suspended robots are categorized as a type of parallel manipulator that has recently attracted interest in terms of manipulation tasks. The main goal of this paper is to develop a novel mechatronic kit with a control methodology for a modularized cable-suspended robot. The advantages of such system owns modular and reconfigurable over conventional robots. In addition, position and orientation of the end-effector is forced toward the desired values by control of cable lengths. Hence, the new approach for forward and inverse kinematic calculation procedure based on the change of the cable lengths is used to measure the position and orientation of the mobile platform. Furthermore, the input shaping algorithm is implemented for point-to-point control purposes. The modified input shaping uses the s curve command (S-type) to offer superior performance than conventional trapezoidal command (T-type) in point-to-point positioning control. Experimental validation demonstrates the cable oscillation suppression effectiveness of the proposed S-type input shaping control command.
We formulate the linear impulsive control systems with impulse time windows. Different from the most impulsive systems where the impulses occur at fixed time or when the system states hit a certain hyperplane, the impulse time in the presented systems might be uncertain, but limited to a small time interval, i.e. a time window. Compared with the existing impulsive systems, the systems with impulse time windows is of practical importance. We then study the asymptotic stability of the case of linear systems and obtain several stability criteria. Numerical examples are given to verify the effectiveness of the theoretical results.
This present paper aims to identify the main components which influence the generation and the propagation mechanisms of railway-induced ground vibrations. It is based on numerical assessments of ground vibrations on the L161 line that runs through Brussels Capital Region, Belgium. The objective is twofold. First, using data collection at a Brussels site, a numerical prediction model is built up. It is based on a two-step approach, recently validated in tramway and high-speed train cases and improved by an accurate description of the foundation. The vehicle/track/foundation and soil subsystems are treated successively. A key advantage of the new approach is that it is capable of including the effect of soil conditions in the vehicle/track simulation. The vehicle is modeled with the help of the multibody strategy. The soil is a three-dimensional finite/infinite element model, with a complex geometry on the surface and inclined soil layers. The track model includes a rail joint defect. The model is eventually validated against experimental data. Then, a sensitivity analysis on parameters of the studied site is performed. The vehicle and foundation modeling are discussed, along with the influence of local defects and vehicle speed variation on ground vibrations.
Modes of vibration of thin cylindrical shells made up of layers with curvilinear fibres (variable stiffness composite laminates (VSCL) shells) are investigated in the linear regime. A p-version finite element type formulation is developed for that purpose; in the absence of data on vibrations of cylindrical VSCL shells, the formulation is verified by comparisons with published data on laminated shells reinforced by straight fibres and on VSCL plates. Parametric studies are performed, in order to investigate how curvilinear fibre paths can influence the modes of vibration. It is found that curvilinear fibre paths can have a very large effect, larger than on plates, on the natural frequencies and natural mode shapes of vibration of cylindrical shells. Factors that strongly influence the modes of vibration of VSCL shells are found; these include the fibre orientation at boundaries and in relation to principal normal sections.
Active vibration control using time delay for a cantilever beam is developed in this paper. The equation of motion of the system is developed using the discrete standard formulation, and the discrete quadratic function is used to design the controller. The original contribution in this paper is using a genetic algorithm to determine the optimal time delay feedback for active vibration control of a cantilever beam. Simulations of the beam demonstrated that the genetic algorithm correctly identified the time delay which produced the quickest attenuation of unwanted vibrations for both mode one and mode two. In terms of frequency response, the optimal time delay for both modes reduced the resonant amplitude. In a mixed mode situation, the simulation demonstrated that an optimal time delay could be identified.
The numerical solution of a fractional optimal control problem having a quadratic performance index is proposed and analyzed. The performance index of the fractional optimal control problem is considered as a function of both the state and the control variables. The dynamic constraint is expressed as a fractional differential equation that includes an integer derivative in addition to the fractional derivative. The order of the fractional derivative is taken as less than one and described in the Caputo sense. Based on the shifted Legendre orthonormal polynomials, we employ the operational matrix of fractional derivatives, the Legendre–Gauss quadrature formula and the Lagrange multiplier method for reducing such a problem into a problem consisting of solving a system of algebraic equations. The convergence of the proposed method is analyzed. For confirming the validity and accuracy of the proposed numerical method, a numerical example is presented along with a comparison between our numerical results and those obtained using the Legendre spectral-collocation method.
This paper presents a study of the multi-objective optimal design of a sliding mode control for an under-actuated nonlinear system with the parallel simple cell mapping method. The multi-objective optimal design of the sliding mode control involves six design parameters and five objective functions. The parallel simple cell mapping method finds the Pareto set and Pareto front efficiently. The parallel computing is done on a graphics processing unit. Numerical simulations and experiments are done on a rotary flexible arm system. The results show that the proposed multi-objective designs are quite effective.
Applications of tuned mass damper (TMD) systems for bridge structures are observed for mitigation of problem related to excessive vibration induced by either wind loading or vehicle loading, where dominant modes usually in one direction (commonly vertical) are taken into account. Considering modes dominant in one direction may not be considered as a robust practice while any bridge structure is having dominant modes along both the transverse and vertical directions and the same bridge structure is subjected to loading along both the directions. In the present study, an approach for simultaneous control of major horizontal, vertical and torsional modes is presented targeting robust vibration control under general loading condition. A strategy using modal frequency response function (FRF) is proposed based on the traditional mode-wise control approach. The proposed modal FRF based approach is applied to an existing important large truss bridge (Saraighat Bridge) to carry out an analytical design of TMD system considering general loading conditions. The designed TMD system is found to demonstrate good performance under various white-noise based general loading conditions.
In this paper, free vibration analysis of functionally graded fibers reinforced cylindrical panels is carried out by a three-dimensional mesh free model. Moving least squares shape functions in cylindrical coordinates are used for approximation of displacement field in the weak form of motion equations. Two kinds of variations of the mechanical properties in the thickness direction are considered. In the first model the fibers are assumed to be oriented in the axial direction and volume fractions of the fibers and matrix are changed continuously according to the power-law distribution. In the second model the volume fractions of constituents are constant and the fibers orientation is changed continuously in the thickness direction according to the power-law distribution. For each model various boundary conditions are considered and effects of boundary conditions, fibers orientation, exponent of volume fractions and the panel geometry on the natural frequencies are investigated.
Nowadays, design and tuning of controllers with predefined structures are among the most popular topics in control system theory. During the last decade, many studies have focused on designing fixed-structure fractional-order compensators. This paper presents a generalized version of fractional-order compensators to achieve the required magnitudes and phases at two given frequencies (for example, to achieve desired phase and gain margins with adjustable cross frequencies). In this generalization, at first some basic analysis of the phase behaviour of this introduced type of fractional-order compensators is presented. Also, exact formulas are found for designing this family of compensators in order to provide the aforementioned control objective. Finally, a numerical example is presented to confirm the effectiveness of the proposed design method in control systems.
Based on the von Karman equation and classical theory of thin plates, a set of nonlinear governing equations for a rectangular high strength low alloy (HSLA) steel plate subjected to low velocity impact is deduced, they are expressed with displacements of the mid-plane for the HSLA steel plate. By using the finite difference method and the Newmark method, the unknown variable functions are discretized in the space and time domains, the whole problem is solved by the iterative method synthetically. Numerical results denote that the thickness to length ratio, boundary conditions and initial impact velocity of the impactor have great influences on the nondimensional deflection and normal stress of the HSLA plate that subjected to low velocity impact, moreover, the initial impact velocity affects a lot on the contact force.
Owing to the complex features of blasting vibration damage assessment systems, a gradient boosted machine (GBM) model is developed for the classification of residential structure damage (RSD) due to blasting vibrations of open pit mining. Twelve indicators are defined as the indices for the prediction of RSD in the proposed model. These are: peak particle velocity, dominant frequency, dominant frequency duration, distance, maximum safe charge per delay, compressive strength of mortar joints, ratio of brick area to house area, height of residential house, roof structures, beam-column frames, quality of construction, and site conditions. The GBM model is achieved by training 108 sets of measured data of blasting vibration. A 10-fold cross-validation procedure was applied to determine the optimal parameter values during modeling, and an external testing set was employed to validate the prediction performance of the model. Two performance measures – classification accuracy rate and Cohen’s kappa – have been employed. The analysis of accuracy together with kappa for the dataset demonstrate that the GBM model has high credibility as it achieves a comparable median classification accuracy rate and Cohen’s kappa values of 91.7% and 0.875 for the prediction of RSD, respectively.
In this paper, two active control schemes are presented to improve simultaneously vehicle ride comfort and steady-state handling performance. First, adaptive H controller is designed for nonlinear vehicle suspension systems with actuator time delay based on Genetic Algorithm Wavelet Support Vector Machines and then adaptive H controller is designed based on Genetic Algorithm Mixed Wavelet and RBF Support Vector Machines. The varying sprung and unsprung masses and the suspension performances with actuator delay are taken into account simultaneously, and the corresponding mathematical model is established. The most important feature of the proposed control strategy is its inherent robustness and its ability to handle the nonlinear behaviour of the system. Simulation results show that the designed controllers can achieve good active suspension performance regardless of the variation on the sprung mass in the presence of actuator time delay.
The random vibration analysis of a four-wheeled vehicle traveling on parallel road tracks with random unevenness is considered. The two parallel road track roughnesses are modeled as a vector of homogeneous, non-isotropic, Gaussian random fields with known auto-power spectral density (PSD) functions but unknown cross–PSD functions. Questions on bounds on the response, when the unknown cross-PSD functions are varied over their permitted ranges, are considered. An exact solution to this problem, based on principles of random vibrations, is arrived at. Based on this theoretical solution, an experimental procedure to determine these response bounds on automotive structural response, without involving mathematical idealization of structural matrices, is developed. Illustrations involving numerical modeling and laboratory testing (using a four-post test rig) of vibratory behavior of a four-wheeled vehicle due to random road loads are presented.
For the trajectory tracking control problem of rigid hydraulic manipulators under heavy uncertainties and nonlinearities, a novel fractional-order nonsingular terminal sliding mode (FO-NTSM) control method based on time-delay estimation (TDE) is proposed. The proposed control scheme mainly contains two parts: a TDE term and a FO-NTSM term. The TDE term is applied to approximately cancel the complex system dynamics using the intentionally time-delayed information leading to an attractive model-free nature. Meanwhile, the FO-NTSM term, based on a novel fractional-order terminal sliding surface, is designed to stabilize the tracking error to zero in finite time. Stability of the closed-loop control system is analyzed based on the Lyapunov stability theory. Finally, comparative degrees of freedom (2-DOF) practical experiments are performed and the results show that the new proposed method can ensure faster convergence rate and higher tracking precision under heavy lumped uncertainties and nonlinearities compared with its integer-order counterpart.
The present paper is concerned with the propagation of plane waves in self–reinforced media. The velocities of quasi-P and quasi-S waves in an unbounded self–reinforced medium under initial stresses and under gravity field have been derived. Also the reflection coefficients and the partition of energy of reflected quasi-P and quasi-SV waves due to incident quasi-P and quasi-SV waves have been obtained under the influence of initial stress and gravity field. It has been noticed that the velocities, reflection coefficients and energy coefficients not only depend on the initial stress and gravity but also on the direction of propagation. The results are in agreement with the classical case in the absence of initial stresses and gravity. In presence of initial stresses and gravity field, the velocities, reflection coefficients and energy coefficients of quasi-P and quasi-S waves are calculated numerically and are presented by means of graphs.
This work addresses the control of vibrations in flexible structures caused by external harmonic disturbances using a boundary control method. The research is motivated by practical systems where beam-like structures require vibration suppression to prevent fatigue and system damage, or to increase efficiency. Importantly, this paper addresses a practical constraint of the actuation points being at the boundaries only. The method presented here is an open-loop control scheme which requires knowledge of the harmonic disturbance and a model of the flexible system. The controller uses the model, developed using the Rayleigh–Ritz method, to predict the reaction of the beam to the known input disturbance and compute an optimized control input which reduces the steady state vibration in the system. By properly choosing the cost function, the controller can be used to reduce the total vibration or to reduce the vibration in certain spatial locations. The method's vibration reduction capabilities are studied over a range of frequencies; data collected from experiments on a physical beam model is used to validate the predicted behavior of the system.
This paper presents the combination of periodic structures with nonlinearly interfaced piezoelectric elements for vibration control purposes. The nonlinear treatment consists of quickly inverting the piezoelectric voltage when the latter reaches either a maximum or a minimum value, hence shaping a voltage with a higher magnitude and reduced phase with the speed. It is shown that the nonlinear interface not only dramatically increases the damping abilities of periodic structures in stopband, but also permits significantly enlarging the latter, hence providing a very adaptive, efficient vibration damping system. Theoretical and experimental investigations on a clamped–clamped periodic beam are conducted, showing the very good abilities for efficiently damping the mechanical vibrations over a very wide frequency band.
An analytical method to obtain the natural frequencies of a cantilever beam under dry friction is described in this paper. The equations of motion of a cantilever beam under dry friction and an equivalent model are established using Lagrange equations of the first and second kinds, respectively. Then the equations expressing the relationship between exciting force and natural frequency are acquired according to the established equations. Lastly, based on the equivalent method of input energy between the two models, we deduce an analytical expression that is concerned with the natural frequencies of the cantilever beam under dry friction. The proposed method verified by numerical results reveals that the results between the analytical and numerical methods are in better consistency with each other. Besides, on account of the natural frequency strongly influenced by friction force, the model can be used as a feasible shock absorber for some structures over a wide frequency range. This is important because the analytical expression obtained by the proposed method can directly indicate the influence of the dry friction on the natural frequencies of a cantilever beam.
Model-based trajectory planning algorithms are capable of providing a high level of performance. However, they are often lacking in robustness, which severely limits their field of application. In this paper the method of parametric desensitization is applied to nonlinear models, providing a feasible solution to the problem of robust model-based trajectory planning for nonlinear plants with parametric uncertainties. By using an indirect variational solution method, the necessary optimality conditions deriving from Pontryagin's minimum principle are imposed, and lead to a differential two-point boundary value problem; numerical solution of the latter is accomplished by means of collocation techniques. The method is applied to two test cases: a nonlinear spring–mass system and a flexible link manipulator with Coulombian friction. Results show that the technique developed in this paper can significantly improve the robustness of the resulting trajectory to parametric model mismatches in comparison with the conventional method.
Shake tables are essential facilities in the laboratory for evaluating structural performance subject to vibration excitation. In this paper, to improve the time waveform replication accuracy of electro-hydraulic shake tables (EHSTs), an improved feedforward inverse control algorithm with adaptive refinement is proposed. The EHST system transfer function and stable inverse model is firstly estimated and designed by multi-step recursive extended least squares algorithm and zero magnitude error tracking controller technology, respectively. To reduce the side effect of model identification errors between the estimated and actual system, a system model corrector is further identified based on the previous estimated EHST model and an inverse corrector is obtained so as to constitute the improved feedforward inverse controller (iFIC) by cascading the inverse corrector to the previous designed inverse model. Then, an adaptive refinement controller using a least mean square algorithm is applied to the iFIC controlled system to cope with system uncertainties and nonlinear effects. Therefore, the proposed algorithm combines the merits of feedforward inverse control and adaptive control. Finally, with the help of xPC rapid prototyping technology, experiments are conducted on a real uniaxial EHST system and the experimental results demonstrate that the proposed algorithm exhibits a better tracking accuracy than the conventional controllers for shake tables.
This paper presents a new numerical method for solving fractional optimal control problems (FOCPs). The fractional derivative in the dynamic system is described in the Caputo sense. The method is based upon Bernoulli polynomials. The operational matrices of fractional Riemann–Liouville integration and multiplication for Bernoulli polynomials are derived. The error upper bound for the operational matrix of the fractional integration is also given. The properties of Bernoulli polynomials are utilized to reduce the given optimization problems to the system of algebraic equations. By using Newton’s iterative method, this system is solved and the solution of FOCPs are achieved. Illustrative examples are included to demonstrate the validity and applicability of the technique.
Some active vibration control methods are based on mathematical models. In these cases, parameter variations play an important role in the system performance. As it is not possible to know in advance the precise values for all parameters of the mechanical system, a possible alternative is to design robust controllers that take into account the uncertainties. In this context, this work presents a vibration active control technique devoted to rotating machinery by incorporating electromagnetic actuators, which considers uncertainties in the parameters of the system. the gains of the electromagnetic actuator are determined by using linear matrix inequalities, which consist in a powerful tool for the cases in which parameter uncertainties are taken into account. In addition, Kalman estimators are employed to deduce the modal states of the system. The model of the rotating system is obtained by using the finite element method and the potentiality of the methodology for applications in engineering was investigated through experimental tests.
Free in-plane and out-of-plane vibrations of two-dimensional magnetically affected ensembles of single-walled carbon nanotubes (MAESWCNTs) are of concern. Using Maxwell’s equations, nonlocal Rayleigh, Timoshenko, and higher-order beam theories, and Hamilton’s principle, the discrete equations of motion of both in-plane and out-of-plane vibrations for the proposed models are constructed. When the number of single-walled carbon nanotubes (SWCNTs) within the ensemble is large enough, evaluation of the frequencies of the nanostructure would not be an easy task. To overcome such a dilemma, some useful nonlocal continuous models are proposed. Through various numerical studies, the accuracy of such models is validated. The obtained results display that the in-plane and out-of-plane frequencies rely on the strength of the longitudinal magnetic field, small-scale parameter, number of SWCNTs with the ensemble, intertube distance, and the geometrical properties of the constitutive SWCNTs of the ensemble. The roles of these crucial factors in the fundamental frequencies of the MAESWCNTs are comprehensively examined via many numerical studies. The capabilities of the proposed nonlocal continuous models in predicting the bending frequencies are also discussed.
This study proposes an application of modal active control to musical string instruments. Its aim is to control the modal parameters of the soundboard in order to modify the sound of the instrument. Using both state and derivative state modal control, a method is given, from the modeling of the active structure through to the design of the control system. Issues such as the identification of the structure’s characteristics or the stability of the control system are dealt with for this original control method. Then, this technique is applied to a model of a simplified string instrument soundboard. Time simulations are conducted to study its effect on the instrument vibration. They show that, thanks to soundboard modal active control, it is possible to modify the amplitude of the sound harmonics to change the timbre as well as the sound level of the instrument.
In this study, an innovative technique is introduced for application of annular tuned liquid dampers (ATLD) in wind turbines subjected to seismic ground motions. The performance of ATLD in mitigating the vibration of wind turbines is investigated using numerical simulations. The wind tower is modeled using finite element method while the fluid domain is simulated by finite volume method. The numerical study considers the dynamic behavior of ATLD under different seismic records. Also, the effects of earthquake amplitude and frequency content, structural damping and detuning on the interaction between the tower and ATLD are investigated. The results of time-history analysis show that the ATLD is effective in mitigating the response of a wind turbine when subjected to large-amplitude seismic loading. The wind tower equipped with the proposed ATLD also behaves in the elastic range of response during the considered earthquake records which is critical for the integrity and safety of these structures.
The vibration signals from sensors monitoring the activity of individual bearings in a power train unit may be linear instantaneous mixtures of vibrations generated by various dynamic components. Generally, an exact physical model describing the mixing process and the contribution of each dynamic component to the received sensor signal is not available. Vibration source signals from defective bearings often overlap in time and frequency, and, as such, the direct use of time- and frequency-domain methods may result in erroneous diagnostic information. This paper implements blind source separation (BSS) to demix sensor signals into correctly identifiable vibration source signals without the need of the vibration path property and sensor layout. Experimental vibration data from spalled, corroded, and healthy rotorcraft bearings are used with five representative BSS algorithms. The separation accuracy of these algorithms is then compared using various performance metrics. Results show that despite the inherent statistical dependence and near Gaussianity, it is possible to isolate vibration sources from mixed sensor signals using second- and higher-order statistics of the signals. The paper also identifies the limitations of the BSS technique and provides a remedy and recommendation for its implementation in rotorcraft bearing fault detection.
A wave-based analytical method is applied to study vibrations in simple spatial structures. From the wave vibration standpoint, vibrations are described as waves propagating along uniform structural elements and being reflected and transmitted at structural discontinuities. Coupled in- and out-of-plane bending, axial, and torsional vibrations are studied based on classical vibration theories. Both free and forced vibrations are studied. Natural frequencies, modeshapes, as well as frequency responses due to various external excitations are obtained. The results obtained using the wave vibration approach are verified both experimentally and through comparison to results available in the literature. Good agreements have been reached. This study provides not only exact analytical solutions to complex vibration problems in spatial structures that have mostly been relying on numerical tools, but also a benchmark to existing numerical solutions.
Noise and vibration induced by turbulent boundary layer (TBL) wall pressure is a widespread issue for aircrafts and vehicles. One way to alleviate this problem is to enhance the structure’s sound isolation performance using active structural acoustic control. It is often difficult and costly to generate TBL excitation in laboratories for academic research, especially when the convection velocity is high. Thus, a numerical investigation in the early stages of research is appropriate. This paper proposes a prototyping method. The updated TBL semi-empirical model is chosen through a detailed survey of relevant literature. A tensioned panel used as a control target is intended to simulate realistic aircraft flight conditions. Decentralized control law is considered for active control. A finite element model is built which takes into account the property of TBL excitation. A model reduction technique is also adopted to decrease the order of the analysis model. Numerical simulation results show that the pre-stress effect and the hydrodynamic coincidence have a significant influence on plate vibro-acoustic performance and control channel number selection. Decentralized control of the tensioned plate structure under the pressure of TBL excitation is revealed in this work. A virtual prototyping loop justifies the control law’s effectiveness for analyzing TBL excitation. Finally, the procedure proposed may be extended to use in other models or real-life applications.
In this work, a new theory of thermoelasticity has been derived based on fractional order of strain (fraction order Duhamel-Neumann stress-strain relation). A new unified system of differential equations that govern seven different models of thermoelasticity in the context of one temperature type and two-temperature types (14 different models of thermoelasticity) has been constructed. The second part of this work, applications of thermoelasticity with fractional order strain for an isotropic and homogenous one-dimensional elastic half-space based on one-temperature thermoelasticity of Biot, Lord-Shulman, Green-Lindsay and Green-Naghdi type II models have been solved.
The dynamic response of a beam under a moving load is a superposition of two components, namely, the moving-frequency component corresponding to the moving load and the natural-frequency component of the beam. This study investigates the closed-form solution of the dynamic response of a damaged simply supported beam subjected to a moving load and examines the effects of the loss of local stiffness on these two components. The study provides deep insights into beam damage detection based on moving load-induced response. Consequently, a simple and intuitive method for damage localization is developed. First, the closed-form solution is derived based on the modal perturbation and modal superposition method. The closed-form solution enables the individual examination of damage-induced changes in moving- and natural-frequency components. The results show that the moving-frequency component is preferred in damage localization. Then, multi-scale discrete wavelet transform is employed to separate the moving-frequency component from the total dynamic response and to subsequently locate the damage. Numerical examples with single or multiple damages are utilized to validate the efficacy of the proposed response computation algorithm and to demonstrate the effectiveness of the corresponding damage localization method. The effects of moving velocity and noise level are carefully studied. In particular, the effects of varying moving velocities and moving vehicular dynamics on damage localization are presented in this paper.
Nanoscale spheres have led to a growing interest in their potential applications in a wide range of technological fields. Hollow nanospheres can be modelled as closed spherical shells in the analysis of their mechanical behaviour, the ratio of thickness to radius being used to ascertain the pertinence of considering only membrane forces, or both membrane forces and bending moments. Nonlocal elasticity theory has been widely used to analyze the mechanical behaviour of nanostructures. This paper investigates the free axisymmetric vibration of nanoscale spherical shells accounting for both types of internal force, by extending the Kirchhoff–Love plate theory to Eringen nonlocal elasticity theory. The influence of coupled size and bending effects on the frequencies and modal shapes is studied, revealing specific features that cannot be observed in an uncoupled analysis. This study could be useful in biomedical and bioengineering applications as well as in other fields related to nanotechnology.
This paper investigates the nonlinear dynamics of microarches with internal modal interactions; the nonlinear size-dependent motion characteristics are analyzed for the system with two-to-one and three-to-one internal resonances. The partial differential equation of motion is discretized into a set of second-order nonlinear ordinary differential equations via the application of the Galerkin scheme. The linear natural frequencies of the system are obtained by eliminating the nonlinearities; these are used to verify the occurrence of modal interactions. The nonlinear resonant dynamics are examined via the pseudo-arclength continuation technique for the systems with internal modal interactions.
Vibration suppression is one of the most important challenges of flexible multi-body dynamic systems. In this paper, a launch vehicle with flexible bodies and fuel sloshing is considered as a flexible multi-body dynamic system. The aim of this paper is to propose a vibration suppression strategy for attitude control of the vehicle based on sub-band adaptive filtering. The advantages of the sub-band analysis leads to the design of a new vibration control system that can simultaneously attenuate the effects of three unknown vibration disturbances. In this regard, the simulation results of a nonlinear dynamic model of the vehicle with the filtering strategy confirm the valuable performance of the proposed vibration suppression approach.
In order to reduce the excessive longitudinal vibration of a suspension bridge induced by vehicle braking forces (as one of the possible dynamic loadings) and earthquake excitations, a mixed control methodology using magnetorheological (MR) dampers is developed in this study. Firstly, the corresponding preferred controls subjected to vehicle braking forces and earthquake excitations, separately, are obtained by simulation analyses for seven control strategies. Then, a mixed control system is established to obtain the best control efficiency and reduce the energy consumption of MR dampers, based on the displacement responses and changing rate of accelerations. Finally, this system is applied to reduce the longitudinal vibration responses of the Pingsheng Bridge. The numerical results show that the passive-on control and the semi-active fuzzy control are the corresponding preferred controls subjected to vehicle braking forces and earthquake excitations, respectively. The mixed control has a good agreement with the corresponding preferred controls under four dynamic loadings including the vehicle braking forces, the Pingsheng Bridge earthquake wave, the El Centro wave, and the Takochi-oki wave, which verifies the reliability and effectiveness of this system. The mixed control has good performance and applicability for different loading combinations composed of vehicle braking forces and earthquake excitations.
A pulsed-laser ablation method for non-contact experimental vibration analysis of completely submerged underwater structures is proposed. Although impact testing with an impulse hammer is commonly used for vibration analysis due to its simplicity, impact testing has limited use in underwater conditions. An input-detection-free frequency response function measurement in water will greatly contribute to the development of high-precision and high-speed positioning autonomous underwater vehicles, underwater vehicle-manipulators, underwater robots, submarines, etc., which are used in dangerous conditions (e.g., deep oceans, under ice, and nuclear reactor plants). To achieve these high-performance underwater systems, vibrations due to hydrodynamic parameters (such as added mass, buoyant force, drag force, and damping coefficient) should be suppressed, and vibration tests should be conducted on the actual equipment submerged in water. The proposed method yields the frequency response function by applying a pulsed-laser-ablation excitation force to an underwater structure and measuring the output using a laser Doppler vibrometer. Because the direction, strength, and effective duration of the pulsed-laser-ablation force are essentially constant, this force can be estimated by measuring these properties in advance. Hence, the proposed method realizes input-detection-free frequency response function measurements in underwater conditions.
This study investigates the dynamic properties of the thickness tapered laminated composite plate. The governing differential equations of motion of the various configurations of a thickness tapered composite plate are presented in the finite element formulation using classical laminated plate theory. The validity of the developed finite element formulation is demonstrated by comparing the natural frequencies evaluated using the present finite element method with those derived from the experimental measurements and presented in available literature. Various parametric studies are also performed to investigate the effect of taper configuration, aspect ratio, taper angle and ply orientation on free vibration responses of the structures. The comparison of the free vibration mode shapes of uniform and various tapered configurations of tapered laminated composite plates are also presented. Influences of taper angle on the free vibration fundamental mode shapes under various boundary conditions and various ply configurations are also presented. The forced vibration response of a composite plate is also investigated to study the dynamic response of tapered composite plate under the harmonic force excitation in various tapered configurations. It is concluded that the dynamic properties of a composite plate could be tailored by dropping of the plies to yield various tapered composite plate.
This paper proposes system identification models of smart concrete structures equipped with magnetorheological (MR) dampers under a variety of high impact loads. The proposed model was used to predict and analyze the highly nonlinear behavior of integrated structure-control systems subjected to impact loading. Highly nonlinear behavior of the integrated structure-MR damper was represented by a wavelet-based time delayed adaptive neuro-fuzzy inference system (W-TANFIS). To generate sets of input and output data for training and validating the proposed W-TANFIS models, experimental studies were performed on a smart reinforced concrete beam under a variety of impact loads. The impact forces and current signals on an MR damper were used as input signals for training the W-TANFIS to predict the acceleration, deflection, and strain responses. As a benchmark, an adaptive neuro-fuzzy inference system (ANFIS) was used. It was demonstrated that the proposed W-TANFIS framework is effective in anticipating the structural responses of the reinforced concrete beam-MR damper system subjected to impact loading. In addition, the comparison of the W-TANFIS and ANFIS models demonstrated that the W-TANFIS model has better performance over the ANFIS model.
It is generally accepted that active control systems provide better structural performance when compared to their passive counterparts. On the other hand, the design of active control systems based on linear control theory is highly dependent on the structural properties. For this reason, their performance is expected to be affected more severely by variations in structural properties compared to those of passive systems. These variations can occur due to nonlinear structural behavior, or even before that due to uncertainties in the estimation of these properties and in numerical modeling. The present work is an investigation of the dependency of various control systems used for supplemental energy dissipation to the changes in structural properties. For this purpose, the performance degradations of most common control systems are studied for structures entering their nonlinear response range. The considered control systems include active control using linear quadratic regulator algorithm and passive control using viscous fluid dampers and yielding devices. These control systems are optimized separately for linear and nonlinear structures by minimizing performance indices based on inter-story drift and absolute acceleration response. It is shown that among these control systems, viscous dampers are affected the least by the alteration of structural properties, which may further support their utilization contrary to the more costly active control systems. It is also shown that the amount of performance degradation depends on the selected structural performance index, and more importantly, the severity of the earthquake excitation.
Induction motors, key elements for industry, are susceptible to one or more faults at the same time; yet, they can keep working without affecting the process, but increasing the production costs. For this reason, a monitoring system that can efficiently diagnose the induction motor condition, even under multiple combined faults, is a demanding task. In this work, a methodology and its implementation into a field programmable gate array for an online and real-time monitoring system of multiple combined faults are presented. First, the fractal dimension approach, using the Katz algorithm, is introduced as a measure of variation of 3-axis startup vibration signals for the induction motor condition, considering that these signals describe changes on its dynamic characteristics due to the different faults. Then, an artificial neural network determines in an automatic way the induction motor condition according to the fractal dimension values. The obtained results show a higher overall efficiency than previous works for detecting broken rotor bars, outer-race bearing defects, unbalance, and their combinations, as well as a healthy condition.
We find the deformation and stresses occurring in an infinite rod of a magnetizable material with square normal cross-section, subjected to an external, transversal and initially uniform magnetic field of arbitrary direction. The numerical solution of the uncoupled problem is obtained using a boundary integral method. This yields the boundary values of all the unknown functions of the problem. The results are discussed in detail. Applications concern the calculation of stresses in straight portions of elastic, magnetizable cylinders subjected to transversal magnetic fields.
This experimental study was conducted for the purpose of enhancing vibration suppression in periodically excited flexible structures by using model predictive control (MPC), an advanced optimal-control method that can be used to handle system constraints at all sampling steps. The Hildreth optimization solver was used to examine two MPC strategies, a basic MPC strategy and a repetitive MPC (RMPC) strategy, and the active vibration-control design and performance of the strategies were evaluated. The disturbance-rejection performance of the applied MPC methods was specifically investigated by using periodic input signals to excite a piezoelectric flexible beam. These comparative studies performed together with parameter analysis offer a design guideline for achieving satisfactory vibration-suppression performance and further demonstrate that the applied RMPC method can effectively suppress the vibration of a flexible-structure system.
In this paper, the effect of rotation on the radial vibrations of elastic hollow cylinder is studied. The fundamental equations of elastodynamic have been solved in terms of radial displacement. The equation of elastodynamic is solved in terms of radial displacement. The frequency equation is obtained when the boundaries are free, fixed and mixed boundary conditions are calculated numerically. The determination is concerned with the eigenvalues of the natural frequency of the radial vibrations in the case of harmonic vibrations. It was shown that the dispersion curves of guided waves were significantly influenced by the rotation of the elastic cylinder. The results obtained theoretically have been computed numerically and are presented graphically The results indicate that the effect of rotation is very pronounced.
This paper presents an input shaping strategy for vibration control of multimode systems. The strategy combines the use of single-mode input shaping techniques with a model-based frequency-modulation system. The strategy utilizes the fact that a single-mode input shaper can eliminate vibrations in a multimode system provided that, there exists a common frequency for which all frequencies of the system are odd multiples of that common frequency. Model-based feedback is used to modulate the frequencies of the system to the point where the odd multiple frequencies condition is satisfied. The primary mode frequency of the model-based feedback system is designed to be the common frequency that satisfies the aforementioned condition. Several single-mode input shapers are implemented with design frequencies equal to the primary mode frequency of the modulated system, thus eliminating vibrations in all modes of the system simultaneously. Simulations and experiments on multiple pendulum models are used to demonstrate the effectiveness of the performance of the frequency-modulation input shaping strategy.
We study curious dynamical patterns appearing in networks of one ring of cells coupled to a ‘buffer’ cell. Depending on how the cells in the ring are coupled to the ‘buffer’ cell, the full network may have a nontrivial group of symmetries or a nontrivial group of ‘interior’ symmetries. This group is Z 3 in the unidirectional case and D 3 in the bidirectional case. We simulate the coupled cell systems associated with the networks and obtain steady states, rotating waves, quasiperiodic behavior, and chaos. The different patterns seem to arise through a sequence of Hopf, period-doubling, and period-halving bifurcations. The behavior of the systems with exact symmetry are similar to the ones with ‘interior’ symmetry. The network architecture appears to explain some features, whereas the properties of the Chen oscillator, used to model cells’ internal dynamics, may explain others. We use XPPAUT and MATLAB to numerically compute the relevant states.
This paper aims to study the dispersion of torsional surface waves in a non-homogeneous anisotropic layer over heterogeneous half-space. We consider the inhomogeneity varies exponentially with depth in the layer and in half-space three types of heterogeneities, namely, quadratic, hyperbolic and exponential are assumed. The dispersion equation has been deducted for each case in a closed form by means of variable separable method. It has been observed that for homogeneous isotropic upper layer over a homogeneous half-space, the velocity of torsional surface waves coincides with that of Love waves. Dispersion curves are plotted for different variation in inhomogeneity parameters. The effects of the medium characteristics on the propagation of torsional surface waves are discussed.
This paper studies the problem of dynamic inflow below the rotor disk for skewed flow. With the information from the adjoint inflow equations plus the normal states, one can calculate the velocity in the hemisphere below the rotor disk plane without losing accuracy or convergence rate. The methodology enables one to calculate the velocity below the rotor disk with the finite-state method with the only cost of adding the uncoupled co-states. The three components of inflow are considered here and compared with the results from the convolution integrals. Numerical results in the frequency domain for simple harmonic motion show the effectiveness of the new method in three-dimensional inflow with big skew angle below the rotor disk.
In order to improve the acoustic source identification performance of beamforming when ground reflection exists, an array point spread function was derived and a corresponding non-negative least squares deconvolution method was given for a mirror-ground beamforming method. Simulations of a known acoustic source indicate that the given method is correct, and it could not only clear the acoustic source identification results effectively by improving the spatial resolution and attenuating the sidelobe interference, but it could also be superior to the conventional beamforming deconvolution method. On this basis, experiments were conducted to validate the correctness of the simulations and the effectiveness of the mirror-ground beamforming deconvolution method in practical application.
The present paper investigates the transverse vibrations and stability of a moving skew thin plate made of functionally graded ceramic–metallic material. The material properties are assumed to vary continuously through the thickness according to a power-law distribution of the volume fractions of the constituents. The Voigt's rule is used to estimate the effective material properties from the volume fractions and the properties of the constituent materials. By the coordinate transformation, the differential equations of motion of the moving functionally graded material (FGM) skew plate are obtained in oblique coordinate system. The boundary conditions with simply supported and clamped edges are obtained in oblique coordinate system. The vibration frequencies are obtained from the solution of a generalized eigenvalue problem. The entire computational work is carried out in a normalized square domain obtained through an appropriate domain mapping technique. Results of the reduced problem revealed excellent agreement with other studies. The dimensionless complex frequencies of the moving FGM skew plate are calculated by the differential quadrature method. The effects of gradient index, aspect ratio, and dimensionless moving speed on the transverse vibration and stability of the moving FGM skew plate are analyzed. Results are furnished in dimensionless amplitude–frequency curves for different dimensionless moving speed and representations of some vibration mode shapes are shown.
An adaptive random control method is presented for a two-axis redundantly actuated electro-hydraulic shaking table system to replicate the reference acceleration power spectral density (PSD). The redundant force controller is developed to reduce the cross-coupling among the actuators. The offline iterations are implemented in conventional random control to compensate for the changes in the frequency response function of the system. Stability and responsiveness of control are determined by operator-selected parameters. In adaptive random control, the reference PSD is transformed into time domain histories by filtering white noise. The adaptive finite impulse response (FIR) filters are used to model and track the inverse system online. The weights of the FIR filters are updated by the forgetting factor recursive least-squares algorithm. The time histories are corrected by the copy of the inverse model. Experimental results obtained in step response and PSD replication demonstrate the effectiveness of the proposed control method.
Bearings are an essential component in all types of rotary equipment. Erosion in the bearing is unavoidable due to radial and axial forces permanently acting on the bearing during the course of rotation. In order to avoid catastrophic breakdown of the equipment, it is a fundamental requirement to monitor the bearings. The scope of the existing bearing fault diagnosis techniques in the literature is limited to only pre-known bearing and machinery. On the contrary, this research develops a generalized protocol for detecting ‘inner’ and ‘outer’ race bearing faults for any unknown rolling element bearing. This automated bearing failure detection model tunes itself adaptively to any type of rotary equipment and the bearing. Automated bearing failure detection is based upon using wavelet transform to scan the spectral contents and applies envelop detection. The raised asynchronous energy in the envelop spectrum is a potential indication for the bearing faults.
In this study, a frequency-dependent algorithm is proposed in independent modal space as an improvement to the linear quadratic Gaussian (LQG) control algorithm. The passive control parameters such as mass, stiffness and damping of a dynamic system are sensitive to different frequency ratios when subjected to external excitation. Depending upon the sensitivity of these parameters, the algorithm is developed in such a way that a response reduction similar to that of an LQG algorithm can be achieved with a significantly smaller control force. An effective gain is obtained by optimizing the H 2 norm of the transfer function. It is observed from the results that the algorithm works well for high frequency ratio and near resonance regimes. Thus, a combination of the LQG and the proposed algorithms is considered as a modified LQG control algorithm, where the effectiveness of both algorithms is utilized. The efficiency of the modified LQG control algorithm is demonstrated by considering a base-isolated structure when subjected to earthquake base excitations. By comparing with the results it is observed that the modified LQG control algorithm is more efficient in terms of response reduction with a much lower control force as compared to the LQG control algorithm. It is envisioned that the modified LQG control algorithm will be highly useful for response control of base-isolated structures.
Model reduction is a significant issue in dynamic system simulation and control, as a consequence of the unmanageable levels of storage and computational requirements for large-scale systems. In this paper, the concept of a balanced truncation approximation method is extended to large-scale systems with interval uncertainties to get the reduced-order model with uncertainties. In order to get the balanced system, the balancing transformation matrix is introduced by using the nominal system, and the reduced-order model with uncertainties is obtained by using balanced truncation. A major characteristic of this model reduction method is that the reduced-order model obtained in this way is also as uncertain as the original model. The closeness of the reduced-order model to the original model relies on the upper bounds of the ignored Hankel singular values. To compare the original model and the reduced-order model, a perturbation method is proposed to give the interval bounds of the responses of the original model and the reduced-order model. As applications of the proposed method, three numerical examples are given.
In this paper, an efficient analytical solution method, namely, multi-level residue harmonic balance, is introduced and developed for the nonlinear vibrations of multi-mode flexible beams on an elastic foundation subject to external harmonic excitation. The main advantage of this solution method is that only one set of nonlinear algebraic equations is generated in the zero level solution procedure while the higher level solutions for any desired accuracy can be obtained by solving a set of linear algebraic equations. In other words, the computation effort to find more accurate nonlinear solutions is much less. In this paper, a multi-mode formulation, which represents the nonlinear beam vibration, is derived and set up. Then, the solution procedures are developed for obtaining the nonlinear multi-mode solution. The results from the multi-level residue harmonic balance method agree well with those from a numerical integration method. The effects of various parameters such as vibration amplitude, foundation modulus coefficient, damping factor and excitation level etc., on the nonlinear behaviors are examined. A convergence study is also performed to verify the solutions. The stability analysis is conducted using the virtue of Floquet theory and steady-state solutions are investigated.
The dynamic vibration absorber (DVA) has attracted attention since its invention. This paper deals with the optimization problems of the standard DVA and two other models of DVA called three-element DVA and non-traditional DVA for damped primary structures. Unlike the standard configuration, the three-element DVA contains two spring elements in which one is connected to a dashpot in a series and the other is placed in parallel. Meanwhile the non-traditional DVA has a linear viscous damper connecting the absorber mass directly to the ground. There have been some studies on the design of three-element and non-traditional dynamic vibration absorbers in the case of undamped primary structures. These studies have shown that both three-element and non-traditional DVAs perform better than the standard DVA. When the primary structure is damped, there are very few studies on the three-element and non-traditional DVAs in the literature. This article proposes a global-local approach to give approximate analytical solutions of the
An approach for correlating the given forced response with the nonlinear normal mode utilizing the modal assurance criterion is explored. The problem is transformed into a nonlinear optimization problem with nonlinear constraints. The modal assurance criterion of the Fourier coefficient vectors which indicates the degree of correlation between the nonlinear normal mode and forced response is set as the objective function whereas the nonlinear constraints are built utilizing the harmonic balance method and the Floquet theory. With the aim to make the modal assurance criterion approach to 1, the unknown optimization variables including the Fourier coefficients and the nonlinear frequency are iteratively sought using the sequential quadratic programming algorithm to fit the given periodic solution. Finally, the validity of the proposed method is demonstrated via two numerical case studies. It is illustrated that the proposed approach can be used to construct the relationship between the nonlinear normal mode and forced response. In addition, numerical examples also confirm that resonance forced responses are in the neighborhood of nonlinear normal modes.
In this paper a novel method based on geometric illustration and frequency response analysis is proposed for evaluating the performance of mathematical morphological (MM) operators in vibration signal processing. With geometric illustration, the working mechanism of MM operators can be disclosed and the frequency response is studied to select suitable MM operators and structural element length. The advantage of combining geometric illustration and frequency response analysis is that it does recognize the characteristics of MM operators which are used to signal denosing or feature extraction. Selection suggestion and comprehensive explanation of MM operators for different purpose are supplied for vibration signal analysis. The paper also proposes a new operator called CMF-hat to extract the impulsive-type signal for bearing fault detection. The experimental results show that CMF-hat can effectively extract the fault features, and the proposed evaluating method advances selection of MM operators and improves the accuracy of fault diagnosis.
There are low frequency horizontal vibration problems in varying degree on the stator frame for operating giant hydro generator unit, those who adopted flexible support. To determine the cause of excessive vibration, the horizontal vibration of the stator frame and core were measured under the operating conditions of variable rotate speed, variable load and variable excitation. The results showed that the low frequency vibration had similar vibration characteristics in each generator unit, that is, the vibration of the stator increased as the excitation increasing and it did not matter to the change of rotate speed and load. This low frequency vibration was obviously caused by the unbalance magnetic pull. Based on the uneven of air gap, which induced by uneven magnetic pole morphology and relative eccentricity of the stator-rotor, low frequency vibration was explained.
Although flapwise bending vibration of rotating tapered beams has been extensively studied since the 1970s, most of these studies were based on approximations with varying degrees of accuracy and complexity. The flapwise bending vibration of rotating tapered beams is re-examined in this paper using the technique of variational iteration, which is relatively new and capable of providing accurate results for eigenvalue problems with good convergence. Natural frequencies and mode shapes of rotating beams are extracted for various rotational speeds and taper ratios, and solutions are compared with results published in the literature where available.
The fault diagnosis and prognosis of low speed machines remains a difficult problem despite remarkable advances in the conditional monitoring domain. The Rolling-element bearing is a vital part of these machines and its failure is one of the main causes of machine breakdown. In order to have an efficient maintenance strategy, fault diagnosis of a bearing and time estimation of its remaining useful life is needed. However, conventional vibration analysis at very low speeds generally fails to detect vibrations issued from a faulty bearing due to its low energy, high and variable loading conditions and to the noisy environment generated by other mechanical components of low speed machines such as gearing systems. In this work, instantaneous angular speed (IAS)-based fault diagnosis is introduced in order to compensate for the shortcoming of conventional monitoring techniques since it is strictly synchronized to shaft rotation and much less dependent on the transfer path between the defect and the sensor contrary to vibration and acoustic emission analysis. At very low speeds and in the case of a seeded spall on the bearing’s race, the shaft IAS reveals the shaft dynamical behavior when the rolling element passes into the spall. It is proven that this behavior is different when entering the spall than when exiting. The determination of entrance and exit moments allows a precise fault size estimation which is a critical step for bearing prognosis. The proposed fault size estimation method is tested on different seeded spall widths at different low speeds. The results gave a satisfactory fault width estimation and show that IAS measurement is a promising tool for the health monitoring of very low speed machines.
Recently, viscoelastic materials have been widely used for vibration control due to their efficacy and flexibility in real engineering problems. Their use as constitutive parts of dynamic vibration absorbers requires the investigation of these materials under different operating situations. In the optimal design of the absorbers, it is essential to know how the dynamical properties of the viscoelastic materials change with temperature. In a previous work, the authors presented a methodology to optimally design a linear viscoelastic dynamic vibration absorber to be attached to a cubic nonlinear single-degree-of-freedom system, in a given temperature. In the present work, a study of how temperature variations affect the optimal design of two viscoelastic absorbers, made of distinct materials (neoprene and butyl rubber), is addressed. The mathematical formulation of the problem is based on the concept of generalized equivalent parameters and the harmonic balance method is employed in the solution stage. A cubic nonlinearity in the primary system is considered and the four parameter fractional derivative model of viscoelastic materials is used. Numerical simulations are performed using a recursive equation, in order to find the new characteristics of the absorbers at different working temperatures. The results show that the answer depends not only on the temperature and the material, but also on the magnitude of the excitation load imposed to the system. For a low magnitude of the excitation load, it is verified that the neoprene absorber is less affected by a temperature variation, in terms of its vibration control capabilities. On the other hand, a large magnitude of the load can significantly affect the performance of both considered devices when the working temperature is different from the design temperature.
It has been known for a long time that the problem of identifying two small cracks in a simply supported beam from the first three natural frequencies can be analytically formulated and solved if the two cracks have equal severity. In this paper we extend this result to the case of cracks with different severity. Each crack is simulated by a rotational elastic spring and the inverse problem is solved in terms of the damage-induced changes in the first four natural frequencies. Closed-form expressions of the damage parameters in terms of the measured frequencies are obtained. The results can be extended to the identification of two cracks in a longitudinally vibrating beam based on a suitable set of natural frequency and antiresonant frequency data. Numerical simulations support the theory, and show that if accurate input data are available and the cracks are not too close, then damage identification leads to satisfactory results.
In this paper we investigated the propagation of SV-waves under effect of the magnetic field, initial stress and two thermal relaxation times. The problem of reflection and transmission of thermoelastic waves at a solid-liquid interface in presence of initial stress and magnetic field has been investigated subjected to certain boundary conditions. The appropriate expressions to find the amplitudes ratios for the incident wave (SV-waves) have been obtained. The reflection and transmitted coefficients for the incident SV-waves are computed numerically, considering the initial stress, relaxation times, and magnetic field effect and presented graphically. The results indicate that the effects of magnetic field, initial stress and two thermal relaxation times are very pronounced.
In this study, a novel five-dimensional hybrid manipulator applied to multi-dimensional (MD) vibration isolation is proposed, a semi-active fuzzy optimal control model is established and the performance of the isolator is validated by the MD vibration isolation experiments. In the hybrid manipulator, the translations and rotations of the manipulator are decoupled and each actuator is replaced by a subsystem combining a magnetorheological (MR) damper with a spring to realize the spatial MD vibration isolation. The primary structure of this MD vibration isolation system (VIS) or multi-dimensional vibration isolation system (MDVIS) is described and the relating isolation principle is explained. Consequently, the closed dynamic model is established so that a fuzzy control model is built to implement vibration control. In the control model, the optimal damping force is obtained from an
Down-the-hole hammer (DTH) drilling is an air hammer drilling technique designed for drilling through bedrock and features a typical drill string length of 200 m or shorter due to its technical specifications. During DTH drilling of granite-like hard rocks, the impacts of the piston-bit-rock system cause the drill string to generate severe vibration and noise pollution. In addition, the rapid wear of the button bit and drill string significantly decreases the drilling efficiency. Based on a distributed parameter drill string model of a DTH, this paper studies the phenomenon of the drill string’s axial forced vibration with a periodic impacting force under DTH drilling in an innovative manner. With the focus of study on the DTH button bit, the transient impact force on the button bit during the drilling of the piston-bit-rock system is determined, and the impact force is converted to a periodic excitation force function using polynomial fitting. Then, the periodic impulse is transformed into a harmonic series using Fourier transforms, and finally, the drill string vibration response under the harmonic excitation force series is determined. The results reveal that a periodic impulse can mainly be determined by the nature of the DTH drill string and rock and the impact frequency during drilling. Further evidence demonstrates that at least one frequency component of the impulse harmonic series will be equal to the modal frequencies of the drill string insofar as the condition
Satellite communication systems are now designed according to an outdated Shannon information theory where all data is transmitted in meaningless bit streams. In this article, a novel noise free digital image communication via satellite has been developed. The proposed scheme is based on fractional compression and a new block cipher cryptosystem based on S8 substitution boxes transformation. The fractal compression technique is selected to compress the aerial images due to its high compression capability. The fractal image compression of the input aerial image is the first stage in the encoding phase. The fractal compression technique divides the original image into two different block sizes called range and domain blocks. The best match between the range and domain blocks is known as the transformation mapping. All the transformation mappings are recorded as the output-compressed file of the input aerial image.
A rotor supported by hydrodynamic bearings may undergo unstable motion and may exhibit several nonlinear phenomena in the vicinity of the critical stability speed. This paper presents a stability analysis of a flexible rotor supported by journal bearings using a nonlinear dynamic model and a short bearing approximation. Numerical continuation is applied to determine the boundaries of stability and the bifurcations of the limit cycles. Nonlinear phenomena such as jumping motion and bi-stability domain are predicted. An extended stability chart has also been determined including the domains of stable oscillatory motion. The investigation also includes the effect of rotor flexibility and bearing characteristics on the stability boundaries and on the safe operating speed range. For a selected range of bearing parameters, two Hopf bifurcation regions are found for high rotor stiffness, three regions for low stiffness and four bifurcation regions in transition between high and low stiffness. It has also been found that the stable operating speed range decreases with rotor flexibility and bearing parameter.
Plates, cylindrical and spherical shells, and in general, doubly curved shell panels are the main parts of each new structural design because their geometrical characteristics give them high strength to weight ratio. Moreover, requiring high mechanical and heat resistant materials leads engineers to use functionally graded material to achieve both of these characteristics. Hence, having a reliable high precision method for free vibration analysis of such shell panels is the first step of each dynamical analysis. This paper used a set of potential functions and auxiliary variables to present an exact Levy-type closed-form solution for free vibration of a doubly curved FG shell panel. The first-order shear deformation theory beside both the Donnell and Sanders strain-displacement relations are considered for mathematical modeling. The results of the present method are checked with the literature and a finite element analysis in which good agreement is observed. Also, a benchmark study is presented that will be useful for future researches.
This paper presents modeling and experimental evaluation of a cantilever-based piezoelectric energy harvester with cavity. The introduction of cavity in the beam shifts the neutral axis of the beam away from the surface of the piezoelectric element which in turn increases the strain and generated voltage. The generated voltage from the cantilever beam with cavity is higher when compared to the beam without cavity and is found to vary with its position and thickness. The analytical and experimental results are in close agreement. The cantilever beam with cavity generates 75% higher voltage than the voltage generated from the beam without cavity.
This study constructs an original mathematical model of a shipboard container crane and proposes a nonlinear controller for the complicated operation duties in which the viscoelasticity of seawater and the flexibility of handling cable are taken into account. By using two inputs, namely, the pulling force of the trolley and the torque of the hoist, the controller simultaneously drives six outputs, including trolley motion, cable length, container swing, axial container oscillation, ship roll, and ship heave. The effects of elasticity factors and wave excitations on system performance are also investigated. The simulation and experiment results reveal that the controlled system responses remain stable and consistent despite disturbances.
This work attempts to examine the scope of applying Kalman filter and H filter individually on the vibration signal acquired for identifying local defects in a rolling element bearing. This is essentially a system dynamic approach, which is another choice, examined to be a better one in comparison with few other signal analysis approaches reported in the literature. Kalman and H filters are optimal state estimators; Kalman filter is the minimum variance estimator while H filter minimizes the worst case estimation error. States, displacement and velocity, of a rotor shaft system are obtained from its equations of motion, which are written by including the process noise and measurement noise to take into account modeling inaccuracies and vibration from other sources. Experiments have been carried out to investigate the performance of Kalman and H filters each with the Envelope Analysis technique, a popular one for identification of bearing faults, in a noisy environment. Envelope Analysis is performed by taking a Hilbert transform of the band pass filtered signal, whose centre frequency and bandwidth are to be properly selected for satisfactory performance of the algorithm. Signals from test bearings running nearly at constant speed and having a single defect on the inner race and outer race have been acquired for different operating speeds of the test rig in the presence of extraneous vibration (noise) generated by running a nearby compressor. The signal obtained after the application of Kalman and H filter demonstrates a significant enhancement in signal to noise ratio resulting in a clear identification of defect frequencies in the vibration spectrum. Therefore, Kalman or H based state estimation approach may be used with confidence to extract bearing signals from noisy vibration signals.
This paper presents a two-step approach based on modal strain energy and response sensitivity analysis to identify the local damages in isotropic plates with moderate thickness. The first step focuses on detection of damage location. The local damage is simulated by a reduction in the elemental Young’s modulus of the plate. It is determined from the modal strain energy change ratio approach. A method to weaken the "vicinity effect" is proposed to reduce the false alarms in the localization of damage. In the second step, an approach based on response sensitivity-based finite element model updating is used to further identify the locations and extents of the local damages in time domain. The identified results are obtained iteratively with Tikhonov regularization using the measured structural dynamic responses. Two numerical examples are investigated to illustrate the correctness and efficiency of the proposed method. Both single and multiple damages can be identified successfully and the effect of measurement noise on the identification results is investigated. Good identified results can be obtained from the short time histories of a few number of measurement points.
In this paper, the free vibration analysis of a double-beam system is investigated. This structure is formed by two beams with elastic restraints at one end and free at the other end. These beams are connected by a mass-spring device. First, the related eigenvalue problem is established in the frequency domain, employing the well-known Fourier transform. Then, by utilizing eight boundary and compatibility conditions and solving two differential equations, the eigenvalues of the system are found and tabulated for different amounts of the parameters. Furthermore, some mode shapes of the mechanical system under study are plotted for various values of the springs' stiffness. In order to verify the results, some special cases are analyzed, and their outcomes are compared with the available ones.
This paper uses a particle swarm optimization (PSO) algorithm, an adaptive weighted PSO (AWPSO) algorithm, and a genetic algorithm (GA) to determine the optimal proportional-integral-derivative controller’s parameters of a hydraulic position control system. A typical hydraulic servo system has been selected as an application. The mathematical model of this hydraulic servo system which comprises the most relevant dynamics and nonlinear effects is considered. The model simulates the behavior of a REXROTH servo valve and includes the nonlinearities of friction forces, valve dynamics, oil compressibility, and load influence. The performance indices, which have been used in the optimization process, are integral absolute error, integral square error and integral time absolute error. The proposed controller is implemented on the simulation model to identify the best method for tuning the controller. Compared with GA and AWPSO results, the PSO method has been found to be more efficient and robust in improving the step response of a position control for hydraulic systems in terms of settling time, maximum overshoot and undershoot.
In this paper, we investigate the anti-synchronization between a class of chaotic real nonlinear systems and a class of chaotic complex nonlinear systems with fully uncertain parameters. According to Lyapunov stability theory, an adaptive control scheme and adaptive laws of parameters have been designed to realize the anti-synchronization between a class of chaotic real nonlinear systems and a class of chaotic complex nonlinear systems with different initial conditions. The anti-synchronization between the real Lorenz system and the complex Lorenz system, the real Chen system and the complex Lü system are presented as two examples to demonstrate the validity and feasibility of the presented control technique.
This paper presents three-dimensional (3D) vibration analysis of functionally graded (FG) sandwich deep open shells with general boundary restraints, including open spherical shells and the cylindrical ones. FG sandwich deep open shells composed of homogeneous cores and functionally graded material face sheets with material properties vary continuously through the thickness direction are considered in the present work. The 3D theory of elasticity in conjunction with an energy-based improved Fourier series method are combined to develop the theoretical formulation, in which each displacement of a deep open shell is approximated in terms of a triplicate product of the cosine Fourier series with the addition of certain supplementary terms introduced to remove the potential discontinuities associated with the original displacement and its relevant derivatives at the boundary faces. By using the present method, FG sandwich deep open shells with general boundary restraints, arbitrary geometry parameters, different material distributions and lamination schemes can be solved in a unified form. The accuracy and reliability of the present formulation are validated by comparisons with FEM solutions and those in the literature, and excellent agreements are obtained. Several 3D vibration results of FG sandwich deep open cylindrical and spherical shells with different dimensions in the meridional, circumferential and normal directions are presented for various types of boundary conditions and many representative lamination schemes, which may serve as benchmark solutions for future researchers in assessing two-dimensional approximate theories.
Piecewise-linear isolators are widely used in spacecraft for satisfying ever more stringent vibration requirements of high precision payloads. This paper focuses on ground tests of such isolators, with special consideration of gravitational asymmetry and mount flexibility. With asymmetrical equivalent isolator parameters derived with the extended equivalent linearization method, a two-step transfer function calculation method is proposed for enhancing the computation efficiency in dealing with studies where huge amount of computations are required, such as design parameter studies. The asymmetrical effect due to the gravity is presented by the movement of dynamic equilibrium positions as well as the softening and hardening characteristics of frequency responses. The effects and differences of the rigid mount and flexible mount, which respectively correspond to the shake table test and the whole spacecraft structure ground test, are studied with various design parameters. Numerical results show that the preload is an important factor in determining such effects and differences.
Real-time hybrid simulation (RTHS) is a testing method which combines the response from an experiment (i.e., experimental substructure) with that of a computer model (i.e., analytical substructure) in real-time. The accuracy and stability of the RTHS are prone to the propagation of error in the measured signals. Thus, critical developments in servo-hydraulic actuator control are needed to enable a wide application of this testing technique. In this study, a new tracking error compensation strategy for servo-hydraulic actuator control is developed, and numerically and experimentally evaluated. This compensation procedure is formulated based on a new set of tracking error indicators, namely, frequency domain-based (FDB) error indicators, which uncouple phase (lag and lead) and amplitude (overshoot and undershoot) errors and quantify them. These indicators are then incorporated into a two degree-of-freedom (d.f.) controller to develop closed-form equations to design an adaptive servo-hydraulic controller with improved tracking performance. The FDB indicators and the new adaptive controller are studied through numerical simulations in Simulink and LabVIEW and also verified experimentally. The proposed controller is computationally efficient, it can be implemented in real-time and it does not require any user-defined (i.e., predetermined) coefficients. As a result of its two d.f. formulation, this adaptive controller can be introduced to any closed-loop servo-controller through a digital or analog interface depending on the experimental setup properties. As such, it can be used to improve the tracking capability of any single hydraulic actuator system, which is essential in RTHS.
Spectral kurtosis (SK) has been proved to be a powerful tool to help extract impulse-like fault characteristics from original non-stationary vibration signals buried in strong masking noise. However, the SK coefficient based on the fourth sample moments suffers from a non-robustness problem, which may affect the accuracy of the SK-based kurtogram. Therefore, robust spectral kurtosis coefficients are defined based on quantiles in order to eliminate the influence of the outliers in original signals. Robust kurtograms are firstly utilized to analyze the fault signals. Subsequently, intrinsic time-scale decomposition followed by envelope demodulation is introduced to decompose the signal filtered by the kurtogram for fault detection. Compared with the conventional kurtogram and empirical mode decomposition, the results demonstrate that the improved method is able to facilitate the ability enhancement of the fault diagnosis of rolling element bearings.
Reflection and transmission of an incident plane transverse wave at a plane interface between two dissimilar generalized porous thermo-elastic solid half spaces is analyzed. The theory of generalized thermo-elastic material with voids in the context of Lord–Shulman theory has been employed to set down the equations of motion and constitutive relations. The reflection and transmission coefficients for a transverse wave incident at a plane interface have been derived. Partition of energy at the interface has also been considered together with the law of balance of energy.
The development of nonstationary signal blind separation, especially an underdetermined mixture of nonstationary sources, has become increasingly important for mechanical multi-fault diagnosis. In this paper, a novel algorithm based on the adaptive parametric time-frequency analysis theory to blindly separate the mixtures of nonstationary sources is presented. The computer simulations illustrate the applicability of our approach, and the performance of the algorithm is successfully tested on the underdetermined blind source separation of five vibration signals of a high speed train from one instantaneous mixture of these signals.
In order to decrease the effects of measurement noise on the trajectory tracking control of discrete-time switched systems, this paper proposes a discrete iterative learning control algorithm with an attenuation factor. The proposed algorithm adds a learning gain attenuated along the iteration horizon into measurement errors interfered by measurement noise for modifying the control rules of switched systems, in order to decay measurement noise as iterations increase. The convergence of each subsystem is proven rigidly with -norm theory, and the convergent condition of switched systems is provided. Theoretical results indicate that the proposed algorithm can effectively suppress non-repetitive measurement noise, and realize the complete tracking of the desired trajectory for the output of a discrete-time switched system within limited time. The final simulation results verify the validity of the proposed algorithm.
In this paper, the reflection and transmission of thermoelastic wave at a solid-liquid interface in presence of initial stress and magnetic field is investigated in context of GL model. After solving the governing equations, we can find the two reflection and refraction coefficients of incident p-(pressure) and SV- (shear vertical) waves in presence of initial stress and magnetic field. The boundary conditions at the interface that: (i) displacement continuity, (ii) vanishing the tangential displacement, (iii) continuity of normal force per unit initial area, (iv) tangential force per unit initial area must vanish, and (v) continuity of temperature is applied. The appropriate expressions to find the amplitude ratios for the two incidence waves (p- and SV-waves) have been obtained. A numerical example is considered for the reflection and transmitted coefficients of the incident waves, in which we study the effect of initial stresses and magnetic field. The results obtained are presented graphically for the effect of magnetic field and initial stress to display the phenomena physical meaning.
Due to the advancements in data measurement and computer technology, automated data collection from multiple sensors has become common in recent years. However, very few papers have dealt with the cost-optimal early fault detection of gearboxes, condition based maintenance policy, and remaining useful life prediction when multiple sensors are used for data collection under varying load. The novel approach presented here is based on vector autoregressive vibration signal modeling and continuous time hidden Markov modeling using the optimal Bayesian control technique. System condition is modeled using a continuous time Markov chain with three states, namely, unobservable healthy state 0, unobservable warning state 1 and observable failure state 2. Model parameters are calculated using the expectation-maximization algorithm. The optimal control policy for the three-state model is represented by a Bayesian control chart for a multivariate observation process. The chart monitors the posterior probability that the system is in the warning state 1 and the system is stopped when this probability exceeds an optimal control limit. Prediction of mean residual life using a posterior probability is also developed in this paper. The validation of the proposed methodologies is carried out using actual gearbox vibration data obtained from multiple sensors.
We investigate the multi-valued responses of a non-linear vibro-impact oscillator with a one-sided barrier subject to random narrow-band excitation. The frequency response of the system is obtained using the Krylov-Bogoliubov averaging method. Meanwhile, the backbone curve and the critical equation of unstable region are also derived for the deterministic case. Then, the method of moment is applied to obtain the iterative calculation equation for the mean-square response amplitude under the stochastic case. Excitation frequency, nonlinearity intensity, damping parameters, especially the distance between the system’s static equilibrium position and the barrier can lead to triple-valued response under certain case. In some conditions the impact system may have two or four steady-state solutions, which is an interesting phenomenon for impact system. The unstable region is one uniform part while under smaller nonlinearity intensity it is divided into two parts. Moreover, we also find that as random noise intensity increases, the pervasion of the phase trajectories strengthens, and then destroys the topological property of the phase trajectories.
Shaking table testing is a common experimental method in earthquake engineering for performance assessment of structures subjected to dynamic excitations. As most shaking tables are driven by servo hydraulic actuators to meet the potentially significant force stroke demand, the review is restricted to hydraulic shaking tables. The purpose of the control systems of hydraulic shaking tables is to reproduce reference signals with low distortion. Accurate control of actuators is vital to the effectiveness of such apparatus. However, the system dynamics of a shaking table and the specimens to be tested on the shaking table are usually very complex and nonlinear. Achieving the control goal can prove to be challenging. A variety of closed- and open-loop control algorithms has been developed to solve different control problems. With the focus placed on the control schemes for hydraulic shaking tables, the paper reviews algorithms that are currently used in the testing industry, as well as those which are the subject of academic and industrial research. It is by no means a complete survey but provides key reference for further development.
A sound absorbing structure of multilayer porous metal materials backed with an air gap is proposed to enhance the normal incidence sound absorption performance. The new sound absorbing structures could improve the sound absorption coefficient in a low frequency range and decrease the fluctuation of the sound absorption coefficient in a high frequency range. The Johnson-Allard model is employed to study the sound absorption characteristics of the porous metal materials. And acoustic wave transmitting in the porous metal materials obeys the law of acoustic wave propagation. The sound absorption coefficient and normalized acoustic impedance of the multilayer porous metal materials with or without an air gap are analyzed theoretically, and then compared with existing experimental values. Furthermore, the influence of several physical parameters on sound absorption characteristics, such as the thickness of the air gap, the number of layers, thickness, porosity and flow resistivity of the porous metal materials, are evaluated. The results indicate that the sound absorbing structures of the multilayer porous metal materials backed with an air gap present a satisfying sound absorption characteristic over a wide frequency range.
In this paper, a particular class of 2-D aeroelastic systems accounting for structural nonlinearities in pitching displacement and operating in an unsteady aerodynamic incompressible flowfield description is considered. By using the flap hinge torque of a trailing-edge flap surface as the control input, a continuous controller is proposed to suppress the aeroelastic vibrations of the wing section model. The control design based on the choice of the pitching angle as the output variable yields a semi-global asymptotic stability result. Furthermore, the system is theoretically shown to be robust to external disturbances. Numerical simulation results verify the efficacy of the proposed control strategy toward suppressing aeroelastic vibration in both pre- and post-flutter flight speed regimes under a multitude of external disturbances.
This paper is concerned with adaptive integral sliding mode control (AISMC) based on a wavelet kernel support vector machine for offshore steel jacket platform subject to nonlinear wave-excited force and parameter perturbations. The sliding mode control technique is combined with adaptive control algorithm and wavelet support vector machine to achieve the desired attenuation on the wave-induced vibration and to limit the displacement of offshore platforms. In this method, wavelet kernel support vector machine is used to establish the adaptive controller and an on-line learning rule for the weighting vector and bias is derived. The most important feature of the proposed control strategy is its inherent robustness and its ability to handle the nonlinear behavior of the offshore platform. By means of this control scheme the performance of the AISMC has been improved. The performance of the proposed control strategy is compared with some existing control schemes. It is demonstrated that the proposed control scheme in this paper is more effective in improving the control performance of the offshore platform. This controller is designed based on solving a set of linear matrix inequalities. It has been illustrated through simulation results that the proposed control scheme is effective in improving the control performance of offshore platforms.
This paper presents comparative studies for various sensor faults and noise effects on the performance of several recently proposed semi-active control algorithms for the control of large-scale magnetorheological dampers. Sensor faults or noises due to various environmental factors and long-term deteriorations may cause degradations in the performance of the control system. In this paper, the authors have carried out an in-depth literature review of the sensor fault or malfunction and noise problems, diagnostic methods and compensation approaches applicable to semi-active control algorithms. For three recently developed semi-active controllers, namely clipped optimal control, decentralized output feedback polynomial control and Lyapunov controller, an extensive study has been carried out on the robustness of these controllers during sensor faults and noise effects. Based on this research, a new real-time qualitative model-based sensor fault detection and diagnosis (RMSFDD) method has been proposed. This novel RMSFDD method shows a good performance during diverse sensor fault types in semi-active control with a real-time application without any training and heavy computational cost.
The present paper deals with the effect of point source on the propagation of Love wave in a heterogeneous layer and inhomogeneous half-space. The upper heterogeneous layer is caused by consideration of exponential variation in rigidity and density. Also in half-space inhomogeneity parameters associated to rigidity, internal friction and density are assumed to be functions of depth. The dispersion equation of Love wave has been obtained by using Green’s function technique. As a special case when the upper layer and lower half-space are homogeneous, our computed equation coincides with the general equation of Love wave. The propagation of Love waves are influenced by inhomogeneity parameters. The dimensionless phase velocity has been plotted against the dimensionless wave number for different values of inhomogeneity parameters. We have observed that the velocity of wave increases with the increase of inhomogeneity parameters.
In this paper, we aim to solve the optimal tracking control problem for the Henon Mapping chaotic system using the direct heuristic dynamic programming (DHDP) setting with filtered tracking error. The fuzzy logic system is used to approximate the long-term utility function. Compared with the results for chaotic discrete-time system, the cost of the controller is reduced. The Lyapunov analysis approach is utilized to prove the stability of the chaotic system. It is shown that the tracking error, the adaptation law and the control input retain the property of uniformly ultimate boundedness. A simulation example is given to demonstrate the effectiveness of the proposed approach.
This paper investigates the control challenges posed by noncollocated mechatronic systems and motivates the need for a model-based control technique towards such systems. A novel way of online constraint handling by penalty adaptation (PAMPC) is proposed and shown to be of particular relevance towards robust control of underdamped, noncollocated systems by exploiting the structure of such systems. Further, a new tunneling approach is proposed for PAMPC to maintain feasibility under uncertainty. The PAMPC is shown to be optimal for control of a benchmark mass–spring–damper system, which poses all the mentioned challenges.
Delamination is a common damage in fibre reinforced composite laminates, usually hidden from external view, that can substantially reduce the structural stiffness which changes the dynamic response of the structures such as natural frequencies. Natural frequencies are the most reliable parameters for detecting damage while they do not directly provide information regarding its location and severity. To determine the location and severity of damage, it is necessary to solve the inverse problem using frequency shifts in multiple modes. In this paper, the graphical approach, which was previously employed for estimating two variables of crack (location and size) in isotropic beams, is extended in the current work to estimate the three variables of delamination (interface, span-wise location and size) in anisotropic composite beams from measured frequency shifts. Compared to the use of optimisation or neural network for detection, graphical technique is computationally inexpensive and quick since it solves the inverse problem without iterations or network training. The present approach has been validated using numerical simulation as well as experimental data from modal testing conducted on quasi-isotropic simply supported and cantilever beams. Results show that the proposed graphical technique can be used to assess the location and severity of delamination in composite beams with a high degree of accuracy.
Fractal signal processing and novelty detection are used for fault detection in rolling element bearings. The former applies the concept of self-similarity based on wavelet variance, and the latter is based on machine learning and utilises artificial neural networks. The method is demonstrated using simulated and experimental vibration data. The work presented involves validation both on laboratory test rig data and industrial wind turbine data. The results show that the method can be used successfully for automated fault detection in ball bearings under real operational conditions.
In this paper a new saturated control design for uncertain systems is proposed. The developed saturated control scheme is based on linear matrix inequality (LMI) optimization to achieve prescribed dynamic performance measures e.g., settling time and damping ratio. In this design, the closed-loop poles are forced to lie within a desired region. The proposed design provides robustness against system uncertainties. The existence of the saturated robust control with regional pole placement is shown using LMI and Lyapunov function analysis. Simulation results of two illustrative examples are given to validate the effectiveness of the proposed controllers. Application to car active suspension to achieve comfortable dynamic performance by pole placement and avoiding actuator saturation is also considered.
A method for updating mass and stiffness matrices without spillover is presented, which requires the knowledge of only the few eigenpairs to be updated of the original undamped model. The finite element model updating problem with symmetric preserving and no spillover is formulated as a semi-definite programming problem, which can be efficiently solved by existing semi-definite programming algorithms. Numerical examples show that, using the presented updating method, the updated model accurately reproduces the "measured" modal data, while keeping the symmetry of mass and stiffness matrices and avoiding spillover.
The aim of the present work is to study the free transverse vibrations of non-homogeneous trapezoidal plates of linear thickness variation in the x-direction under thermal gradient effect. The non-homogeneity of the plate is assumed to arise due to parabolic density variation in the y-direction. A two term deflection function has been taken for clamped-simply supported–clamped-simply supported boundary conditions. The Rayleigh-Ritz method is used to obtain a frequency equation for the first two modes of vibration. The effect of non-homogeneity constant, aspect ratios, taper constant and thermal gradient on the frequencies of non-homogeneous trapezoidal plate has been illustrated for the first two modes of vibration. Results are presented in graphical form. Confirmation of results in special cases with authors published one has also been presented.
The Stockbridge vibration damper is widely used in overhead transmission lines to reduce Aeolian vibration. Although a linear analytical model has been developed to interpret characteristics of the vibration damper, a much more detailed model is needed to investigate how the nonlinear factors of the structure affect its vibration characteristics. The paper presents a full-scale finite element model of the Stockbridge vibration damper, in which contact conditions are taken into account using the linear perturbation method. Relations between the contact conditions and mode frequencies were studied. It was proved that contact conditions between each two parts of the damper have significant influence on the stiffness of the whole structure. Results obtained from the numerical model compare well with those from the experiment. Finally, this numerical model was applied to investigate how the bonding material between the counterweight and steel strand cable affects the mode frequencies of the vibration damper.
This study focuses on the free linear vibrations of doubly curved shallow shells reinforced by any number of beams of arbitrary lengths. Distributed elastic restraints are used to specify generally the boundary conditions along the shell edges and the coupling conditions between the shell and its reinforcing beams. Both the shell and stiffening beams are considered as independent structural components carrying three-dimensional displacement fields. Each of the displacements is invariably expressed as a simple trigonometric series with accelerated and uniform convergence over the solution domains of interest. All the unknown expansion coefficients are treated as the generalized coordinates and solved using the Rayleigh-Ritz technique. As illustrated by examples, the current method provides a unified means for solving a wide range of shell problems involving various practical complications with respect to, for example, the boundary conditions, the coupling conditions, the number of stiffeners, and the lengths and locations of the stiffeners.
The act-and-wait concept is a recently developed type of controller, which is receiving growing interest because of its promising features with respect to the control of systems with feedback delay. Although most of its advantages have been widely discussed and verified experimentally, a detailed analysis of the nonlinear behavior of this type of controller is still missing. In this paper, we apply the act-and-wait controller to the digital position control of a single-degree-of-freedom system. The analysis shows both the linear stability and the post-bifurcation behavior of the system, comparing the system with a regular proportional-differential controller and with the act-and-wait controller. The performed investigation confirms most of the advantages of the act-and-wait controller, already known in the literature, regarding the enlargement of the stable region and the possibility of achieving deadbeat control, also in the presence of delay. On the other hand it shows some drawbacks of this controller, related to the post-bifurcation behavior, which presents unbounded motions, and to the robustness of the stability, which appears to be limited.
The paper deals with an instantaneous angular speed (IAS) based algorithm for fault detection in a multistage gearbox. Fast Fourier transform (FFT) is a well established technique for analysis of a stationary signal. However, the IAS signal from the multistage gearbox is a combination of periodic signal and structure borne noise. This structure borne noise makes the IAS signal non stationary. Hence, FFT is no longer suitable for this non stationary signal analysis. Therefore in this paper, the IAS signal is time synchronously averaged with respect to lay shaft speed and then followed by FFT reveals the gear mesh frequency and rotational frequencies which are synchronous with the gearbox’s rotating speed. Thus, the algorithm can accurately and reliably detect the fault in multistage gearbox using the IAS. The paper also investigated the behavior of IAS signal for three different gearboxes (healthy, one tooth and two teeth broken) under two different speeds and three different loading conditions.
The vibrations of circular, annular, and sector plates are traditionally considered as different boundary value problems and often treated using different solution algorithms and procedures. This problem is further compounded by the fact that the solution for each type of plate typically needs to be adapted to different boundary conditions. In this paper, a simple solution method is proposed for a unified vibration analysis of annular, circular and sector plates with arbitrary boundary conditions. Regardless of the shapes of the plates and the types of boundary conditions, the displacement solutions are invariably expressed as a new and simple form of trigonometric series expansion with an accelerated convergence rate. The unification of seemingly different boundary value problems for the circular and annular plates and their sector counterparts is physically accomplished by applying a set of coupling springs to ensure appropriate continuity conditions along the radial edges. The accuracy, reliability and versatility of the current method are fully demonstrated and verified through numerical examples involving plates with various shapes and boundary conditions. It should be noted that the current method can be easily applied to sector plates with an arbitrary inclusion angle up to 2.
In this paper, the dynamical simulation of a nonlinear aircraft rotor system in Herbst maneuvering flight is carried out, though which the load control is discussed for safety purposes. The equations of motion of the system are set up by using Lagrange’s equation, in which, the effects of maneuvering flight are formulated by the flight parameters of the aircraft. By employing the method of closest unstable equilibrium point, the stability of periodic solutions for the primary resonance of the system in steady flight is analyzed to demonstrate the existence of double steady solutions in some rotation speed region near the critical speed and the possibility of the switch of them due to the effect of maneuvering flight. By introducing the Herbst flight parameters from the results of a relative control simulation, the dynamical simulation of the system is carried out, from which the switch of the smaller solution of amplitude to the larger solution is observed. Furthermore, the load control is designed by adding a gain to the Herbst flight parameters to avoid the switch. Through numerical experiments, it is found that = 0.679 is the critical condition of the switch. The results in this paper will provide a better understanding for the effect of aircraft maneuvering flight on the dynamics of the rotor system.
This paper presents a study aimed at evaluating how viscoelastic materials embedded in composite plates affect structural damping during the flight of a civil aircraft. The vibro-acoustic responses of composite fuselage structures realized with embedded viscoelastic damping treatments have been experimentally characterized at different temperature conditions. The real influence of viscoelastic materials on composite structures has been investigated, focusing the investigations on aspects still unknown, related mostly to temperature effects. In order to simulate the temperature level of commercial transport aircraft in cruise flight conditions, tests were performed using a climatic room where temperature and humidity were controlled. Vibrational tests were performed on two composite fuselage skin coupons: one treated with embedded viscoelastic damping treatments and the other one untreated. The tests were performed at temperatures of
A model is extremely important to the controller designing and system analysis of an active vibration control system. However, the influence of actuators is always ignored by considering them as proportion links when modeling the control system. In this work, a joint model of a clamped-free shell structure and electrodynamic actuators was constructed. The shell was modeled using the finite element method while the actuators were simplified as lumped parameter models. It was found that the connections of actuators diminish the natural frequencies and smooth the resonance peaks of the structure. The optimal configuration of actuators and sensors was studied by harmonic response analysis and modal analysis. It was suggested to avoid the central line and give priority to the free end or the edges of the clamped-free shell when mounting actuators and sensors. The active control was carried out using the FXLMS algorithm, which effectively suppressed the disturbance of the vibration source. The control was conducted point by point on the transient response model of the structure and can easily be extended to a real life system.
Base isolator devices are widely used for mitigation of vibrations induced in structures by seismic actions. In order to achieve high performances in the mitigation of seismic effects, base isolator mechanical properties should be designed by an optimum criterion. In common approaches, the nature of dynamic loads is assumed as the only source of uncertainty. In the present paper a robust optimization criterion for base isolator devices design is proposed, considering the unavoidable effects of uncertainty in structural properties and seismic action. Uncertain parameters are modeled as random variables and are represented by bounded independent probability density function, with uniform law. The structure is described by a single-degree-of-freedom model and is protected by a linear base isolator in order to reduce vibration levels induced by base acceleration, here modeled by the stationary Kanai-Tajimi stochastic process. The optimal design is formulated as a constrained minimization problem, assuming as an objective function a suitable measure of the isolator efficiency and imposing a constraint on the maximum isolator displacement. A sensitivity analysis is carried out on the robust solution in order to assess characteristics and differences with respect to the conventional deterministic solution.
A geometrically nonlinear frequency-domain analysis of functionally graded plates integrated with an active constrained layer damping (ACLD) arrangement is performed by developing an incremental nonlinear closed-loop dynamic finite element model of the overall plate. The active constraining layer is made of piezoelectric fiber reinforced composite (PFRC) and a heated substrate-plate surface is considered. The analysis is mainly for investigating the effect of temperature on the nonlinear vibration characteristics of the overall plate in the frequency domain and also, on the corresponding control authority of the PFRC constraining layer. A negative velocity feedback control strategy is utilized to achieve active damping. The temperature dependent material properties of the substrate plate are graded in the thickness direction according to a power law, and expressed in terms of the power law exponent and the constituent material (metal and ceramic) properties. Using the Golla-Hughes-McTavish method for modeling the viscoelastic material, the incremental nonlinear finite element equations of motion are derived in the frequency domain assuming periodic motion of the overall plate. An arc-length extrapolation solution technique is used in combination with a new strategy for determination of incremental arc-length. The numerical illustrations show a potential use of PFRC actuator in the ACLD arrangement and suggest an optimal thickness of viscoelastic layer for more effective use of PFRC. The analysis reveals the significant effects of initial thermal bending of the overall smart plate on its nonlinear dynamic behavior in the frequency domain. The effects of temperature, metal-volume fraction in substrate, fiber volume fraction in PFRC and the fiber orientation angle in the PFRC on the control authority of the ACLD layer are presented. For the use of the ACLD layer in the form of a patch, a new numerical strategy for determining its optimal location and optimal size for effective control is presented.
In this study, the vibration responses of a partially treated laminated composite magnetorheological (MR) fluid sandwich plate have been investigated. The governing differential equations of motion for a partially treated laminated sandwich plate embedding MR fluid and rubber as the core layer and the laminated composite plate as the face layers are presented in finite element formulation. The validity of the developed finite element formulation is demonstrated by comparing the results in terms of natural frequencies derived from the present finite element formulation with the experimental measurements. Various configurations of a partially treated laminated composite MR fluid sandwich plate are considered to study the effect of location and size of the MR fluid segment under various boundary conditions. The effect of magnetic field on the variation of natural frequencies and loss factor of the partially treated laminated composite MR fluid sandwich plate are also analyzed for various configurations at different boundary conditions. The free vibration mode shapes of various configurations of a partially treated laminated composite MR fluid sandwich plate are also presented. The forced vibration responses of the various configuration of a partially treated laminated composite MR fluid sandwich plate are also analyzed under harmonic force excitations. This analysis suggests that the natural frequency, loss factor and transverse displacements of the partially treated laminated composite MR fluid sandwich plate are strongly influenced by the location and size of the MR fluid segment apart from the intensities of the applied magnetic field. The application of the partial treatment alters the deflection pattern of the sandwich plate, particularly the location of peak deflection, which shows that it can be applied to critical components of a large structure to realize a more efficient and compact vibration control mechanism with variable damping.
The dynamic stability of a coupled tower-blade wind turbine system is investigated analytically and experimentally. Coupled equations of motion and associated boundary conditions for the wind tower and a rotating blade are derived by considering the lateral acceleration of the nacelle at the tip of the tower, which is the base of the flexible blade. The coupled eigenvalues are computed for various blade rotational speeds and densities of the tower material by using Galerkin’s method in spatial coordinates. The results indicate that the coupled tower-blade system becomes unstable when certain vibrational modes of the tower and blade coalesce. Additionally, the vibration of the rotating blades is measured using a wireless telemetry system attached to the small-scale tower-blade wind power system, and the results are compared with those of the analytical study. The experiment shows that instability is observed in the same ranges of the blade rotational speed as those predicted by our analytical study.
In this paper the competitive relationship between the geometric dispersion and the viscous dissipation in the wave propagation of the KdV-Burgers equation is investigated by the generalized multi-symplectic method. Firstly, the generalized multi-symplectic formulations for the KdV-Burgers equation are presented in Hamiltonian space. Then, focusing on the inherent geometric properties of the generalized multi-symplectic formulations, a 12-point difference scheme is constructed. Finally, numerical experiments are performed with fixed step-sizes to obtain the maximum damping coefficient that insures that the scheme constructed is generalized multi-symplectic, and to study the competition between the geometric dispersion and the viscous dissipation in the wave propagation of the KdV-Burgers equation. The competition phenomena are comprehensively illustrated in the wave forms as well as in the phase diagrams: for the KdV equation (a particular case of the KdV-Burgers equation without dissipation), there is a closed orbit in the phase diagram; and the closed orbit is substituted by a heteroclinic one with the appearance of the viscous dissipation; moreover, the heteroclinic orbit changes from the saddle-node type to the saddle-focus type with an increase of the damping coefficient.
Vibration signals collected after propagation are usually different from the real ones of some vibration source due to the corresponding stop band of a particular propagation media. Here, the propagation characteristics of longitudinal wave are investigated when the signals pass through a multi-step rod with variable cross-section. Firstly, the transfer matrices for a single rod are derived based on the three wave theories, i.e. the elementary wave theory, the Love wave theory and the Mindlin-Herrmann wave theory, respectively. Next, the matching conditions for any two adjacent segments are analyzed, from which the transfer matrix for any step-rod with two or more segments are presented. Moreover, possible elastic constraint is also taken into consideration. Finally, several numerical examples for a step-rod with three segments are given by the present theoretical predictions and the finite element analysis, from which the performance of the three wave theories are compared with each other. The results show that the influences of the Poisson’s effect and shear deformation cannot be neglected, and the propagation characteristics of longitudinal wave in this multi-step rod may also be affected by the magnitude and location of the elastic constraint as well as the discontinuity of the cross-sections of adjacent segments.
A periodic truss beam is designed by connecting an array of identical elements in parallel to gain excellent Bragg band gaps, after which locally resonant (LR) oscillators are attached to the truss beam to form the periodic LR truss beam, which can achieve both an LR gap in low frequency and Bragg gaps in high frequency. Firstly, dynamic models of the periodic LR truss beams in which longitudinal and flexural waves propagate are established. Then, transfer matrices of the periodic elements are derived by using the transfer matrix method and are further used for computing frequency-dependent propagation constants and acceleration frequency response (AFR) on semi-infinite and finite periodic LR truss beams. Furthermore, vibration reduction performance of the periodic structures in the frequency range below 1400 Hz is numerically analyzed in detail. Finally, an experimental setup for measuring AFR on the periodic LR truss beam is carried out to validate the predicted numerical results. Both the numerical simulation and experimental results reveal that the LR gap in low frequency and the Bragg gap in high frequency coexist in the periodic LR truss beam; within the frequency ranges of the two types of band gaps, vibration transmitted in the periodic structure can be substantially attenuated.
The majority of the current research on the mounting system has emphasised on the low/medium power engine, rare work has been reported for the high-speed and heavy-duty engine, the vibration characteristics of which exhibits significantly increased complexity and uncertainty. In this work, a general dynamics model was firstly established to describe the dynamic properties of a mounting system with various numbers of mounts. Then, this model was employed for the optimization of the mounting system. A modified Powell conjugate direction method was developed to improve the optimization efficiency. Basing on the optimization results obtained from the theoretical model, a mounting system was constructed for a V6 diesel engine. The experimental measurement of the vibration intensity of the mounting systems shows excellent agreement with the theoretical calculations, indicating the validity of the model. This dynamics model opens a new avenue in assessing and designing the mounting system for a high-speed and heavy-duty engine. On the other hand, the delineated dynamics model, and the optimization algorithm should find wide applications for other mounting systems, such as the power transmission system which usually has various uncertain mounts.
In this paper, the free vibration of an orthotropic beam undergoing finite strain are studied. The second Piola-Kirchhoff stress tensor and Green-Lagrange strain tensor according to finite strain assumption were used to obtain Euler-Bernoulli beam governing equations. The Galerkin method and Generalized Differential Quadrature method were employed for solving the governing equations and boundary condition. The effect of beam thickness and different boundary conditions were considered in finite strain formulation of the beam equations. Natural frequencies of different composite materials are obtained and compared. The results revealed that by increasing the beams thickness, the difference between maximum vibration amplitude increased between von Karman and finite strain formulations. Also, in a beam with simply- simply supports, differences between linear and non linear mode shapes was remarkable.
Based on the governing equation of inclined cable segment vibration, an equilibrium equation formulated in dynamic stiffness is built to describe the force balance status at arbitrary location along cable where transverse force is applied. A closed-form solution to transverse dynamic stiffness matrix corresponding to two degrees-of-freedom and dynamic stiffness corresponding to one degree-of-freedom is proposed herein, which considers the effects of sag, flexural rigidity, clamped boundary condition, and inclined angle of real inclined cable simultaneously. A real cable damper system vibration test is used to verify the rationality and credibility of the proposed closed-form solution. The effects of cable parameters above mentioned on the dynamic stiffness of cable are investigated by using this approach. It shows that, by the influence of these factors, the cable transverse dynamic stiffness takes on complicated behaviors. Due to the marked errors or even wrong results induced, it is unreasonable to evaluate the cable transverse dynamic stiffness both by the approach of taut string theory and by treating the inclined angle to horizontal attitude.
Modeling and simulation of a new device concept of an electrically actuated resonant switch (EARS) is presented in this paper. This EARS can be tuned to be triggered at low levels of acceleration, as low as those of earthquakes. The device is made by mounting an electrostatically actuated cantilever microbeam, with a tip mass, on top of a compliant board or a printed circuit board (PCB), which is modeled as a hinged–hinged beam. A distributed-parameter model of the device is derived for the microbeam and the PCB using Hamilton’s principle based on Euler–Bernoulli beam theory. The equations are then discretized using the Galerkin procedure. A nonlinear numerical dynamic analysis is performed in order to characterize the behavior and performance of the device when subjected to acceleration pulses. A parametric study showing several curves of dynamic pull-in thresholds for various values of electric voltage loads and frequencies of excitation is conducted. It is shown that the device can be triggered at a wide range of accelerations ranging from 0.33 g to 200 g for various values of DC and AC voltages.
Here, forced vibration of a rectangular plate with a side crack of arbitrary length, orientation and position is studied by the Ritz method. Simply supported and clamped boundary conditions are used in the analysis. Numerical results obtained from the Ritz method are validated by finite element method software (ABAQUS). Good matching was found for first five modes. Mobility curves are presented for variation in force location, crack length, crack orientation and crack position in a square plate. Normalized mobility is found to increase with an increase in crack length ratios and decrease with an increase in crack angle. Again, it is observed that a change in crack position from side towards middle increases the normalized mobility. The results can be used for mobility-based crack detection.
The purpose of this paper is to propose a useful method to implement active magnetic bearings (AMBs) on an existing rotating shaft which rotates on conventional bearings. This is feasible if AMBs can produce the same reaction loads of conventional ones and if the size of the vane is large enough to host an AMB. As this substitution could give some difficulties due to the different size between magnetic bearings and conventional ones, a set of equations are performed to show that a variation of some parameters can solve this problem. The coil ratio is the geometrical parameter introduced to develop the present analysis. The variation of coil ratio does not produce a variation of the pole’s surface so that the reaction load does not change. The results are analyzed by numerical analysis by mathematical relationships involving the design parameters, magneto-static simulations and dynamic simulation on the shaft when it is tested by a step response and performing frequency response parameterized with coil ratio. Results show that the displacement carried out by the step response is always the same, when the journal ratio and frequency response are varied, confirming that the reaction load, produced by pole expansion, remains the same when the coil ratio varies. The simulations and results are performed by finite element method magnetic and MATLab software.
This paper proposes a multiclass nonlinear relevance vector machine (MNRVM) model for health monitoring of smart structures equipped with magnetorheological (MR) dampers. The proposed model will be used to classify the damage statuses of the integrated structure-control systems subjected to ambient excitations. A numerical model of a three-story building equipped with an MR damper is studied to demonstrate the effectiveness of the proposed health monitoring schemes. Dynamic responses of the smart structures subjected to random excitations are measured. Discrete wavelet transform is applied to the obtained data to compress and filter noises of the measured data. As a next step, the compressed and de-noised signals are used for developing autoregressive (AR) models. Then the MNRVM is applied to the AR-coefficient data to classify them with respect to the damage statuses. As a baseline, the support vector machine (SVM) algorithm is considered. It is demonstrated that the proposed MNRVM framework is effective in classifying various damage statuses of the nonlinear smart structures subjected to ambient excitations. Simulation results also show that the MNRVM performs similar to the SVM with faster computation time.
In this paper, control of the stationary response of a half-car model with a magnetorheological (MR) damper moving over a random road is considered. The MR damper is characterized using Bingham and modified Bouc–Wen models whose parameters are determined optimally using a multi-objective optimization technique and nondominated sorting genetic algorithm II. The multi-objective optimization problem is solved by minimizing the difference between the root mean square sprung mass acceleration, the sum of the front and rear suspension strokes and the sum of the front and rear road holding response of the half-car model with the MR damper, and those of an active suspension system based on linear quadratic regulator (LQR) control. The control force of the MR damper suspension is constrained to lie within ±5% of the control force corresponding to the active suspension system based on LQR control. It is observed that the MR damper suspension systems with optimal parameters perform an order of magnitude better than the passive suspension and perform as well as active suspensions with limited state feedback, and closer to the performance of fully active suspensions. In the case of MR damper suspensions, the vehicle response statistics are obtained using the equivalent linearization method and verified by Monte Carlo simulation.
The oil film force induced from bearings has a direct influence on the stable operation of a rotor system because the change in motion characteristics will lead to variation of the oil film force. An accurate oil film force model is therefore critical to predict the motion characteristic state of a rotor system. The linear oil film force model and the Muszynska model are employed by many scholars to predict linear force and nonlinear oil film force respectively. When the rotor system has a larger eccentricity ratio, the changing law of the rotor system is not predicted by the Muszynska model. In this paper an improved oil film force model is developed for the motion changing law. This model is based on short bearing assumption with the turbulence effect and rotor motion equation included. The motion law is well described by this model. In particular the dynamic characteristics can be described well by the modified model. To verify the simulation results of the modified model, an experiment is carried out. Finally, there is a comparison between theoretical and experimental results and it is found that the theoretical results are in good agreement with the experimental results. This paper provides a reference for further research of the motion changing law of rotor systems.
In this paper, a multi-objective particle swarm optimization algorithm is used to obtain the Pareto frontiers of the different commensurable and conflicting objective functions for fuzzy controller design. Also, the Lorenz dominance method is used to illustrate the equitable solutions. The nonlinear benchmarks are the inverted pendulum and ball-beam systems. The objective functions for the inverted pendulum system are the normalized angle error of the pendulum and the normalized distance error of the cart; and for the ball-beam system they are the distance error of the ball and the angle error of the beam, which must be minimized simultaneously. The comparison of the obtained results with those in the literature demonstrates the superiority of the results of this work.
In this article, the controllability of asynchronous Boolean control networks (ABCNs) with time-invariant delay is studied. Using semi-tensor product, Boolean control networks under Harvey’s asynchronous update with time delay are converted into linear representation, and a general formula of control-depending network transition matrices is achieved. Firstly, a necessary and sufficient condition is proposed to verify that only control-depending fixed points of ABCNs can be deterministically controlled. Secondly, respectively for three kinds of controls, the controllability of the non-deterministic logical dynamics is investigated, and formulas are given to show: a) the reachable sets at time s under a group of specified controls; b) the reachable sets at time s under arbitrary controls and c) the probability values from a given initial state to different target states. Moreover, we also discuss how to find the particular control sequence to reach a specified target state with the maximum probability. Examples are shown to illustrate the feasibility of the proposed scheme.
This paper applies a newly developed mechatronic inerter network to suppress vibrations of a full optical table. Optical tables are normally applied to insulate precision machines from two types of disturbances: ground disturbances from the environment and load disturbances from the equipment. These two disturbances can be independently controlled by disturbance response decoupling (DRD) techniques. For example, we can isolate the ground disturbances by soft passive suspensions and improve the load responses by active control. However, the passive elements cannot be easily adjusted according to the operating conditions. Therefore, this paper applies mechatronic inerter networks to a full optical table, and optimizes the ground responses by connecting the networks to suitable electric circuits. We then apply DRD techniques to improve the load responses without influencing the ground responses. The designed mechatronic inerter networks and active controllers are implemented to a full optical table for experimental verification. Based on the results, the proposed mechatronic inerter networks and DRD structures are deemed effective in improving system responses.
Vibrating structures, such as gas turbine engines, are assemblages of multiple components interfaced with each other through physical contact. The friction produced at these contact interfaces, by sliding or slipping at the interface, is a source of energy dissipation, resulting in damping effects. This passive approach to damping is exploited by engineers to provide optimal energy dissipation to attenuate vibration in a variety of systems (such as bladed disc assemblies and airfoils), to prevent wear and premature failure. However, the highly nonlinear nature of friction renders accurate predictive modeling of such a problem challenging. This article gives an overview of the current state of the art, and the methods used for mathematical and predictive computational modeling of vibrating systems under the influence of dry friction.
In this paper, an active controller for a nonlinear and hysteretic structure with time delay is studied. The nonlinear and hysteretic behavior of the system is illustrated by the Bouc-Wen model. The genetic algorithm is used to identify the optimal parameters of the Bouc-Wen model in order to describe the hysteresis phenomenon of the experimental system. By specific transformation and augmentation of state parameters, the motion equation of the system with explicit time delay is transformed into the standard state space representation without any explicit time delay. Then the fourth-order Runge-Kutta method and instantaneous optimal control method are applied to the controller design with time delay. Finally, numerical simulation and experimental results of a flexible beam using the proposed time delay controller are carried out. The results indicate that the control performance will deteriorate if time delay is not taken into account in the controller design. The time delay controller proposed in this paper can not only effectively compensate time delay to get better control effectiveness, but also work well with both small and large time delay problems.
This paper describes the direct torque and flux control (DTC) of a self-excited induction generator (SEIG) for wind energy conversion systems (WECS). The DTC-based WECS is more suitable for low power applications, owing to several advantages such as good torque control in steady-state and transient operating conditions, not requiring an accurate generator model, the absence of coordinate transforms and current controllers. The SEIG is excited by a voltage source converter (VSC) with a capacitor and start-up battery on the direct current (DC) side. The required reactive power for the SEIG is provided by the capacitor. The terminal voltage of the SEIG varies with wind speed and load conditions. The proposed DTC strategy is used to control the terminal voltage of the SEIG and DC voltage at a constant value when the load and wind speed are varied. The gate signals for the VSC are derived from an inverter switching table. The torque and stator flux of the induction generator are controlled through the voltage space vector selection. The proposed system gives good dynamic and steady-state performance. The effectiveness of the proposed control strategy is verified through simulations. Experimental results are presented to validate the simulation results.
This research is focused on a comparison of classic and strain experimental modal analysis (EMA). The modal parameters (the natural frequencies, the displacement mode shapes (DMSs) and the damping) of real structures are usually identified with classic EMA, where the responses are measured with motion sensors (e.g. accelerometers). Strain EMA is a special approach in the field of EMA, where the responses are measured with strain sensors. Classic EMA is the preferred method, but strain EMA offers advantages that are important for particular applications: for example, the direct identification of strain mode shapes (SMSs), which is important in the vibration-fatigue and damage-identification models. The next advantage is that strain EMA can sometimes be used, for experimental/geometrical reasons, where classic EMA cannot. There are also drawbacks: for example with strain EMA only, the mass-normalization of the DMSs and SMSs cannot be performed. This study researches the theoretical similarities and differences of both EMA approaches. Furthermore, the accuracy of both approaches for the case of a free–free supported beam and a free–free supported plate is investigated. Classic and strain EMA were performed with a piezoelectric accelerometer and the piezoelectric strain gauges, respectively. The results show that the accuracy of strain EMA results (the natural frequencies, DMSs and the damping) is comparable to the accuracy of classic EMA.
This paper presents the optimal tracking control methodology for an offshore steel jacket platform subject to external wave force. Based on a dynamic model of an offshore steel jacket platform with an active mass damper mechanism and a linear exogenous system model of the external wave force on the offshore platform, an optimal tracking control scheme with feedforward compensation is proposed to attenuate the wave-induced vibration of the offshore platform. A feedforward and feedback optimal tracking controller (FFOTC) can be obtained by solving an algebraic Riccati equation and a Sylvester equation, respectively. It is demonstrated that the wave-induced vibration amplitudes of the offshore platform under the FFOTC are much smaller than the ones under the feedback optimal tracking controller (FOTC) and the feedforward and feedback optimal controller (FFOC). Furthermore, the required control force under the FFOTC is smaller than the ones under the FOTC and the FFOC.
Periodic rib-skin structure is composed of an array of identical elements connected in parallel and each element is a stiffened structure consisting of skins and ribs which are modeled as elastic beams and rigid bodies respectively. The periodic structure is designed to gain excellent longitudinal and flexural vibration band gaps in which corresponding waves cannot propagate in the structure freely. Firstly, longitudinal and flexural vibration mobility matrices of the skins and ribs are derived to obtain mobility equations of single-floor and multi-floor periodic elements. Then, propagation constants of the infinite rib-skin structure are calculated and an in-depth numerical study is performed to examine the relationships between the wave propagation constants and dynamic response of semi-infinite and finite periodic structures. Furthermore, flexural vibration reduction performances of the periodic rib-skin structure below 3000 Hz are discussed in detail. Finally, an experimental setup for measuring the acceleration frequency response of a two-floor periodic rib-skin structure is carried out to verify the numerical solution. Both predicted and measured results have demonstrated that longitudinal and flexural band gaps exist in the periodic rib-skin structure. The flexural vibration transmitted through the structure is substantially suppressed in a wide frequency range below 3000 Hz.
In this paper, the vibration band gap properties of a two-dimensional square lattice are studied using the spectral element method. Before assembling the spectral equations of whole structures, the spectral stiffness matrices of the tensional and bending elements are established. The frequency responses of the lattices are calculated and compared with those obtained by the finite element method. It can be observed that the results in the spectral element method are more accurate, especially in high frequency ranges. The frequency band gap properties are analyzed based on the accurate frequency responses. The effects of the material and structure parameters on the band gap properties are investigated.
The present work investigates the adverse effects of non-collocated sensors and actuators on the phase characteristics of flexible structures and the ensuing implications on the performance of structural controllers. Two closed-loop systems are considered. The first one consists of a pinned-free flexible beam with the control torque applied at the pinned-end. The second one is a clamped-free deformable beam with the control moment generated by two piezoelectric actuators bonded at the top and bottom surfaces near the clamped-end. The phase angle contours for both systems were generated as functions of the normalized sensor location and the excitation frequency. They illustrate the loci of the imaginary open-loop zeros along with the resulting minimum and non-minimum phase regions of the systems as the sensors sweep the entire span of the beams. Two structural controllers are designed based on the sliding mode methodology and the active damping control strategy to attenuate the undesired in-plane transverse deformation of the pinned-free beam. The results have revealed three distinct regions for the sensor’s location whereby the performance of the sliding mode controller can be stable, unstable, or stable after incorporating a remedial action into the control algorithm based on the phase angle contour information of the open-loop system. On the other hand, the active damping controller eliminated the overall in-plane transverse deformation by both active damping and having the first two elastic modes being equal in magnitude and opposite in sign. The dissipative nature of this controller and the dependency of its gains on the mode shapes of the beam have yielded a robust and stable performance of the closed-loop system irrespective of the sensor location.
Vibration neutralizers provide an effective method of attenuating tonal vibrations within a structure. In this paper, variable stiffness vibration neutralizers are used to impose zero displacement or nodes to reduce vibration at desired locations on a Euler-Bernoulli beam subjected to forced harmonic excitation. An iterative procedure is developed to find the required resonance frequencies of neutralizers to create nodes at selected locations. Numerical tests are performed to show the viability of the procedure that is developed. Experimental tests are conducted and results are compared with those obtained by numerical tests.
Stepped beams with elastic end supports have been extensively investigated due to their importance in structural engineering fields, including active structures, structural elements with integrated piezoelectric materials, shaft-disc system components, turbomachinery blades and many other structural configurations. Considering the importance of the use of discontinuous structures in the engineering, the authors propose a mathematic modeling which advantage is that the results are independent of the degree of mesh refinement. The analysis is based on the classical Euler-Bernoulli beam theory. In comparison with the published literature on the transverse vibration of single cross section change beams, there are relatively few works covering beam vibration when there is more than one change in the beam cross section. In the present study, the natural frequencies and the mode shapes of beams with variable geometry or material discontinuities are investigated. The mode shapes of a beam with multiple step changes in cross section are discussed theoretically and experimentally. Numerical results obtained by Euler-Bernoulli beam theory are compared with experimental results.
The present study attempts to diagnose severity of faults in ball bearings using various machine learning techniques, like support vector machine (SVM) and artificial neural network (ANN). Various features are extracted from raw vibration signals which include statistical features such as skewness, kurtosis, standard deviation and measures of uncertainty such as Shannon entropy, log energy entropy, sure entropy, etc. The calculated features are examined for their sensitivity towards fault of different severity in bearings. The proposed methodology incorporates extraction of most appropriate features from raw vibration signals. Results revealed that apart from statistical features uncertainty measures like log energy entropy and sure entropy are also good indicators of variation in fault severity. This work attempts to classify faults of different severity level in each bearing component which is not considered in most of the previous studies. Classification efficiency achieved by proposed methodology is compared to the other methodologies available in the literature. Comparative study shows the potential application of proposed methodology with machine learning techniques for the development of real time system to diagnose fault and it’s severity in ball bearings.
In this paper, an optimal adaptive fuzzy sliding mode controller is presented for a class of nonlinear systems. In the proposed control, in the beginning, the boundaries of parametric uncertainties, disturbances and un-modeled dynamics are reduced using a feedback linearization approach. Next, in order to overcome the remaining uncertainties, a sliding mode controller is designed. Mathematical proof shows that the closed-loop system with the proposed control is globally asymptotically stable. Using sliding mode control causes the undesirable chattering phenomenon to occur in the control input. Next, in order to remove the undesirable chattering phenomenon, an adaptive fuzzy approximator is designed to approximate the maximum boundary of the remaining uncertainties. Another mathematical proof shows that the closed-loop system with the proposed control is globally asymptotically stable in the presence of structured and unstructured uncertainties, and external disturbances. Finally, the self-adaptive modified bat algorithm is used to determine the coefficients of the adaptive fuzzy sliding mode control and the coefficients of the membership functions of the adaptive fuzzy approximator. To investigate the performance of the proposed controller, an inverted pendulum system is used as a case study. Simulation results verify the desirable performance of the optimal adaptive fuzzy sliding mode control.
An application of the finite spectrum assignment (FSA) control technique is presented for unstable systems with feedback delay. The FSA controller predicts the actual state of the system over the delay period using an internal model of the real system. If the internal model is perfectly accurate then the feedback delay can be compensated. However, parameter mismatches of the internal model or implementation inaccuracies of the control law may result in an unstable control process. In this paper, the stabilizability of an undamped second-order system is analyzed for different system and delay parameter mismatches. Theoretical stability and robustness to implementation inaccuracies of the control law are discussed. It is shown that, for small parameter uncertainties, the FSA controller allows stabilization for significantly larger feedback delays than conventional delayed proportional-derivative-acceleration controllers do.
The effect of internal parametric damper on periodic and quasi-periodic (QP) galloping of a wind-excited tower is studied analytically in this paper. We use a simple degree of freedom model and consider the cases where the turbulent wind activates external excitation, parametric one or both. The method of three stage perturbation analysis is performed to obtain an approximation of periodic and QP solutions as well as the QP modulation envelope. We explore the effect of internal parametric damping (PD) on the amplitude and the onset of periodic and QP galloping. It is revealed that for specific turbulent wind excitation, the PD significantly influences the critical wind speed above which periodic and QP galloping occurs. In the case where external and parametric excitations are activated simultaneously, QP galloping persists for all ranges of wind velocity. The results also show that the modulation frequency of the QP galloping depends strongly on the type of excitation induced by the turbulent wind.
This paper presents an adaptive control strategy for a unified chaotic system with unknown functions and full state constraints. The unknown functions in the unified chaotic system are approximated by using the radial basis function neural networks. At present, a great many of the results for chaotic system neglect the situation of full state constraints. In the proposed scheme, we successfully utilize the barrier Lyapunov function approach to prevent the full state from violating constraint condition. In addition, when the full state constraints are considered, the computation online burden is very large in the previous works. In contrast with the existing results for unified chaotic system, the number of the adaptation laws has only two. The state feedback controllers and the adaptive laws for estimating the uncertainties were derived based on the Lyapunov stability theory. Finally, it is proved that all the signals in the unified chaotic system are bounded and the constraints are not violated. The performance of the proposed scheme was validated by using a simulation example.
Parametric uncertainties play a significant role in the response predictions of a rotor system. In this paper, the quantification of uncertainty effects on the dynamic responses and vibration characteristics of a multi-rotor bearing system with the fault of angular misalignment is investigated. First, the motion equations of the rotor system are derived by taking into account the nonlinear supporting bearing and the displacement constraint between two rotors. The stochastic modeling with uncertainties of misalignment, damping and nonlinear support stiffness are then developed based on the polynomial chaos expansion technique in a stochastic framework, and traditional Monte-Carlo simulation is used as a comparison reference. Finally, the response statistics and dynamic behaviors of the stochastic system are demonstrated by mean and its probability density function (PDF). The results show that the super-harmonic resonance occur at the 1/2 of the critical speed due to the effect of misalignment, and as the uncertainty increases the realization amplitudes are spread over a wider band of amplitudes. Furthermore, P-bifurcation in the response PDFs is also presented in some situations.
An analytical solution for vibration of a parallel robot where its end-effector is flexible and has a passive prismatic joint(s) has not been presented before. In this research vibration analysis of a
A new method of modified optimization of double helical gears is proposed based on reducing vibration and noise and raising machining efficiency. Firstly, the straight profile of rack-cutter edge is replaced by three segment parabolas, and the equation of the rack-cutter profile is ultimately represented in the rack-cutter surface. Secondly, the physical and mathematical model of tooth contact analysis and loaded tooth contact analysis of double helical gears are introduced and then the loaded transmission errors are obtained. The optimal modification parameters are achieved based on the minimum amplitude of loaded transmission error. Finally, a set of equipment for measuring loaded transmission error, the analysis software platform and the test-bed of vibration and noise are designed, respectively. The feasibility of the method of modified optimization is verified. Compared with vibration and noise before modification, those after modification averagely decrease 18% and 2.7 dB.
The present investigation is concerned with a study effect of rotation and magnetic field on the plane deformation and the corresponding stresses in hollow elastic cylinder rotating about its axis with a constant angular velocity. The material of the cylinder is assumed to the non-homogeneous and orthotropic. Results of this paper are presented graphically and then compared with others in the absence of magnetic field, rotation and non-homogeneity. The results indicate that the effect of rotation and non-homogeneity are very pronounced. The variation of stresses and displacements has been shown graphically.
A nonlinear aeroelastic characterization of wind turbine blades is performed. A two-dimensional aerodynamic model based on the quasi-steady approximation is coupled with a plunging and pitching blade section. The governing nondimensional equations are derived. The normal form of the Hopf bifurcation is derived and used to characterize the behavior of the system. Using linear analysis, it is demonstrated that, as the blade radius and/or operating rotational speed are increased, wind turbine blades become more susceptible to flutter at freestream velocities that are close to the cut-out speed. The nonlinear analysis, based on the normal form of the Hopf bifurcation, shows that, depending on the nonlinear structural parameters and initial conditions, subcritical instability may take place which means that high limit-cycle oscillation amplitudes may take place at freestream velocities that are lower than the linear flutter speed.
A unified formulation of finite prism methods (FPMs) based on Reissner's mixed variational theorem is developed for the three-dimensional (3D) free vibration analysis of functionally graded (FG) carbon nanotube-reinforced composite (CNTRC) plates and laminated fiber-reinforced composite (FRC) plates, the edge conditions of which are considered such that one pair of opposite edges is simply supported and the other pair may be combinations of free, clamped or simply supported edges. The single-walled carbon nanotubes (CNTs) and polymer are regarded as the reinforcements and matrices, respectively, to produce the CNTRC plate. Four different distributions of CNTs varying in the thickness direction are considered (i.e. the uniformly distributed, and FG V-, rhombus-, and X-type variations), and the through-thickness distributions of effective material properties of the CNTRC plate are determined using the rule of mixtures. In the formulation, the CNTRC/FRC plate is divided into a number of finite prisms in the
Studying the problem of a moving load causing fracture is used in the interpretation analysis of geophysical fracture. This paper aims to study the stress produced in an irregular fiber-reinforced half-space due to a normal moving load on a free surface. The stress produced in this case has been obtained in a closed form. Three different cases of irregularity, viz. rectangular, parabolic and no irregularity, have been discussed and compared. The effects of depth, irregularity factor and maximum irregularity depth on stress have been investigated. Also, the stress produced from a normal moving load in an irregular isotropic half-space has been deduced as a special case of the problem and comparative study has been made with that of fiber-reinforced medium. Moreover, some important peculiarities have been depicted with the use of graphs.
A lot of effort has been put into accurately modelling virtual prototypes prior to physical building of structures, in order to minimize cost and time while improving performance. However, there are often significant discrepancies between the dynamics of virtual prototypes and actual physical structures, which are mainly caused by improper joint dynamics modelling and assumptions. To overcome these challenges, we propose a method for the identification of multiple joints in structures using the inverse receptance coupling method. This method enables the determination of the joint properties by finding the differences between the measured receptances of the assembled structures and the simulated receptances obtained from rigidly coupled substructures. The receptances are obtained either through the finite element model or experimental modal measurements. The only measurements required in the proposed identification method are measurements on the translational degrees of freedom of the substructures and assembled structure. Knowing the joint’s dynamic properties allows for the prediction of behavior of a new assembled structure that uses the same joint configuration, without the necessity of direct measurements on the structure.
This paper proposes the use of inverse disturbance response decoupling (DRD) for an optical table to suppress vibration in precision machinery. Optical tables are normally adopted in precision engineering to repress two vibration sources: ground disturbances from the environment and load disturbances from machines. The suspension settings for restraining these disturbances are conflicting; therefore, in previous studies, we developed a DRD structure that could independently control the disturbance responses: using soft passive elements to isolate the ground disturbances and improving the load responses by active control. This paper extends these ideas by proposing an inverse DRD structure that uses stiff passive elements to suppress load disturbances and improve ground responses by active control employing robust loop shaping techniques. The designed inverse DRD structure and controllers are implemented and verified by experiments. Based on the results, the proposed inverse DRD structure and robust control are deemed effective in improving the performance of an optical table.
This paper proposes a new method to investigate the characteristics of pitch-resistant hydraulically interconnected suspension (HIS) systems for two-axle vehicles in the pitch plane. The equations of motion for the mechanical and hydraulic coupled system are developed, in which the hydraulic strut forces are derived using the impedance transfer matrix method. The stiffness and damping matrices of the coupled systems are described in a manner similar to the generalized form of uncoupled conventional suspension (UCS) systems. The additional properties of HIS systems are explicitly described via hydraulic physical parameters. Based on the generalized form, (1) the accumulators of HIS systems can be functionally equivalent to a combined system with tandem bump and pitch-angular springs; (2) the direction damper valves (DDVs), which are located at the outlets of actuator cylinders, function like uncoupled tandem dampers; (3) the pitch damper valves (PDVs), which are fitted on the hose to connect the accumulators, alter the mode damping similar to the accumulators changing the mode stiffness; (4) the opposite installation corresponding to the schematic of front piston-rod-upward and rear piston-rod-downward produces higher mode stiffness and damping than the other installations. The dynamic responses are studied between the vehicles with HIS and UCS. Moreover, the damping coefficients are evaluated with the modal analysis method. The obtained results indicate that (1) the top and bottom DDVs mainly affect the vehicle body’s pitch motion and bounce vibration, respectively, (2) the PDVs are able to alter the load distribution among wheel stations, and (3) damping parameters can be designed to minimize the vehicle body’s pitch motion.
According to the framework of the Flügge’s shell theory, the Winkler and Pasternak foundations model, the transfer matrix approach and the Romberg integration method, the vibration behavior of an isotropic and orthotropic cylindrical shell with variable thickness is investigated. The governing equations of the shell based on the Pasternak foundation model are formulated and solved. The analysis is formulated to overcome the mathematical difficulties related to mode coupling which comes from the variable curvature and thickness of the shell. The vibration equations of the shell are reduced to eight first order differential equations in the circumferential coordinate. Using the transfer matrix of the shell, these equations can be written in a matrix differential equation. The proposed model is adopted to get the vibration frequencies and the corresponding mode shapes for the symmetrical and antisymmetrical modes of vibration. The sensitivity of the frequency parameters and the bending deformations to the Winkler and Pasternak foundations moduli, the thickness ratio, and the orthotropic parameters are demonstrated.
It is often desirable to simultaneously optimize the damping and stiffness distribution in the design of shell structures incorporating damping material layers for achieving the best vibration mitigation performance. This paper investigates the integrated topology optimization of host structures and damping layers for reducing the vibration level in the presence of harmonic excitations. Therein, the global damping matrix is a nonproportional one due to distributed damping effects. For an efficient frequency response analysis of the system with nonproportional damping, reduced-order equations are obtained by using lower-order eigenvectors of the undamped system, and then the method of complex mode superposition is employed for solving the dynamic equations in the state space. In the optimization model, the vibration amplitudes at specified positions are taken as the objective function. The relative densities of the elements are considered as design variables, and an artificial damping material model relating the local damping properties to the elemental density variables is employed. The Rational Approximation of Material Properties model is adopted to avoid localized modes in low-density areas during the optimization process. Numerical examples are presented to illustrate the effectiveness and efficiency of the proposed framework.
Using Mihailo Petrović's theory of mathematical phenomenology elements, phenomenological mapping in vibrations, signals, resonance and dynamical absorptions in models of dynamics of chain systems – the abstractions of different real dynamics of a chain system are identified and presented. Using a mathematical description of a chain mechanical system with a finite number of mass particles coupled by linear elastic springs and a finite number of degrees of freedom expressed by corresponding generalized independent coordinates, translator displacements and corresponding analysis of solutions for a free and forced vibrations series of multi-frequency regimes and resonant states as well as dynamical absorption states are identified. Using mathematical analogy and phenomenological mapping, analyses of the dynamics of other chain models are made. Phenomenological mapping is used to explain dynamics in systems with multiple deformable bodies (beams, plates, membranes or belts) through resonance and dynamical absorptions in the system and transfer of mechanical energies between bodies. Amplitude-frequency graphs for homogeneous and non-homogeneous chain systems are presented for a system with 11 degrees of freedom. Expressions for generalized coordinates of a chain non-homogeneous system in resonance regimes for a general case are derived. A theorem is defined and proven.
The optimal parameters of the support vector machine (SVM) are very important for accuracy modeling and generalization performance. The quantum particle swarm optimization (QPSO) algorithm takes on the characteristics of the rapid global optimization, scale chaos method provides the characteristics of the fast convergence and the SVM has the characteristics of the nonlinear fitting. These advantages of the scale chaos method and the QPSO algorithm are used to propose a scale chaos QPSO (SCQPSO) algorithm. Then the SCQPSO algorithm is used to optimize the parameters of the SVM model. A new information fusion method based the SCQPSO algorithm and the SVM model (SCQPSO-SVM) is proposed in this paper. The SCQPSO-SVM algorithm uses the global optimization ability of the SCQPSO algorithm to comprehensively optimize the penalty coefficient, kernel parameter and hybrid weight of the SVM model. The goal is to improve the solved speed and solution accuracy of the SVM model. The SCQPSO-SVM algorithm is applied in the testing function and the rotor fault diagnosis of traction motor. The experimental results show that the SCQPSO algorithm can search for the good optimization results and the SCQPSO-SVM algorithm can reduce the error rate of the fusion recognition. So the SCQPSO-SVM algorithm takes on better generalization performance and prediction accuracy in the real application.
This paper deals with the abatement of the tonal noise inside the fuselage of a mid-range tiltrotor aircraft, as generated by the propulsive system. The problem is basically multidisciplinary, involving interactions among the exterior noise field, elastic fuselage dynamics, interior acoustics and control system. A stiffened fuselage, with piezoelectric patches embedded into the structure, is supposed to be impinged on by the aeroacoustic field generated by propellers and excited by the wing/pylon/proprotor vibratory loads at the wing–fuselage attachment. An optimal linear quadratic regulator cyclic control formulation, coupled with a genetic optimization algorithm, is applied to synthesize the control law driving the smart actuators so as to alleviate cabin noise. The aeroacoustoelastic model considered in the control problem is obtained by combining cabin interior acoustics, fuselage smart shell dynamics and wing/pylon/proprotor aeroelasticity described through modal approaches with the exterior pressure field provided by boundary element method solvers. Numerical results examine the effectiveness and robustness of the proposed active control strategy.
The inertia flywheel pendulum exhibits several characteristics, such as underactuation and nonlinearity, that make it attractive for research and advanced control education. The main goal of this paper is to develop a novel mechatronic kit with a control methodology for an inertia flywheel pendulum. The mechatronic kit has a motor and flywheel mounted at the top of the body. It is a physical pendulum with a symmetric wheel attached to the end, which is free to spin around an axis parallel to the axis of rotation of the pendulum. The flywheel is actuated by a direct current motor and the coupling torque generated by angular acceleration of a wheel disk is used to dynamically control the system. The hybrid control strategy for stabilization of the inertia flywheel pendulum is presented and examined. The control aim is achieved by the solution of the following two particular control problems: swinging the pendulum up to a certain neighborhood of the inverted position and balancing it in this position. The energy control was designed for swing-up of the inverted pendulum. The genetic algorithm proportional-integral-derivative controller was implemented for balancing the inverted pendulum. The proposed hybrid control methodology has successfully performed stabilization control, even when unexpected loading conditions occur. Consequently, the novel flywheel pendulum system is ideally suited for advanced control courses for educating university students.
In this paper, a novel synchronization method of modified function projective lag synchronizations (MFPLS) between identical and nonidentical hyperchaotic complex nonlinear systems with parameter perturbations and external perturbations is proposed. In the method, the states of two hyperchaotic complex systems with parameter perturbations and external perturbations are asymptotically lag synchronized up to a desired scaling function matrix, and all the perturbations in the parameters asymptotically converge to zero. Base on the Lyapunov stability theory, the adaptive controller and updating laws of parameter perturbations are designed to achieve MFPLS between the drive and response systems. Theoretically the proof that the drive and response system will asymptotically lag synchronization and numerical simulations verify the feasibility and effectiveness of the proposed scheme.
The present paper is concerned with the propagation of waves in microstretch thermoelastic solid with microtemperatures. The phase velocity, attenuation coefficient, penetration depth and specific loss of longitudinal displacement wave, thermal wave, microstretch wave, longitudinal microtemperature wave, coupled transverse displacement wave, microrotational wave, transverse microtemperature wave are obtained. Microstretch, microtemperatures and microrotational effects on the phase velocity, attenuation coefficient, penetration depth and specific loss have been evaluated numerically and presented graphically. Some special cases of interest are also shown.
In this study, an active vibration suppression control is presented for use in a two degree-of-freedom piezoelectric flexible structure system containing a rectangular plate driven by dc motors. A mathematical model involving a clamped-free-free-free cantilever flexible plate, piezoelectric transducer, and motor dynamics is derived for modal analysis and control design. To simplify the control design of this multivariable system, a two-stage design strategy is proposed because the plate motion exerts a comparatively small effect on the dc motors. Both the plate vibration and coupling effect in the motors are considered when designing a centralized motor tracking controller. Given a well-designed two-axis motor control system, piezoelectric actuators are used on the plate to perform efficient active vibration suppression control. Hybrid proportional-derivative and repetitive control methods are extended to manage the multiple-period disturbances and resonant excitation. Three sets of simulation experiments were conducted, focusing on suppressing the plate vibration response and demonstrating the effectiveness of the proposed method.
The pressure distribution in an aerostatic bearing has an important effect on the performance of the associated mechanical equipment. To more accurately predict performance, a new dynamic modeling method has been developed that takes into account the pressure distribution in the bearing by integrating the principle of flow equilibrium and finite element theory. The direct corresponding relationship between the fluid film characteristics and spindle dynamic performance is established using this method. The simulation and experimental results show that the new dynamic modeling method for the aerostatic bearing is more efficient and reliable than traditional modeling methods.
DC motors have been extensively used in many industrial applications. The control of the speed of a DC motor is therefore an important issue and has been studied since the early decades of the last century. This paper presents a novel neural network (NN)-based model reference adaptive control (MRAC) to improve the trajectory tracking performance of a DC motor. In this scheme, the controller is designed using a parallel combination of the conventional MRAC scheme and an NN controller. The controller is used to change the duty cycle of the converter and, thereby, the voltage fed to the armature of the separately excited motor to regulate the speed. The operating characteristics of the proposed drive system are compared with MRAC control to verify the effectiveness under various conditions by investigating the transient responses for the step change of the speed command and the load torque. Finally, simulated and experimental results show that on the one hand the proposed controller provides high-performance dynamic characteristics, and on the other hand that this scheme is robust with respect to load disturbances.
When the velocity of fluid flow in a cantilevered pipe is successively increased, the vibration characteristics of the system may vary remarkably. This paper is concerned with exploring the evolution of the actual mode shapes of the pipe with increasing flow velocity. Results show that the mode shapes of the cantilevered system may dramatically change due to the increment of flow velocity. At higher flow velocity, these mode shapes, indeed, differ much from those of the classical cantilevered beam. When a critical mass ratio at which the so-called ‘mode exchange’ phenomenon occurs was chosen, the corresponding two modes of the cantilevered pipe would have the same shape. In addition, the nonlinear responses of the system have also been linked to the lowest three mode shapes by comparing the calculated mode shapes with the limit-cycle motions obtained experimentally.
Owing to the inherent complexity and variability of the machining process, the sound signals of the cutting process are usually polluted by chip breakage signals and environmental noise which makes it very difficult for tool breakage detection based on sound signals. An approach based on empirical mode decomposition (EMD) and independent component analysis (ICA) is presented to deal with the blind source separation problem of cutting sound signals in face milling with the objective of separating cutting oriented sound signals from those background noises. The advantage of EMD is its ability to adaptively decompose an arbitrary complicated time series into a set of components, called intrinsic mode functions (IMFs). With EMD, cutting sound signals in face milling process are composed into a set of IMFs. Using fast ICA to analyze these series, some independent components are obtained, from which different types of sound signals can be extracted. Experimental results show that the proposed EMD-ICA method is capable of separating cutting sound signals in face milling, where different source components related to a normal insert and a broken one are extracted successfully. This makes tool breakage detection possible.
The issue of synchronization between dynamical systems has attracted much attention, and the systems with integer-order dynamical networks have been well studied. The synchronous behavior of fractional-order dynamical systems is very interesting and importance, but has rarely been studied. In this paper, we studied the synchronization and anti-synchronization behavior between integer-order dynamical networks and fractional-order dynamical systems via a Takagi-Sugeno fuzzy model. Remarkably, there is synchronous behavior in such a system, and this is dramatically different from the behavior of integer-order dynamical networks. Moreover, we studied the impact of different coupling strengths on the dynamical process of synchronization and robustness of the designed controller to different coupling functions, different dimensions of dynamical equations and different fractional orders. Finally, we propose the theoretical analysis, which coincides well with the numerical simulations of five typical examples.
Subspace-based methods for estimation of modal parameters are briefly reviewed in this study and a time-varying modal parameter identification algorithm, based on finite-data-window Projection Approximation Subspace Tracking, is presented to investigate the time-varying modal parameters of a trapezoidal titanium-alloy plate in temperature-varying environments. An experiment conducted on a steel beam with a removable mass is used to confirm the proposed method with a brief discussion on the factors of this method. Two groups of experiments are conducted to reveal the effects of varying temperature and heating speed on the natural frequencies of the plate, and the identified natural frequencies evidently show the effect of thermal stresses caused by temperature gradients in experiment.
In this paper optimal power flow control of power transmission networks using graph theory is presented. Graph theory is employed to trace the optimal path of power flow in transmission lines. Graph theory-based search algorithms such as Depth First Search and Breadth First Search are used for determining the sequence of tracing of nodes. Loops in the network are formed such that each loop contains at least one active source. The algorithms are tested on a six bus system using MATLAB programs. Considering the real power losses and the time required for computation of power flow tracing, the graph algorithms give better results compared to the conventional Newton–Raphson method.
The frequency response analysis of antagonistic shape memory alloy actuators and the influence of temperature, stress and strain on its speed of operation are studied and presented. Based on the decisive results an interesting servo control application is designed and tested such that the operating angle utilizes only partial strain of shape memory alloy (SMA) wire. The application developed is an open loop unstable, under actuated, a renowned highly dynamic ball balancing beam system driven by antagonistic SMA wires. The control scheme of proportional derivative controller cascaded with sliding mode controller is designed in order to demonstrate the tracking control capability of SMA wires under partial transformation. Experimental results show the motion control with significantly faster response of SMA under partial transformation. The robustness of the control system for disturbance rejection is also tested. The implication is that this design scheme can be extended to all other dynamic applications including robotics, automotive, aerospace, etc.
Since there are nonlinearities in an electro-hydraulic servo shaking table, when the shaking table corresponds to sinusoidal shaking tests, its response contains higher harmonics, resulting in harmonic distortion and deteriorating the control performance. It needs to provide harmonic information for harmonic cancellation. The purpose of the paper is to develop an online acceleration harmonic identification algorithm for the shaking table. The unscented Kalman filter is applied to achieve this task. A nonlinear state space of the sinusoidal acceleration response is built for the unscented Kalman filter, which estimates the state of the nonlinear model, and the amplitude and phase of each harmonic, including the fundamental, can be directly decomposed from the identified state vector. The state transition equation is linear and the measurement equation is nonlinear. The efficiency and real-time performance of the developed acceleration harmonic identification are validated by simulation and experiment, in which the estimation error is further used to testify the estimation accuracy.
The detection and diagnosis of bearing health status using vibration signal has been an important subject for extensive research over the past few decades. The objective of this paper is to proposed permutation entropy as a tool to select best wavelet for feature selection for the detection as well as fault classification of ball bearings. The continuous wavelet coefficients of the time domain signal are calculated at real, positive scales using various real and complex wavelets. Best wavelet and corresponding scale is selected based on minimum permutation entropy. Eleven statistical parameters were used for defect classification in outer race, inner race, ball defect and healthy bearing respectively. Proposed methodology for fault classification is compared with two artificial intelligence techniques such as artificial neural network and support vector machine. Results revealed that permutation entropy based feature extraction techniques provide higher classification accuracy even when there is a slight variation in operating condition which is useful for development of online fault diagnosis.
An online multi-input multi-output (MIMO) random vibration control method is presented for a multi-axis hydraulic shaking table system to replicate the reference acceleration power spectral density (PSD) by the reproduction of the acceleration time domain histories that are proportional to the reference. The offline iterations are implemented using conventional random vibration control to compensate for the changes in the frequency response function (FRF) of the system. The successful test mainly depended on the experience of the operator. In online MIMO random vibration control, the reference PSD is transformed into time domain histories by filtering white noise. The impedance matrix of the shaking table system, which is the inverse of the FRF, is calculated and updated online. The time histories are compensated based on the system impedance matrix and then used as the drive signals to the shaking table. The overlap-save method and fast Fourier transformation are proposed to implement the transformation and compensation online. Two-axis random vibration experimental results obtained with the proposed control method show that both the reference PSD and the time domain histories can be replicated with high precision in the output of the shaking table without operator intervention.
Based on the study of the dynamic properties of the Maglev vehicle-guideway coupling vibration system under the control of a full state feedback controller, the similarity processing was carried out between the coupling vibration system and a small scale model. The similarity ratio coefficients were obtained according to the similarity theory. The results show that the Maglev control method, calculating the controller output with the vibration information of the guideway low order mode and the magnet, is effective and can keep the system stable. For the coupling vibration system the first three modes can give, respectively, an accurate description of the system dynamic characteristics. When investigating the lower frequency characteristics of the system, the first mode will also be sufficient, especially when a large difference between the lower frequencies exists. The small scale model obtained according to the similarity theory is coincident with the original model in dynamic performance, which provides an effective methodology to set up small scale test rig for the investigation of the Maglev vehicle-guideway coupling vibration.
For low frequency signals under 10 Hz, effective control methods are urgently needed to realize active vibration control for precision instruments. Based on our previous works on design and dynamical modeling of micro-parallel manipulators, a mixed H 2 /H control model is proposed for controlling a compliant three universal-prismatic-universal (3-UPU) parallel platform in this paper, which is established in a state-space framework considering the stiffness of flexure hinges. Moreover, other control methods in terms of LQR, H 2 and H are approached for a multiple-input and multiple-output (MIMO) active vibration isolation system, and the mixed H 2 /H method has proved more effective than the three methods mentioned above. Finally, an experimental system is built up to implement the active vibration control using an improved 3-UPU compliant parallel manipulator prototype. With the hardware and software developed, the real-time active vibration control methods have been tested at random signals; frequency rates at 0.5 Hz and 1 Hz are selected for illustrations. The experimental results demonstrate that the vibrations acting on the base and the moving platform are significantly reduced, and are limited to 0–10 Hz vibration signals. This active vibration control system provides a reliable experimental platform for validating the theoretical analysis work.
This paper considers the parameter estimation problem of controlled autoregressive moving average systems. The basic idea is to use the noise polynomial to filter the input-output data, then a controlled moving average identification model and a noise model are obtained. A maximum likelihood recursive least squares algorithm and a recursive least squares algorithm are used to interactively estimate the parameters of the two identification models by using the hierarchical identification principle. A numerical example is provided to show the effectiveness of the proposed algorithms.
Problems involving vibrations occur in many fields of engineering. Thus, it is necessary to increase the knowledge of the damping, offered by new structural configurations and materials in order to reduce the vibration levels. The present paper focuses its attention on the measurements of the structural loss factor of different types of sandwich panels made of eco-friendly materials. The interest in natural materials, for structural applications, has considerably increased in the last years thanks to the growing environmental concerns. The influence on the loss factor of face sheet materials, core types and configurations is experimentally evaluated by means of measurements of the reverberation time (RT 60). The reported data represent a good initial database for more detailed analyses of these new materials.
In this paper, boundary control of a composite shell vibrations containing fluid (partially filled with a fluid) is studied. The linear boundary control laws consisting of forces and moments from the boundaries of the composite shell stabilize the vibrations. The fluid has free surface and boundary stabilization is attained without using in domain attached actuators. This research utilizes semigroup techniques and LaSalle invariant set theorem to prove the boundary stabilization.
This article presents multiple channel estimation (MCE) that is a multi-sensor access wireless system model. An avionics wireless system needs a power control device to match the power received from the multiple sensors. Without a power control device, the aircraft control unit is unable to receive the signals from sensors due to signal reflections, refraction and transmission loss. The MCE system is designed to suppress multi-sensor signal noise and interference while a sensor, with lower power than the other sensors, is received. This article investigates overcome the power difference based on the MCE system. The performance of proposed MCE model is investigated and validated for a safe indoor avionics wireless system and it improves the overall performance of the wireless system to perfect power stability.
In this study, the axial vibration of double-walled carbon nanotubes (DWCNTs) is studied using nonlocal elasticity theory. The nonlocal constitutive equations of Eringen are used in the formulations. The van der Waals forces are considered in the axial direction.An interaction coefficient is obtained in terms of the previously proposed van der Waals coefficient and effective thickness of the single-walled carbon nanotubes. The effect of various parameters like geometry of nanotubes, van der Waals forces and nonlocal parameters on the axial vibration of DWCNTs is discussed. Some mode shapes are also depicted in order to show the relative motion of the nested tubes. The van der Waals forces have strong effects on the axial vibration characteristics of DWCNTs. The present results can be used in the continuum modeling of nanoscale linear motors and oscillators.
This paper presents an experimental study of the nonlinear characteristics of an axially moving string. An experimental system with a simple configuration, which is similar to a practical application, was built. Two laser sensors were used to monitor the vertical and horizontal vibrations of the moving string under different conditions. Using the Hilbert-Huang transform method, the detailed results of a typical measured data series, which include intrinsic mode decomposition, Hilbert spectrum and marginal spectrum, are introduced. For comparison, marginal spectra for almost all test cases are also given. Based on the results, several observed nonlinear phenomena, which include whirling motion, resonances, quasiperiodical and a beating motion, torus doublings and one chaotic motion, are presented. The quantitative nonlinear vibrating details and the observed rich behaviors help explain the great complexity of a single moving string.
The trajectory tracking problem for nonlinear brushless direct current drive is solved by combined robust and flatness state feedback control. The drive's nonlinear model is shown to have the flatness property. The proposed controller consists of two parts, linear and nonlinear. Linear matrix inequalities (LMI) optimization is used to design the linear part which achieves robust stability against system uncertainties, desired swiftness, and guaranteed cost performance. System uncertainty due to changes in the drive's parameters is represented with a norm-bounded structure. The nonlinear control part solves the motion planning problem through flatness which avoids integrating the differential equations of the dynamics. The main advantages of this technique are that the LMI algorithm includes an optimal part to preclude high control efforts, and the control burden is heavily placed on the linear part to achieve flatness properties. In some systems, in which flatness cannot be achieved, adding robust linear control can overcome or alleviate this problem.
In this study, a controller which was based on fuzzy logic, was mounted to a suspension system in parallel and was controlled in the multi degree of freedom model of a vehicle.The body splashes, inputs of control power and the frequency responses of the acceleration were obtained when the vehicle went through a hollow profile way and the simulation results were compared with the uncontrolled vehicle body movement.Taking into account the driving comfort performance of the controller and the development of system, response were shown.
This paper deals with the free vibration characteristics of woven fiber glass/epoxy delaminated doubly curved composite panels in a thermal environment based on the finite element approach. First-order shear deformation theory is used for a composite shell model with provision of mid-plane strip delamination at arbitrary locations. An isoparametric quadratic shell element with eight nodes and five degrees of freedom per node is used in the analysis. For modeling the delamination, a multipoint constraint algorithm is incorporated in the analysis. The thermal field includes elevated temperatures up to 400 K and sub-zero temperatures up to cryogenic range of 123 K to simulate the temperature surrounding the aircraft during flight and ground conditions and submarines. The effects of delamination size, temperature, boundary conditions and curvature on the natural frequencies of composite panels are investigated. The results indicate that the percentage of strip delamination, curvature with different boundary conditions in a thermal field have significant effects on the vibration behavior of the composite panels.
In this paper, the basic dynamical properties of a complex chaotic system are investigated by the imaginary part and the real part of the complex chaotic system are separated. Based on Lyapunov stability theorem, a feedback control method is proposed for synchronization of a complex chaotic system with parameters perturbation and external disturbances. The simulation results show the feasibility of the method.
Numerous developments have been witnessing in manufacturing industries the ability of the machines to change the tools automatically during their wear or damage. In general, tool failure contributes about 7% to the down time of machine centers. Therefore, online monitoring of tool wear is an important phenomenon in producing quality products at reasonable cost. This also increases the production rate in the industries. Tool condition monitoring using the acoustic emission technique (AET) are real methods identified by researchers for online quality assessment of machine tools. The genetic algorithm (GA) is used to optimize the tool wear rate parameters. The practical significance of applying GA to tool wear rate has been validated by means of computing the deviation between predicted and experimentally obtained process parameters. Based on this research work, an experimental setup has been developed for online monitoring of a single point cutting tool using AETs. The experimental tool wear rate results are compared with online measurements using mean acoustic emission parameters (average value, root mean square value and area).
In this paper the dispersion relation of surface wave for a fluid layer overlying a slightly compressible, finitely deformed half-space is discussed. It has been observed that as the wave number tends to zero the dispersion relation transformed to the speed equation of surface waves. For graphical representation we have considered Neo-Hookean form of strain energy function. Phase speed curves have been plotted and different discussions have been made.
In the maintenance of motor driven systems, detection of cracks in shafts play a critical role. Condition monitoring and fault diagnostics detect and distinguish different kinds of machinery faults, and provide a significant improvement in maintenance efficiency. In this study, we apply the discrete wavelet transform theory and multiresolution analysis (MRA) to vibration signals to find characteristic patterns of shafts with a transversal crack. The feature vectors generated are used as input to an intelligent classification system based on artificial neural networks (ANNs). Wavelet theory provides signal timescale information, and enables the extraction of significant features from vibration signals that can be used for damage detection. The feature vectors generated for every fault condition feed a radial basis function neural network (ANN-RBF) and apply supervised learning designed and adapted for different fault crack conditions. Together, MRA and RBF constitute an automatic monitoring system with a fast diagnosis online capability. The proposed method is applied to simulated numerical signals to prove its soundness. The numerical data are acquired from a modified Jeffcott Rotor model with four transverse breathing crack sizes. The results demonstrate that this novel diagnostic method that combines wavelets and an artificial neural network is an efficient tool for the automatic detection of cracks in rotors.
The characteristics of the beam-mode stability of the fluid-conveying shell systems are investigated in this paper, under the clamped-clamped condition. A finite element model algorithm is developed to conduct the investigation. A periodic structure of functionally graded material (FGM) for the shell system, termed as PFGM shell here, is designed to enhance the stability for the shell systems, and to eliminate the stress concentration problems that exist in periodic structures. Results show that (i) the dynamical behaviors, either the divergence or the coupled-mode flutter, are all improved in such a periodic shell system; (ii) the critical velocities u cr for the divergent form of instability is independent of the normalized fluid density β; (iii) various critical values of β exist in the system, for indentifying the coupled modes of flutter (Païdoussis-type or Hamiltonian Hopf bifurcation flutter) and for determining the mode exchange; (iv) changes of some key parameters, e.g., lengths of segments and/or ‘grading profiles’ could result in appreciable improvement on the stability of the system.
This paper addresses the vibration reduction of a simple structure, simulating a workpiece carrier plate, through a cancellation technique based on the use of smart compensation actuators. The proposed compensation strategy is implemented resorting to magnetostrictive actuators acting far from their resonant frequencies. Specifically, the procedure has been tested on two test rigs designed with particular reference to machine tools applications: they require the use of one and three magnetostrictive actuators for one-dimensional (1D) and three-dimensional (3D) vibrations compensation. The parameters of the compensation strategy are identified from the direct characterization of the actuators embedded in the structure. The resulting reduction of the lateral vibrations of 1D and 3D plates in the frequency range up to 400 Hz proves to be very satisfactory.
The capabilities of wavelet networks in function approximation make them appealing for black box system identification. In this paper, a new active noise control (ANC) algorithm is developed based on adaptive wavelet networks. The proposed adaptive nonlinear noise control approach employs frames from POLYnominal WinOwed with Gaussian wavelets. Also, a novel network structure for active noise control is derived incorporating a nonlinear static mapping cascaded with an infinite impulse response filter to model the dynamic part of the network. Online dynamic backpropagation learning algorithms based on gradient descent method are applied to adjust the network parameters. Local convergence of the closed-loop system is proved using discrete Lyapunov function.The performance of the proposed ANC system is examined for typical linear/nonlinear cases. The simulation results demonstrate superior performance of this method in terms of stability, fast convergence rate and noise attenuation while avoiding curse of dimensionality.
Magneto-rheological (MR) fluids consist of magnetic particles in carrying fluid. One of the drawbacks in using MR dampers in laboratory work is their price. At present, there is a compelling need for the production of the laboratory scale of MR fluids to lower their production cost. In this study, to show that the MR fluid is an applicable prototyped laboratory scale of single ended and mono-tube, MR dampers with a prototyped MR fluid are presented. The main features of produced MR fluid and dampers are simplifying in constructing and their low cost. These dampers are useful for laboratory research work. To illustrate the validity of the MR fluids, using this fluid, four MR dampers are made and based on the neuro-fuzzy (NF) algorithm are experimentally tested on a light commercial vehicle. The results of the experiment are analyzed for passengers comfort during driving. In this paper, the NF strategy is trained according to simulation results. The results that are obtained from the experiment are good and acceptable. The results have shown that the new prototyped MR dampers are implementable on actual cars for research studies with a low price.
Substantial developments have taken place in the areas of structural health monitoring, wherein, the objective is not only to detect damage but also to determine its size and location across the structure. Often, the damaged structures do not become obsolete unless the damage is severe. Thus, it is important to mitigate the growth of damage and prevent the possibilities of a structural failure. Vibration is an important source of damage growth. Therefore, it is important to control vibrations such that the damage growth is mitigated. Supposing an effect of damage in the structure is said to be mitigated when the vibration response of the damaged structure with control is the same as the vibration response of the undamaged structure, then one of the requirements is that the closed loop eigenstructure of the damaged structure needs to match with the open loop eigenstructure of the undamaged structure. In this framework, this paper uses a linear algebraic technique to assign the undamaged eigenvalues and eigenvectors for the damaged structure with a stiffness loss using a state feedback controller. Through this technique, it is shown that the vibration control using an actuator load can help to mitigate damage growth by reducing the vibration response magnitudes at the damaged structural degrees of freedom, while these magnitudes at other nodes are allowed to increase due to the actuator loads. Vibration control in this sense for structural damage mitigation is illustrated using discrete and continuous structures.
The active control method is a popular way to control mechanical vibration. However, for some industrial needs and military requirements, it does not only need to control vibration, but also has to change the online constant working frequency responses, for example to improve the dynamic performance of mechanical devices and the stealth of military equipment. Because the present active control methods mainly focus on vibration control, the dynamic frequency responses active control method (DFRACM) is constructed to deal with this problem. The constructed DFRACM can not only accomplish vibration control but can also arbitrarily change the dynamic frequency responses of mechanical equipment. Besides, in order to satisfy engineering requirements, the multi-objective DFRACM, which can control the dynamic frequency responses of the controlled object to reach separate specific objectives at different places in one time, is also studied in this paper. The effectiveness of the constructed method is verified through experiments of the open cylindrical shell structure.
The thermo-mechanical nonlinear dynamics of an axially moving beam with coupled longitudinal and transverse displacements subjected to a distributed harmonic external force is numerically investigated. This includes a case where the system is tuned to a three-to-one internal resonance between the first two transverse modes and a case where it is not is considered. Two coupled nonlinear partial differential equations for the longitudinal and transverse motions are obtained using Hamilton’s principle and constitutive relations, as well as taking into account the thermal effects. The Galerkin method is then used to discretize these equations into a set of coupled nonlinear ordinary differential equations. Two different techniques are employed to solve the resulting equations; the pseudo-arclength continuation method and direct time integration to investigate the periodic vibrations and the global dynamics of the system, respectively. The effect of different parameters on the dynamics of the system is investigated through the frequency-response curves of the system and the bifurcation diagrams of Poincaré maps. Furthermore, time histories, phase-plane portraits, and fast Fourier transforms are presented for a few different system parameter sets. It is illustrated that the system shows a broad variety of rich dynamics, depending on system parameters and the temperature rise.
Ship stabilization against roll motion caused by uncertainties, such as external waves or wind impact, nonlinear roll damping and parametric variation etc., is an important problem. Among announced approaches, the active fin stabilizer is a very effective and widely adopted procedure; however an accurate model of a whole nonlinear dynamic system is difficult to obtain. On the other hand, the mobile-wheeled platform also has highly nonlinear dynamic characteristics and it is difficult to evaluate the appropriate control effort to steer and balance on a bumpy road. To deal with these two systems, there existing some restricted resemblance between them, an intelligent roll-motion controller is developed in this paper. Firstly, to confront the uncertainties, a hetero-associative neural observer is added into a novel translated fuzzy sliding-mode controller (FSMC) to predict uncertainties. The neural observer can speed up the response and increase the self-tuning capability of the FSMC. In the proposed roll-motion controller, a compact gyroscope and accelerometer are used to detect the rolling conditions; the gathered data are sent to a microcontroller to calculate the command. Finally, to verify the effectiveness of the proposed controller, some preliminary simulations for ship stabilization are provided under the assumption that the sea surface is modeled as a one-dimensional linear free surface. Then, some experimental results are provided for a mobile-wheeled platform steered on a bumpy road. The performance is also compared with a conventional PD controller and a pure FSMC under the same conditions.
The vibration of a single-conductor transmission line with a Stockbridge damper is examined by modeling the system as a double-beam concept. The equations of motion are derived using Hamilton’s principle, and expressions are presented for the frequency equation, mode shapes, and orthogonality conditions. The analytical results are validated experimentally. The effect of the damper characteristics and location on the system natural frequencies is investigated via a parametric study. The role of the latter with respect to frequency is inconclusive. The present approach enables transmission lines designers to determine the exact natural frequencies and mode shapes that are required in the study of the vibrational response of a single conductor with a Stockbridge damper.
This paper presents a numerical study on the control of frequency-domain bifurcation in forced Duffing oscillators, through the use of pole placement techniques. First, the bifurcation frequency range of the Duffing oscillator is identified using the system and forcing parameters. A linear state feedback controller is then applied to the system, in order to assign the peak resonance frequency to a prescribed value, such that bifurcation is minimized or eliminated in the closed-loop system. Additional constraints are applied to the pole placement in order to minimize the control effort, such as assigning the closed-loop poles within an elliptical region in the complex domain. Finally, a constraint is placed on the maximum forcing level, such that bifurcation will not occur at relatively small forcing amplitudes. These techniques are demonstrated using several numerical examples.
A mechanical system containing compliant element is investigated. Such an element can be, for example, a compliant platform where the operated object (plant) is installed or an elastic gear that connects a motor with this movable object. The control parameter (force or torque) is bounded in magnitude. Only the first (lowest) resonance frequency is taken into account. Thus the system under consideration has two degrees of freedom and one control input. A double zero eigenvalue and two complex eigenvalues are in the linear mathematical model of this system. Control laws to steer the plant from the given initial state to the given final state in finite time are designed. These controls are divided into intervals on which it varies linearly depending on time or is constant. The time intervals where the control varies are equal to the period of the natural vibrations of the system. If there is no damping, this makes it possible to completely avoid vibrations on the time intervals where the control is constant including the time when the control signal becomes zero (identically). Another way to avoid the vibrations is to put the total time of the transient process equal to a multiple of the doubled period of the natural vibrations.
The operational efficiency and life of mechanical systems/structures depends to a large extent on their vibration control. Continuously occurring vibrations on the systems can cause fatigue and the effects of these vibrations are particularly severe if they occur at a frequency matching with that of the concerned system’s natural frequency – a stage called resonance. This paper focuses on achieving active vibration control of a smart cantilever beam at its first resonant frequency as it is at this stage that maximum damage to the system performance is expected. The smart system is modelled in the parametric domain using finite element modeling techniques and the obtained model is validated through experimental means. The active vibration control is achieved by employing two control algorithms namely – output feedback and error based control through general purpose operating system (LabVIEW on Windows 7) as well as in real time operating system (LabVIEW FPGA coupled with compact reconfigurable input output modules) and the performances are compared thereby justifying the importance of the deterministic and reliable real time control over the usual PC based control in experimental studies.
Achieving balance between robustness and performance is always a fundamental challenge we are faced with in control design of systems in the presence of uncertainties. H robust control theory has been extensively used to deal with the problems of robust stabilization and disturbance attenuation of uncertain systems. However, in traditional H robust control, the most frequently used method for dealing with uncertainties is adopting the assumption of norm-bounded perturbations of arbitrary structure about a nominal plant and the design techniques are based on the deterministic worst-case scenarios that may never occur in a particular control system and thus often led to over-conservative results. In this paper we focus on developing a reliability method for probabilistic H robust control of linear uncertain systems by describing the uncertain parameters as random variables. A new efficient reliability method for robust control of dynamic systems with probabilistic parametric uncertainties is presented systematically. Robust control design is carried out by solving a reliability-based optimization problem where the disturbance attenuation and control cost are minimized under the condition that reliability requirement is satisfied. One of the advantages of the presented reliability method is that it can be used directly for robust control design of parametric uncertain systems. Another advantage of the presented method is that it makes it possible to consider the factors such as system performance, control cost, and reliability simultaneously in an integrated framework and provides an essential basis for the coordination and tradeoffs between these important factors in control design of uncertain systems. Compared to traditional H robust control, the presented method is less-conservative and more reasonable for dealing with probabilistic uncertainties. The presented formulations are within the framework of linear matrix inequality and thus can be carried out conveniently. Two numerical examples are investigated to demonstrate the effectiveness and feasibility of the presented method.
The stability and bifurcation of a flexible rod-fastening rotor bearing system (RBS) is investigated in this paper. The rod-fastening rotor has two kinds of special structural features – rods and interfaces. The circumferentially distributed rods are modeled as a constant stiffness matrix and an add-on moment vector, which is caused by the unbalanced pre-tightening forces. The stiffness matrix of interface is composed of normal and tangential contact stiffness, which are determined by the pre-tightening forces. After the shaft is discretized by Timoshenko elements, the system is reduced by a component mode synthesis. Periodic motions and stability margins are obtained by using the shooting method and path-following technique, and the local stability of system is obtained by using the Floquet theory. Comparisons indicate that the rod-fastening and complete RBS have a general resemblance in the bifurcation characteristics when mass eccentricity and rotating speed are changed. The unbalanced over-tightening of rods brings initial bending to the rotor, which leads to obvious influence on the nonlinear responses of the system. Moreover, the pre-tightening forces should be sufficiently applied because the small pre-tightening forces make the system more flexible and unstable through the effect of contact interfaces. Generally, this paper presents a method for analyzing the stability and bifurcation of the rod-fastening RBS.
Structural health monitoring (SHM) in-service is very important and definitely demanded for the safe working of high performance composite structures in situ. Fiber Bragg grating-based sensors were usually embedded inside a composite to compose a smart structure for a real time monitor. However, the mechanical performance of the materials would be unfavorably influenced. To lower the influence, a smaller diameter optical fiber is preferred. In this paper, a new non-destructive evaluation sensor system based on small diameter fiber Bragg grating (SDFBG) was proposed. The impact results show that the SDFBG sensor could be used in dynamic strain measurement and detect the natural frequency of the structure. Furthermore, the sensor would be applied in SHM.
Generally, a low damping system has a small phase margin. One should deal with the problems of long time delay and unmodeled dynamics for active vibration control of a low damping system sometimes. For a pneumatic drive flexible manipulator system, time delay or phase lag and unmodeled nonlinear dynamics problems have raised the level of concern. It is vital but difficult to regulate the phase of vibration controller, to compensate for the time-varying phase lag or time delay due to the gas compression and parametric uncertainty of the pneumatic control system. The objective of this investigation is to formulate an active vibration control law with practical approach of phase adjusting for a pneumatic drive flexible manipulator system. A control strategy named adaptive phase adjusting control is designed and applied. The adaptive phase adjusting controller is implemented by using the phase angles as explicit parameters. These parameters are tuned online, depending on the corresponding control performance index. To evaluate the control performance of the designed adaptive phase adjusting technique, experiments are conducted on a pneumatic drive flexible manipulator experimental setup. The experimental results demonstrate the adaptive phase adjusting controller has the ability to optimize the phase angle accordingly. Vibration suppression is accomplished by using the designed adaptive phase adjusting controller, even with time delay and unmodeled dynamics in the system.
Active vibration control is one of the most efficient systems to mitigate excessive vibrations by providing significantly superior supplemental damping in civil engineering structures. One of the most challenging components of active control is development of an accurate analytical approach with minor computational expenses. Active mass damper (AMD) is one of the most commonly used active control devices, including a mass-spring-damper system with an actuator to increase the amount of damping in structures. Block pulse functions have been studied and applied frequently in recent years as a basic set of functions for signal characterizations in systems science and control. The purpose of this study is to establish an innovative method by using block pulse functions to minimize expenses of computations. Numerical simulations of earthquake-excited 10-story shear buildings equipped with an active mass damper are provided to verify the validity and feasibility of the proposed method. The proposed method's uncontrolled and controlled responses of structural system are compared with linear quadratic regulator method's results. The results reveal the proposed method can be beneficial in reducing seismic responses of structures with less computational expenses and high accuracy.
Tuned liquid dampers (TLDs) are dynamic vibration absorbers used in suppressing structural vibration under wind and seismic loads. They are easy to design and implement with low cost and low maintenance. However, due to their highly nonlinear behavior, it is difficult to establish representative models for TLDs that are accurate for a wide range of operations. In this paper, a new numerical model (finite volume method/finite element method (FVM/FEM method)) is introduced by simultaneously using finite volume and finite element approaches to represent fluid and solid domains, respectively. In order to assess the accuracy of the FVM/FEM results a state of the art experimental technique, namely real-time hybrid simulation (RTHS), is used. During the RTHS the response from the TLD is obtained experimentally while the structure is modeled in a computer, thus capturing the TLD–structure interaction in real-time. By keeping the structure as the analytical model, RTHS offers a unique flexibility in that a wide range of influential parameters are investigated without modifications to the experimental setup. This is not possible in traditional shake-table dynamic tests where a physical model of the structure needs to be built and tested together with the TLD. As a result, the verification of the numerical models for TLD–structure interaction available in the literature only consider a smaller, restricted dataset. In this study three numerical models from the literature are selected and together with the FVM/FEM developed here, the accuracies of these four models are assessed in comparison with RTHS results that consider a wide range of influential parameters. Results show that the proposed FVM/FEM model can accurately predict TLD behavior in both sinusoidal and ground motion forces and Yu’s model is the most accurate among the investigated simplified models.
This work presents an investigation into the effect of nonlinearities on the response of a micro-electro-mechanical system gas sensor under mechanical shock and electrostatic loading. The gas sensor consists of a cantilever microbeam with a rigid microplate (micro-paddle) attached to its tip. A nonlinear Euler-Bernoulli beam theory is used to model the system, accounting for both geometric and inertia nonlinearities, in addition to the nonlinear electrostatic force used to actuate the system. The system of integro-partial-differential equations is discretized using a Galerkin procedure to extract a reduced-order model, which is then used for dynamic simulations of the system responses. The influences of the different components of nonlinearity such as geometric and inertia nonlinearities are examined. The results of the nonlinear model are compared to results obtained from linear beam theory and finite element simulations. For mechanical shock loading, both quasi-static and dynamic responses of a microbeam are considered. The effect of nonlinearity is found to be significant when the deflection of the microbeam exceeds around 30% of its length. The consequence of the large deflection is that the geometric nonlinearity has a much stronger influence on the response in comparison to the inertia nonlinearity. It is also apparent that the effect of the paddle is to enhance the dynamic, as opposed to the quasi-static, response of the microbeam to mechanical shock. For electrostatic actuation, it is found that using a nonlinear beam model to predict the pull-in and the deflection produces a slight improvement over using a linear beam model.
A two-variable first-order shear deformation theory in combination with surface free energy and small scale (size-effect) is employed to present a simple and computationally efficient formulation for the free vibration of nanoplates with arbitrary boundary conditions. The free surfaces are modeled as two-dimensional membranes adhering to the underlying bulk material without slipping. To take into account the small scale effect, the nonlocal constitutive relations of Eringen are used. The equations of motion and the related boundary conditions are derived by employing Hamilton’s principle. An analytical solution for the free vibration of simply supported nanoplates is obtained and comparison studies with the results of other two-dimensional theories available in the open literature are performed to validate the proposed formulation. Then, by using the differential quadrature method, an approximate solution for nanoplates surrounded by an elastic media and with arbitrary boundary conditions is developed. Consequently, the effects of surface free energy, the small scale parameter and elastic constant of surrounding media together with geometrical parameters on the natural frequencies of nanoplates are investigated.
To evaluate a structural component’s fitness for service and quantify its remaining useful life, aging and service-induced structural flaws must be quantitatively determined in service or during scheduled maintenance shutdowns. Resonance inspection (RI), a non-destructive evaluation (NDE) technique, distinguishes the anomalous parts from the good parts based on changes in natural frequency spectra. Known for its numerous advantages, e.g., low inspection cost, high testing speed, and broad applicability to complex structures, RI has been widely used in the automobile industry for quality inspection. However, compared to other contemporary direct visualization-based NDE methods, a more widespread application of RI faces a fundamental challenge because such technology is unable to quantify the flaw details, e.g., location, dimensions, and types. In this study, the effectiveness of a maximum correlation-based inverse RI algorithm on a variety of common structural flaws, e.g., stiffness degradation, voids, and cracks, either in monotype or the coexisting form, has been systematically investigated. The prediction results are found to be able to accurately locate the damages and quantitatively measure the physical characteristics of the defects, which can effectively help retrieve the actual state of health of the engineering structures in a computationally efficient way.
This paper presents an experimental investigation of the loop shaping force feedback controller for the effective force test method with nonlinear test structures. Using loop shaping techniques a force feedback controller is designed to compensate for the control-structure interaction and suppress the oil-column resonance of the hydraulic actuator. A series of effective force tests using historical earthquake ground motions are conducted to assess the performance and robustness of the loop shaping force feedback controller at the Johns Hopkins University, USA. The effective force tests were successfully performed beyond the linear range of the test structures, developing nonlinear hysteresis loops and residual displacements. Experimental results proved that the loop shaping force feedback controller provides robustness despite the nonlinearities of the test structures. However, the investigation also revealed that the loop shaping force feedback controller has limited capabilities to produce accurate force tracking in nonlinear region of the test structure.
This paper presents a theoretical and experimental analysis of broadband sound transmission control of an aluminum panel in the frequency range between 30 Hz and 1 kHz. Based on the analysis of characteristics of sensor-actuator pairs, piezoelectric patches bonded on the structure are used as actuators, and collocated accelerometers are used as sensors. Then a hybrid decentralized control law is derived, which has a broad control band and puts more control authority on the most sound radiation effective mode. This control law comprises two parts: one is the direct velocity feedback controller, and the other one, relatively new, is called the negative acceleration feedback (NAF) controller. The control architecture is decentralized, which means each controller works independently. Due to the second-order dynamic property of the NAF controller and the fact that the structure’s frequencies may shift, the Hilbert-Huang method is used for quick and automatic identification of the natural frequency. Finally, open loop and closed loop experiments are presented to support the theoretical analysis. The active control results demonstrate that the panel’s vibration level can be suppressed by 16.7 dB and the broadband sound pressure level could be lowered by more than 7 dB.
The nonlinear dynamics of an actuator are considered during the output feedback control design of a quarter-car active suspension system with uncertainties. Because of the complexity of the suspension system with hydraulic actuator dynamics, a simple and effective sliding-mode strategy is employed to obtain both controller and observer. Instead of dividing the system into an actuator subsystem and a suspension subsystem, the system is repartitioned into a linear subsystem and a nonlinear subsystem, which facilitates controller design greatly. By specifying suitable sliding functions for the two subsystems respectively, and forcing the output of the nonlinear subsystem to track the desired fictitious input of the linear subsystem, the sliding-mode controller is created. By Lyapunov theory, robust stability is analyzed. For linear growth vanishing bounded uncertainties and nonvanishing bounded uncertainties, different observer forms are given to simplify the observer in different situations. Based on the constructed sliding-mode observer, the sliding-mode output feedback control suspension closed-loop system is accomplished. The convergence of observation error is subsequently proved. Simulation results verify the effect of the presented method.
An ample review of the published literature of skew (rhombic) plate vibrations in a companion Part I paper serves as a background that motivates the need for accurate solutions incorporating stress singularity-based methodologies for analyzing the titled problem. Such an accurate method is presented in this Part II paper. The prime focus here is that the vibration analysis explicitly considers the bending stress singularities that occur in the two opposite, clamped-free corners with obtuse angles of the rhombic plates. The strength of these singularities increases significantly, as the obtuse angles at the clamped-free corners exceeds 95o. A single-field energy-based Ritz procedure is employed with the dynamical energies derived from classical Kirchhoff thin-plate theory. The normal displacement of the rhombic plate is approximated as a hybrid series of (i) admissible and mathematically complete algebraic polynomials, and (ii) corner functions which account for both the kinematic boundary conditions and the bending stress singularities at the obtuse clamped-free corners. It is surmised from extensive convergence studies that the corner functions accelerate the convergence of upper bounds on the exact solutions, and that these functions are required if accurate solutions are to be obtained for highly skewed plates (including very thin ones incorporating shear deformable plate theories). Accurate non-dimensional frequencies and normalized contours of the vibratory transverse displacement are presented for rhombic plates having a large enough skew angle of 750 (i.e., obtuse angle of 1650), so that a significant influence of clamped-free corner stress singularities may be understood. Given the double symmetry axis of the rhombus domain, accurate solutions for a number of isosceles and right triangular plates (depending on the symmetry axis invoked) with various combinations of clamped, free, and sliding edges are also available from the frequency and mode shape data presented. Frequency data obtained from the present analysis are compared with nearly six decades of previously published data obtained using alternative theoretical plate analyses (including shear deformable ones) and classic experimental bench tests, clearly answering the inquiry of whether the stress singularities at the obtuse clamped-free corners of rhombic plates must be explicitly taken into consideration to obtain accurate three to four significant digit upper bounds on exact clamped-free skew (rhombic) plate vibration solutions reported in this work.
In this paper, non-probabilistic reliability indices for frequency and static displacement constraints are analyzed based on the ellipse convex model of elastic modulus and mass density. The dynamic non-probabilistic reliability-based topology optimization model of a truss is built, where the cross-sectional areas and nodal topology variables are taken as design variables. The objective is to minimize the structural total mass. Constraints are imposed on static stresses and non-probabilistic reliability indices of static displacement and natural frequency. A genetic algorithm is used as the optimization method to find optimal solutions in the outer loop and an analysis method is adopted to seek non-probabilistic reliability index according to implicit forms of the limit state function in the inner loop. Results of numerical examples show that the optimal mass of a non-probabilistic reliability-based topology optimization is larger than that of the deterministic topology optimization and the optimal mass increases with the increase of the non-probabilistic reliability requirement in order to ensure structural safety.
This paper describes an electromechanical fatigue stand which was developed in Opole University of Technology in a research and development project financed by the Polish government. It shows the principle operation of the strength testing machine and functionality of its electronic and software control system. Different types of possible fatigue tests were presented, i.e. uniaxial and biaxial (bending and torsion), cyclic and polyharmonic. Equations were discussed concerning the strain density energy parameter in bending and torsional axes. The theory was implemented in LabVIEW software in the control system of the machine. The main aim of this paper is the presentation of fatigue of a machine control system for material tests under polyharmonic bending and torsion based on the recently defined energy fatigue damage parameter.
In this paper, passive and active control methods are applied to reduce the torsional vibration of a nonlinear dynamical system. This system is subjected to multi parametric excitation forces and modeled by the coupled nonlinear differential equations. This leads to two degrees of freedom and three degrees of freedom when the torsional absorber is connected to the system. A multiple scale perturbation technique is applied to obtain an approximate solution and investigate the response of the system. The stability and the steady-state response of the system near the simultaneous sub-harmonic and internal resonances are studied and discussed using the frequency response function method. The numerical solution and chaotic response of the nonlinear dynamical system for different parameters are also studied. The simulation results are achieved using MATLAB 7.0 programs.
In this paper, we study the effect of a delayed feedback controller on stabilizing microelectromechanical systems (MEMS) resonators when undergoing large amplitude motion. A delayed feedback velocity controller is implemented through modifying the parallel plate electrostatic force used to excite the resonator into motion. A nonlinear single-degree-of-freedom model is used to simulate the resonator response. Long-time integration is used. Then, a finite difference technique to capture periodic motion combined with the Floquet theory is utilized to capture the stable and unstable periodic responses. We show that applying a suitable positive gain can stabilize the MEMS resonator near or inside the dynamic pull in instability bands. We also study the stability of the resonator by tracking its basins of attraction while sweeping the controller gain and the frequency of excitations. We notice significant enhancement in the safe area of the basins of attraction in the cases of positive delayed gains.
In this paper (part I) an ample review of the published literature of skew plate vibrations summarizes well over 100 references as background, bringing forth a need for accurate solutions incorporating stress singularity-based methodologies for analyzing this applied mechanics problem. Such an accurate method is presented in a part II companion paper for analysis of flexural vibrations of rhombic plates with all combinations of clamped and free edge conditions. The prime focus therein is that the analysis explicitly considers the bending stress singularities that occur in the two opposite, clamped-free corners with obtuse angles of the rhombic plates. The strength of these singularities increases significantly as the obtuse angles at the corners increase. Frequency relations summarized herein from this review of Mindlin and Reddy skew plate vibrations research enable investigators to obtain accurate 3–4 significant digit upper bounds on exact solutions of shear deformable skew plates, including the effects of stress singularities, given analogous Kirchhoff skew (rhombic) plate frequency solutions, and thereby eliminating the need to solve the complicated equations of shear deformation theories including stress singularity effects published elsewhere.
This paper investigates the performance of magnetorheological (MR) dampers to mitigate the effect of earthquake loading on civil engineering structures. MR dampers are semi-active fluid dampers containing an MR fluid. They can generate large controllable damping forces by tuning the magnetic field applied to the fluid, which changes its viscosity. Their fast response time and low electric power requirements make them attractive for potential applications in earthquake engineering. In this study the behavior of a prototype MR damper was simulated computationally using the Bouc-Wen model. A new clipped-optimal control strategy, the improved clipped-optimal algorithm (ICA) control model, was developed and aims to reduce the acceleration response of a structure. It was implemented for a scaled three-story building in Simulink. The structural response to seven earthquakes was simulated and compared with two other established control algorithms as well as passive damping. The ICA control algorithm generated the largest reduction in acceleration and displacement response while keeping low the electric power requirements and the force generated by the damper.
The present paper is devoted to study the propagation of Love wave in a piezoelectric layer overlying an inhomogeneous half-space. This paper deals with two different piezoelectric layers, one is an electrically open and another is an electrically short circuit. As mathematical tools, the method of separation of variables and Whittaker’s function are applied to obtain the dispersion equation of Love wave. In a particular case the dispersion equation reduces to the classical equation of Love wave when the layer is not piezoelectric and half-space is homogeneous. The numerical values of the dimensionless phase velocities are calculated and presented graphically to illustrate the effects of inhomogeneity, piezoelectricity and dielectric constants. It is observed that the phase velocities decrease with the increase of inhomogeneity parameters and electricity constant. It is also found that the phase velocity increases with the increases of the dielectric constant. Graphical user interface software has been developed by using MATLAB software to generalize the effect of various parameters.
In this paper, tests on viscoelastic (VE) dampers are carried out, and the results indicate that VE dampers have high energy dissipation capacity and excellent anti-fatigue properties. To clarify the mechanical properties of VE dampers, a new mathematical model, named the equivalent fractional Kelvin model, which considers temperature and frequency effects simultaneously, is proposed. The numerical results using this model are in good agreement with experimental results. Then, through analysis on a five-story reinforced concrete frame structure with and without VE dampers, it is found that the seismic responses of the structure with VE dampers are significantly reduced and VE dampers have high energy dissipation capacity.
Harmonic currents, which are caused by rotor imbalance and sensor runout in active magnetic bearing (AMB) systems, can induce undesirable harmonic vibrations and superfluous power consumption. To analyze and reduce these harmonic currents, a comprehensive model of the AMB system is developed and a repetitive control method is proposed. First, dynamics of the four radial degrees-of-freedom rotor with the rotor imbalance and the sensor runout are introduced, and electrical equations of the AMB control system including power amplifiers and motion induced voltage (MIV) are described. Next, how synchronous and multiple harmonic vibration forces and torques, which result from the harmonic currents through both the current stiffness and the displacement stiffness, are induced by static imbalance, dynamic imbalance, and the sensor runout through controllers and the MIV, are explained and analyzed in detail. Then the AMB system is divided into two subsystems related to translational and rotational motions, respectively. The dynamic equations for the two coupled rotational motions of the rotor are combined into a complex function. The rotor imbalance and the sensor runout are transformed to input disturbances of the power amplifiers, and a repetitive control method is proposed to suppress these periodic disturbances by reducing the harmonic currents. Finally, the validity of the proposed method is demonstrated by simulations with MATLAB and experiments on a test rig of a magnetically suspended control moment gyro. It is superior to existing techniques due to the comprehensive AMB model and the effective control method with a short computation time.
An analytical modified method is presented to investigate the clearance effects on the dynamic behavior of cantilever beams. In this work, apart from clearance, all other nonlinearities are avoided to be considered during the analytical solution. The beam is idealized using an equivalent single-degree-of-freedom structure. A tri-linear stiffness system is also adopted to simulate the beam together with the clearance. Subsequently the analytical solution is derived for a cantilever beam structure with and without considering structural damping. The experimental method is employed to verify the results from the presented analytical solutions. It is noted that the results obtained by the presented analytical solutions are in very good agreement with those from the experimental method.
This paper deals with the dynamic behavior of a non-uniform column reinforced by single-walled carbon nanotubes resting on an elastic foundation and subjected to follower force. The method of solution is the differential quadrature method. The carbon nanotube reinforced composite (CNTRC) columns have smooth variation of carbon nanotube (CNT) fraction in the thickness direction and the material properties are estimated by the extended rule of mixture. Detailed parametric studies have been carried out to reveal the influences of the kind of distribution and volume fractions of CNT on natural frequencies and the critical load for the CNTRC column.
Controlling an industrial robot is mainly a problem of dynamics. It includes nonlinearities, uncertainties and external perturbations, which should be considered in the design of control laws. In this paper, a variable structure control method with a mathematical tool is proposed and applied to nonlinear systems to solve the trajectory tracking problem for rigid robot manipulators. The aim is to implement a methodology to control errors in a controller that is robust to uncertainties in the model of the system. Variable structure theory provides the technique for the design of such a controller. The design steps are presented, first from a theoretical perspective and then applied to the control of a two degree-of-freedom manipulator. Simulation results that backed the implementation are presented followed by the experiments conducted, and then the results are presented. The conclusion is that the proposed mathematical tool with variable structure control is readily applicable to industrial robots for the robust control of positions.
Free vibration of a cracked nanobeam with consideration of surface energy and transverse shear deformation is studied. The cracked nanobeam is simplified to a system of two segments joined by a rotational spring located at the cracked section. Numerical examples demonstrate that the surface energy increases the natural frequency of the beam. However, the influence of surface energy on the natural frequency becomes smaller for the higher modes. In addition, the effect of transverse shear deformation on the frequency becomes more significant for the higher modes.
An adaptive control scheme is studied for unified chaotic systems with unknown function and dead-zone input. Because uncertain nonlinear property is included in the considered unified chaotic systems, the neural networks are used to approximate the uncertainties. An adaptive technique is employed to construct the neural controllers and compensate for the dead-zone parameters. By using the scheme, the chaotic phenomena for unified chaotic systems are overcome. It is proven that the proposed algorithm can guarantee that all the signals in the closed-loop system are bounded and the system states can converge to a neighborhood of zero based on the Lyapunov analysis method. The simulation example for a unified chaotic system is provided to demonstrate the effectiveness of the proposed method.
The accuracy of a support vector machine (SVM) classifier is decided by the selection of optimal parameters for SVM. An artificial chemical reaction optimization algorithm (ACROA) is a new method to solve the global optimization problem and is adapted to optimize SVM parameters. In this paper, a SVM parameter optimization method based on ACROA (ACROA-SVM) is proposed. Furthermore, the ACROA-SVM is applied to diagnose roller bearing faults. Firstly, the original modulation roller bearing vibration signals are decomposed into product functions (PFs) by using the local mean decomposition (LMD) method. Secondly, the ratios of amplitudes at the different fault characteristic frequencies in the envelope spectra of some PFs that include dominant fault information are defined as the characteristic amplitude ratios. Finally, the characteristic amplitude ratios are used as input to the ACROA-SVM classifiers, and the fault patterns of the roller bearing are identified. The result shows that the combination of this ACROA-SVM classifiers and LMD method can effectively improve the accurate rate of fault diagnosis and reduce cost time.
This paper proposes a novel data mapping technique to develop a fault diagnosis method. The data mapping technique takes advantage of rising empirical mode decomposition and non-negative matrix factorization to transform nonlinear and non-stationary signals into characteristic power spectral density (PSD) bases with physical interpretations. A number of mapped PSD basis vectors not only bear more distinctive features compared to the original data form, but also fuse separate features into an integrated one. Feature recognition quantifies the degree of similarity between different PSD bases to achieve fault recognition and classification. A simulated mechanical vibration signal is presented to illustrate that adopting PSD basis as a data feature yields better diagnostic performances than those obtained from other feature forms. Real faulted bearing data are also analyzed in different experiments to give a comprehensive verification of the proposed fault diagnosis method.
In the present paper, an efficient computational method for the solution of bang–bang optimal control problems is investigated. The method is based on control parametrization and belongs to the direct methods for numerical solution of optimal control problems. In this method, control functions are considered to be piecewise constant with values and switching points taken as decision variables. Thereby, the problem is converted into a mathematical programming problem which can be solved by well-developed parameter optimization algorithms. The main advantages of the present method are that: (i) it obtains good results and the switching points can be captured accurately; and (ii) an incorrectly guessed number of switching points can be detected by the results of the method. These are illustrated through three examples and the efficiency of the method is reported.
This study analyzes the elastic vibration of a simultaneously spinning and precessing cantilevered rotor for its stability margin and whirl frequency. The governing equations suggest that the stability is largely governed by two counteracting effects – the centrifugal stiffening and the precession softening. The concentrated mass and inertia of the disc as well as the distributed mass of the shaft contribute to both of these effects. A finite element formulation shows that along with the standard matrices for conventional rotor dynamic analysis, two completely new ones are obtained to account for the effect of precession. Two- and four-degrees-of-freedom models indicate that the rotor is always stable irrespective of its precession speed. But, interestingly, results from the converged finite element model show that the rotor will be unstable beyond a moderately high value of precession speed. The reason for this can be attributed to the shape of deformation of the rotor during its motion. This shape is only approximate in two- and four-degrees-of-freedom models. The Campbell diagrams computed using the four-degrees-of-freedom model and the finite element model are compared and presented.
Proportional-integral-derivative (PID) control has been widely adopted for stable and reliable operation of rigid rotors supported by a pair of active magnetic bearing systems. Conventional centralized PID control methods manipulate the feedback gains in prescribed forms until they achieve the desired control performance. In this study, an eigenvalue assignment for decoupled translational and conical modes is proposed in the complex domain to yield a unique PID controller in a closed form, preserving the isotropic bearing characteristics. The eigenvalue assignment necessitates the constraints required for decoupling of the translational and conical whirl motions from the complex equation of motion written in the center of gravity coordinates of the rigid rotor. The complex equation of motion integrates the rigid rotor and electro-magnetic control force models defined in two different coordinate systems by utilizing complex coordinate transformation relations. A flywheel energy storage system is taken as a simulation example in order to demonstrate the validity and effectiveness of the proposed eigenvalue assignment. The simulation results show that the eigenvalue assignment algorithm is superior to conventional control methods at systematically ensuring sufficient stability margins for the lightly-damped and unstable conical modes.
Shortly after the discovery of carbon nanotubes (CNTs), the existence of differently shaped CNTs other than straight ones was predicted theoretically. Recently photomicrographic images show that CNTs are not actually straight but have significant curvature. This aspect was mostly neglected in previous studies on CNTs’ dynamic behavior. In this paper a new formulation governing the in-plane motion of curved CNTs conveying viscous fluid is derived to study their in-plane free vibration. In this formulation the fluid is considered to be viscous and the size effects of nanotubes are also taken into consideration through nonlocal elasticity theory. In this study CNT is modeled as a hollow cylindrical tube and the moving fluid inside is modeled as a plug flow characterized by its mass density, viscosity, and mean velocity. The new formulation is used to study the vibration and instability characteristics of curved and wavy carbon nanotubes. Using finite element analysis it is shown that the nonlocal parameter, the viscosity of fluid, and also the curvature have considerable effects on the natural frequency and critical flow velocity of carbon nanotubes. Also the effect of boundary conditions on natural frequency and critical flow velocity is studied.
Although most real building structure controllers are in the form of proportional-derivative/proportional-integral-derivative (PD/PID), there have been few published theory results of PD/PID on structural vibration control. In order to minimize the regulation error, a PD/PID control needs relatively large derivative and integral gains. These deteriorate the transient performances of the vibration control. In this paper, a natural combination of industrial PD/PID control with fuzzy compensation is proposed. The main contribution of this paper is that the stability of the fuzzy PD/PID control is proven with standard weight training algorithms. These conditions give explicit selection methods for the gains of the PD/PID control. Experimental studies on a two-story building prototype with the controllers are addressed. The experimental results validate our theoretical analysis.
A first-order shear deformation plate theory model of laminated composite plates subjected to a combined electromagnetic and thermal field is developed. The coupled equations of motion are based on the electromagnetic equations (Faraday, Ampere, Ohm, and Lorentz equations) and thermal equations which are involved in constitutive equations. In order to determine the implications of a number of geometrical and physical features of the model, one special case free vibration of a composite plate immersed in a transversal magnetic field is investigated. Special coupling characteristics between the magnetic, elastic and thermal fields are described in this paper. In addition, the free vibration responses of finite composite rectangular plates immersed in a transversal magnetic field are investigated. The vibration response characteristics of a composite plate are exploited in connection with the magnetic field intensity, thermal load, and electric conductivity of fibrous composite materials. Some pertinent conclusions, which highlight the various effects induced by the electromagnetic-thermo-elastic couplings, are outlined.
Employing Biot’s theory of poroelasticity, three-dimensional vibrations in a poroelastic solid that is subjected to static stresses is investigated. By considering second-order coupling between stress and strain, pertinent governing equations are derived. A frequency equation is obtained in the case of static uniaxial stress or strain. Phase velocity against static uniaxial stress is computed in the case of two poroelastic solids and results are presented graphically.
This paper presents the design, stability analysis and experimental validation of a computationally non-intensive, model-free, intelligent proportional-integral (iPI) controller for flexible joint manipulators. In order to show the performance of the iPI controller, it is compared with classical proportional-integral and proportional-integral-derivative controllers. Based on this comparison, the iPI-controlled system achieved a better than 60% tracking accuracy for both kane trajectory and sine input tracking. The iPI controller also significantly reduced transient swings in the flexible joint of the manipulator, when tracking a train of pulses. Moreover, the iPI controlled system successfully eliminated both disturbances and noise effects from the dynamics of the manipulator.
The vibration analysis of the natural frequencies and mode shapes of a class of doubly-curved shells with different boundary conditions is presented. The doubly-curved shells are geometrically taken from various parts of a hollow torus with annular cross-section. The small strain, three-dimensional, linear elasticity theory is adopted to establish the governing equations of the problem in terms of the toroidal coordinate system (r, , ). The Chebyshev-Ritz method is used to set up the eigenvalue equation: displacement in each direction is taken as a triplicate product of the Chebyshev polynomials in r, and , multiplied by a boundary function along with a set of generalized coefficients to yield upper bound values of the natural frequencies. The natural frequencies converge monotonically to the exact values as more terms of Chebyshev polynomials are included in the Ritz approximation. The effects of thickness ratio, radius ratio, toroidal angle in direction, initial angle and subtended angle in direction on natural frequencies and mode shapes are discussed in detail.
In this article, an adaptive modified projective synchronization scheme of fractional-order chaotic systems with unknown parameters and disturbance is investigated. The synchronization can be completed with any desired accuracy. Based on the stability theory of fractional-order systems, the adaptive controllers and the parameters’ updated laws are designed to achieve modified projective synchronization between the fractional-order chaotic systems with disturbance. Furthermore, all unknown parameters of the response system are identified simultaneously. Numerical simulations on the fractional-order chaotic Lorenz system further demonstrate that the proposed method is effective and robust.
To simulate large loading and intensive vibration in fatigue experiments for insulators, the hydraulically driven fatigue test machine is researched in the present study, because it has the advantages of large power, fast response and high precision. An open-closed-loop proportional-derivative (PD)-type iterative learning control (ILC) scheme is designed for control of this fatigue test machine to obtain ideal vibration performance. Firstly, the hydraulic scheme and control principle are introduced, including static and dynamic control subsystems, and then the actual fatigue test machine based on such principles is described. The mathematical model of the electro-hydraulic servo load system is built, which shows that this system is completely different from traditional hydraulic position-control systems, and indicates that with conventional proportional-integral-derivative (PID) control it is difficult to achieve a satisfactory result. Therefore an open-closed-loop PD-type ILC method has been designed and applied to the fatigue test machine to achieve the high-precision control for dynamic force with repetitive regularity. This control method is simulated and experimented fully, and it is compared with PID control, open-loop and closed-loop ILCs. The experimental results have verified the correctness and feasibility of the hydraulic scheme and control principle, as well as the superiority of the open-closed-loop PD-type ILC. The fatigue test machine based on electro-hydraulic principles and the open-closed-loop ILC discussed in the present study have been applied to fatigue experiments for a serial of the compound insulators and gave an ideal performance, with specifications of 150 KN maximum static force, 20 KN maximum dynamic force, 0.5 KN force control precision and 100 Hz maximum dynamic frequency.
The reduction of train-induced ground vibration by elastic elements such as rail pads and sleeper pads has been analyzed by a combined finite-element boundary-element method. The dynamic compliance of the track, the transfer function of the total force on the ground and the ground vibration ratios have been calculated for a variety of isolated and un-isolated track systems. It has been found that the soil force transfer, which describes the excitation force of the soil, is an appropriate quantity to predict the reduction of the ground vibration and the effectiveness of isolated tracks. All force transfer functions of isolated tracks display a vehicle–track resonance where the wheelset on the compliant track is excited by wheel and track irregularities. At higher frequencies, considerable reductions of the amplitudes are observed as the benefit of the resilient element. The influence of the stiffness of the rail or sleeper pads, the ballast and the soil, and the mass of the sleeper and the wheelset on the resonance frequency and the reduction has been investigated. Sleeper pads are advantageous due to the higher mass that is elastically supported compared to the rail-pad track system. The combination of elastic rail and sleeper pads has been found to be disadvantageous, as the second resonance occurs in the frequency range of intended reduction.
In this study, a robust adaptive control method is employed for an active engine mount in a six-degree-of-freedom model of the engine on the mounts to improve vibration behavior of the engine. The vibration isolation performance and robustness of the employed robust adaptive controller are compared with a robust and an adaptive control technique. In addition, effectiveness of the robust adaptive control is evaluated in transient conditions (accelerating and gear change conditions). In this regard, a dynamic model for the engine supported by rubber and active mounts and its governing equations are presented. Then, a robust adaptive control, namely the robust Model Reference Adaptive Control (robust MRAC) technique, based on the gradient method with -modification, is designed by selecting a proper reference model. Moreover, a robust control, namely the H control scheme and an adaptive control, namely MRAC, are employed for the active mount. Simulation results show that the robust MRAC has a better control performance (in reducing the transmitted force to the chassis) as compared with the H scheme. In addition, in the face of large uncertainties, MRAC may diverge and become unstable. However, the robust MRAC is robust in the presence of large uncertainties. Also, robust MRAC is effective not only in constant engine speeds, but also in transient conditions.
In this paper, the authors propose an approach to control a class of nonsmooth continuous and discontinuous dynamical systems which is based on a generalization of derivative and Chebyshev pseudospectral (PS) methods. First a generalized derivative for nonsmooth functions, which is proposed by Kamyad et al. is considered. Therefore the obtained generalized derivative of a nonsmooth function is approximated with the Fourier series. So, the nonsmooth control problem is approximated by a smooth optimal control problem and in what follows, it is solved by Chebyshev PS method and the approximate solution for the state and control of the main problem is achieved. Finally, some numerical examples of the control of nonsmooth dynamical systems are solved to illustrate the efficiency of the authors’ approach.
A prediction method of characteristic parameter degradation for a hydropower unit is presented based on radial basis function (RBF) interpolation, empirical mode decomposition (EMD), approximate entropy, artificial neural network and grey theory. Considering the effect of active power and working head, the characteristic parameter degradation model of a hydropower unit is built by using RBF interpolation. The EMD method is used to decompose the characteristic parameter degradation time series of the hydropower unit into a number of intrinsic mode function (IMF) components. The approximate entropy of each IMF component is calculated. According to their different properties, the neural network or grey theory is used to predict them, respectively. All the predicted results are added to obtain the final forecasting result of the original characteristic parameter degradation time series. The case study results demonstrate that the proposed method has an extremely high prediction accuracy, and can be applied in the hydropower unit condition prediction effectively.
A passive vehicle suspension has constant spring and damper properties that compromise either ride or road holding ability, depending on whether the suspension is designed to be hard or soft. This study examines the implementation of a gear mechanism in a vehicle suspension system to alter its suspension characteristic while keeping the same spring and damper properties. In the study, a rack-and-pinion mechanism was used to modify the suspension force which acted between the sprung and unsprung masses of a quarter vehicle model. The system with proposed suspension layout was modeled mathematically and solved to obtain the vehicle response due to step excitation for various gear ratios. Results indicated that the use of such a mechanism was capable of changing the equivalent suspension force of the system. It was noted that different gear ratios would amplify or reduce the equivalent suspension force, hence emulating a harder or softer suspension setting compared to that of the original suspension. Additionally, it was found that with optimized gear ratio and gear mass, the implementation was capable of overcoming the compromise between the ride and road holding ability associated with conventional passive suspensions, as simultaneous improvement on both criteria was observed.
A nonlinear stochastic optimal bounded control strategy for quasi-Hamiltonian systems with actuator saturation is proposed based on the stochastic averaging method and stochastic maximum principle. First, the averaged Itô stochastic differential equations are derived by using the stochastic averaging method for quasi-Hamiltonian systems. Then, the stochastic Hamiltonian system for optimal control with a given performance index is established based on the stochastic maximum principle. The bounded optimal control consisting of unbounded optimal control and bounded bang–bang control is determined by solving the forward-backward stochastic differential equations with control constraint. Finally, three examples of quasi-Hamiltonian systems with controls are given to illustrate the application of the proposed strategy. Numerical results show that the proposed control strategy significantly improves the control efficiency and chattering attenuation of the corresponding bang–bang control.
Within the drive-response configuration, this paper deals with the problem of fault-tolerant full-order and reduced-order observer synchronization for differential inclusion chaotic systems with unknown disturbances and parameters. Even if there are unknown disturbances and parameters in the drive system, a robust fault-tolerant adaptive full-order observer can be used to realize chaos synchronization with the response system for some assumptions whether or not fault occurs. What’s more, a reduced-order observer differential inclusion response system which can synchronize part states of the drive system is developed for the same assumptions. Finally, some numerical simulations for Lorenz chaotic systems with differential inclusion are designed and the simulation results are analyzed in detail.
In this paper the generalized form of a non-ideal system which contains a pure nonlinear oscillator and a non-ideal energy source is studied. In the non-ideal oscillator-motor system there is an interaction between the motions of the oscillator and those of the motor, as the motor has an influence on the oscillator and vice versa. The mathematical model of the system is represented with two coupled nonlinear differential equations. The averaging method for solving these differential equations is based on the application of the Ateb function, which is the exact solution of the pure nonlinear oscillator. Using the obtained approximate solution, the resonant motion of the system is considered. Significant attention is paid to the steady-state motion and to the Sommerfeld effect. The influence of the order of nonlinearity on the dynamics of the nonideal system is evident. In the paper the procedure for determination of the parameters for suppression of the Sommerfeld effect of the non-ideal system is also given.
This paper first shows that two motors on the same plate can enter into synchronization with the phase difference equal to zero, or 2 depending on the physical characteristics of the motors and the plate. Both motors are considered as non-ideal oscillators and act as external excitation on a specific area of the plate. The analysis of the vibration of the plate indicates through numerical simulation that one can obtain a reduction of vibration when the motors phase difference is equal to .
Control of flapping micro-air-vehicles (MAVs) is challenging because the system models are nonlinear and time-varying. Moreover, as internally actuated multi-body systems, flapping MAVs are inherently underactuated. With stringent weight and size constraints, the actuator mechanization must be as simple as possible, introducing a further challenge for control design. Geometric control and averaging theory can be used to design control laws for underactuated nonlinear systems. In this work, we consider control design for a flapping plate with three degrees of freedom and two actuators. The averaging theorem and geometric control methods are used to stabilize and control the system. The simple example demonstrates an algorithmic approach that could be used within a multi-disciplinary design optimization framework for the design of biomimetic vehicles and their gaits.
The current investigation has been conducted to examine the effect of the vertical component of earthquake on the responses of base-isolated structures mounted on a triple concave friction pendulum (TCFP) bearing. The varying inherent stiffness and damping of this new generation of friction isolators make smart behavior to mitigate damages during different earthquake hazard levels. To investigate, the structure was idealized as a two-dimensional single story (single degree of freedom) resting on a TCFP isolator and the coupled differential equations of motion were derived and solved using state-space formulation. Based on these equations, a computer program was developed to study the influence of the vertical component of earthquake on the seismic responses of a TCFP isolated structure such as bearing displacement and base shear of the isolated structure. The variation of essential parameters such as superstructure period, isolation period and friction coefficient of sliding bearing surfaces was studied when the TCFP isolated structure was subjected to seven near field earthquake motions. This study demonstrates the significant effects of the vertical component of earthquakes on seismic responses of base-isolated structure mounted on TCFP bearings, which is why the maximum error caused by neglecting the vertical component of earthquake in calculating the base shear of the structure is 29.5%.
In this paper, the active vibration control tools are implemented for the vibration control of functionally graded material (FGM) beam with piezoelectric actuators and sensors. The properties of FGM are functionally graded in the thickness direction according to the volume fraction power law distribution. An analytical formulation, based on an efficient trigonometric shear deformation theory, is used to obtain a state space equation. The main steps to set up active control of FGM vibrations are considered in this work. The actuators’ and sensors’ locations are defined from two optimization problems using controllability and observability gramians. The linear quadratic regulator (LQR) control law, including a state observer is computed. Numerical examples show the influence of the volume fraction index on the observability and controllability properties of the system. The LQR leads to efficient active damping for several kinds of excitations. The study of the uncertainty in the volume fraction index shows the robustness of the control method, and also the possible induced defects.
We extend the use of cantilever beams as flow sensors for small aircraft. As such, we propose a novel method to measure the airspeed and the angle of attack at which the air travels across a small flying vehicle. We measure beam deflections and extract information about the surrounding flow. Thus, we couple a nonlinear beam model with a potential flow simulator through a fluid–structure interaction scheme. We use this numerical approach to generate calibration curves that exhibit the trend for the variations of the limit cycle oscillations amplitudes of flexural and torsional vibrations with the air speed and the angle of attack, respectively.
An analysis of the energy dissipation sources acting in a vibrating aluminum plate is presented in this paper. In the first step, the contact-free modal analysis of a suspended plate is conducted using a laser vibrometer and an acoustic excitation to obtain reference data. The thin nylon suspension set-up guarantees a low boundary damping, which is assumed to be negligible. In the second step, a number of damping sources are modeled. Acoustic damping due to the noise radiation of the nonbaffled plate is computed using the boundary integral method and a light fluid approximation to express the vibroacoustic coupling in analytical terms. The damping due to the sheared air flow along the free-plate borders is determined on the basis of a simple two-dimensional boundary layer model. Thermoelastic damping is assessed using a Fourier series expression for the temperature field along with a perturbation technique to take thermoelastic coupling into account. Since no robust model is available so far to quantify viscoelastic material damping in aluminum, it is determined in a last step by subtracting measured values of damping from those previously computed. Aluminum viscoelastic damping turns out to be very small and almost independent of frequency.
This paper presents a new approach of proportional-integral-derivative (PID) controller tuning via an evolutionary algorithm that optimally suppresses the vibration of a flexible beam system using a piezoelectric actuator. The system’s dynamic model is identified based on autoregression with exogenous input (ARX) structure using recursive least square. The input-output data were obtained experimentally. This ARX model represents the physical system and is used for the controller optimization process. Evolutionary algorithms such as differential evolution (DE) and genetic algorithms (GA) were applied to optimize and tune the controller parameters offline based on a defined performance index, i.e. mean square error of the vibration signals. The optimum PID parameters were validated experimentally. The performance of PID tuned by DE and GA are compared with conventional PID tuning (using Ziegler Nichols method). Experimental study showed that PID tuned by DE and GA offer a better transient response than the conventional tuning method.
In this study, the dynamic behavior of trapezoidal and sinusoidal corrugated plates, which are widely used in the fields of space, aviation, automotive design, construction, and shipbuilding, was analyzed. A total of 330 different surface models of corrugated plates with varying corrugation heights, widths and numbers of corrugations were created, which have various manufacturing parameters. At this stage, the total number of natural frequency and mode shape analyses conducted for different boundary conditions is 660, where 330 are for four sides free and 330 are for four sides encastre. Mode shapes were also obtained using the finite element method. In addition, changes in the trapezoidal cross-sectional profile were investigated by analyzing 38 different plates with varying cross-sectional profiles. Examining these results, the effects of corrugation height and number on the natural frequencies and mode shapes of the plate were determined. As a result of the study, a total of 368 plate drawings were prepared, and 736 analyses for two types of boundary conditions were performed. Moreover, the theoretical results were verified using the experimental modal analysis technique for some selected models that are being manufactured in the market.
Nowadays high quality power is essential for medical, research and industrial applications to produce good quality results and analysis. In this work an attempt has been made to improve the power quality by minimizing the harmonic content in the output voltage of a cascaded multilevel inverter using the selective harmonic elimination pulse width modulation technique. Sinusoidal PWM technique is used to generate the switching signals. A single phase nine-level cascaded multilevel inverter with identical DC supply is designed to reduce the harmonic components of the output voltage. Particle swarm optimization technique is applied to determine the optimum switching angles, thereby reducing some higher-order harmonics while maintaining the required fundamental voltage. This generalized technique can be extended to multilevel inverters with any number of levels. The total harmonic distortion is measured accordingly for different modulation indices. A prototype model of a field programmable gate array-based nine-level inverter has been designed, fabricated and tested. The results are presented and analyzed and hence the hardware results are verified with the simulation results.
The planetary gear system is the important part of the cutting unit in a coal shearer, and its performance is directly related to the output efficiency in coal mines. Analyzing the natural frequencies and vibration modes of a planetary gear system in a coal shearer is helpful for designing and monitoring the planetary gear system. So a lateral-torsional coupled free vibration model is proposed with the shaft stiffness of the sun gear based on the analysis of a purely torsional model. The solutions are determined by using the modal superposition method. Taking the planetary gear system in the cutting unit of a YBCS2-400 type coal shearer as an example and studying the natural characteristics, the vibration modes of the undamped system could be classified into three types – rotational mode, translational mode and planet mode. The associated reduced-order eigenvalue for each type of vibration mode is derived and the analytical expression of natural frequency is presented for the planet mode. The established model is validated by comparing it with the results of a finite element model, and the effect on the vibration frequencies of the transmission and width ratio has been obtained by means of the finite element model.
Wave propagation is one of the famous approaches for analyzing the vibration of solid structures. Literature reviews show that most bodies analyzed with this approach are one-dimensional waveguide structures. In this paper, the free vibration of annular circular and sectorial membranes are analyzed using the wave propagation approach. Firstly, the propagation and reflection matrices are derived. Then, a concise and systematic approach for obtaining the natural frequencies is presented which can be a reference for future studies. The solution obtained by this method is exactly the same as those derived by the classical method.
In this paper we have discussed the propagation of torsional wave in a composite layer overlying an anisotropic heterogeneous half space with initial stress. The method of separation of variables is applied to find the dispersion equation. Numerical results analyzing the dispersion equation are discussed and presented by means of graphs. The effect of reinforcement, inhomogeneity parameter and the initial stress on the propagation of torsional surface wave is the main objective in our study. It has been observed that the directional rigidities of the half space have a favoring effect on the phase velocity, whereas the density and initial stress parameter in the half-space have the adverse effect on the velocity of torsional surface wave. It is remarkable to quote that reinforcement prevails in the medium, the phase velocity increases significantly.
This paper presents a new control scheme for a flexible-joint manipulator using a higher-order differential feedback controller (HODFC). Two higher-order differential operators were designed and used to perform observations of both the reference input and the output of the manipulator, together with the requisite state derivatives. An error-based state-space model was then derived from the observed states. A pole-placement procedure with filtering was then used to drive the system error to zero. Practical controller implementation was carried out using the dSPACE real-time prototyping system. For the comparative validation of the performance of the HODFC with respect to a classical proportional-integral and proportional-integral-derivative (PID) controller, several experiments were undertaken. In these experiments, the step input, sine waves, kane trajectories, and external disturbances were applied to the controlled flexible-joint manipulator. The results showed that the HODFC controller eliminated disturbances within one second of occurrence, and produced superior kane trajectory tracking. Moreover, based on the root-mean-square tracking error criterion, the HODFC was observed to track both the sine and kane function trajectories with one-fourth the tracking error obtained with classical PID control.
In this paper, an efficient method based on rationalized Haar (RH) wavelets is proposed for the numerical solution of optimal control problem for systems governed by Volterra integral equations with a quadratic performance index. Many problems in economics, biology, epidemiology and memory effects can be modeled as Volterra control problems. The main advantage of the RH wavelet is based on its efficiency and simple applicability. The properties of RH wavelets are represented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the solution of the optimization problem to a nonlinear programming one to which well-developed algorithms may be applied. The convergence analysis of the method and illustrative examples are included to demonstrate the validity and applicability of the technique.
This article focuses on the adaptive control problem for Arneodo chaotic systems. It is considered a phenomenon of single state constraint for the systems. In the proposed scheme, the barrier Lyapunov function approach was successfully used to prevent the single state from violating constraint conditions. In the current circumstances, a great many of the results for chaotic systems neglect the situation of constraint. Finally, it is proved that all the signals in the Arneodo chaotic system are bounded. A representative example is proposed in numerical simulations compared with existing results. The performance of the proposed control scheme was validated by using a simulated example.
This study considered the hybrid position/force control of robots with an oscillatory base. The objective when controlling such a system is to control the contact force between the environment and the object in the constrained directions. The auxiliary control input laws with the ANFIS tuning methodology were successfully applied to robot manipulators mounted on an oscillatory base to provide hybrid position/force control. Linguistic fuzzy information from human knowledge was incorporated into the fuzzy system, which was equipped with a training algorithm. The advantage of the proposed control scheme is that only select control inputs are needed to select control inputs for task space trajectory tracking. In other words, such a system does not require the redesign of the vibration damping controller. Tracking performance comparison is also presented for the proposed control scheme and the other existing control techniques. It is shown that the proposed fuzzy control scheme offers several implementation advantages such as less steady-state errors, reduced effect of overshoot, and a fast convergent rate in real-time verification. The experimental results of this study confirmed the efficiency of the proposed control design and its feasibility for use in various mechanical systems, including mobile robots, gantry cranes, underwater robots, and other dynamic systems mounted on oscillatory bases and used to perform constrained motion tasks.
This paper discusses the vibrations of a coil, which is excited axially, in helical compression springs. The mathematical formula is composed of a system of four hyperbolic partial differential equations of first order with unknown variables, which are angular and axial deformations and velocities. The numerical resolution is based on the conservative finite difference scheme of Lax-Wendroff. The impedance method is applied to calculate the frequency spectrum. The spring is excited by a sinusoidal axial velocity at its end. The results obtained by using this method are used to analyze the evolution in time of deformations and velocities in different sections. These results clearly show the effect of the interaction between the slow axial waves and the fast angular waves. Indeed, the amplification was more important for the axial strain than for the rotational one that was caused by the effect of coupling Poisson. In addition to this, the resonance phenomenon and other phenomena related to wave propagations such as wave reflections and beat are analyzed.
This paper presents a wave-based, analytical method for the computation of power transfer coefficients (PTC) to evaluate vibratory power transmitted through a set of angled structural joints that connects an arbitrary number of composite plates. Each joint is only used to hold two adjacent plates together. The elastic wave motions and dispersion properties of the plate are calculated by considering shear deformation, rotary inertia, and material anisotropy. The joint is modeled with stiffness and damping in both translational and rotational directions, and the joint parameters are allowed to differ from one joint to another. The equilibrium conditions at the joint set are derived to solve for the complex amplitude of waves propagating away from it. From the PTCs computed for a particular angle of wave incidence at the junction, the diffuse-field PTCs are calculated using weighted integral of the incidence angle. A comparison with published numerical results for simpler configurations has been performed in order to validate some key aspects of the present analytical formulation. Several numerical examples of two coupled composite sandwich panels are considered to compute PTCs, through which it is clearly demonstrated that the joint compliance and damping as well as the transverse shear deformation and rotary inertia of composite sandwich panels influence the vibratory power transmission through coupled composite plates.
A two-degree-of-freedom floating vibration isolator (TDOFFVI) based on an anti-resonance mechanism is presented. This isolator has two tunable anti-resonance frequencies capable of attenuating vibrations at one or two frequency excitations simultaneously. A mathematical model of the TDOFFVI is developed. The force transmissibility and the anti-resonance frequencies in conjunction with design parameters are formulated and the optimal design of the TDOFFVI is given. A physical prototype of the TDOFFVI has been designed, built and tested. The experimental results validate the theoretical analysis and show that the TDOFFVI can perform effectively in vibration isolation.
To reduce high frequency vibration propagated into the optical payload on spacecraft, multiple vibration isolation platforms are employed. This means that the vibration isolation platform can not only be used to isolate the disturbances caused by the actuators such as control moment gyros or the reaction wheels (RWs), but it can also be placed between the spacecraft bus and optical payload. The dynamic modeling of the spacecraft with multiple vibration isolation platforms and its applications are discussed. Firstly, the spacecraft dynamic model with only one vibration isolation platform is derived using the Newton-Euler approach. Then the integrated spacecraft dynamic formulation is obtained based on the above dynamic model with only one vibration isolation platform. Multiple vibration isolation platforms are used to interface the disturbance source with the spacecraft bus. For example, each RW could have a vibration isolation platform to reduce the vibration. The frequency domain characteristics and the safety reliability of the spacecraft with multiple vibration isolation systems are discussed based on the above dynamic model. Finally, the validity of the dynamic model of the integrated spacecraft with multiple vibration isolation platforms can be proved by numerical simulation. Other than that, the simulation results illustrate the ameliorative effect of multiple vibration isolation platforms on the optical payload attitude stabilization.
Multi-fault diagnosis of rotor systems is a topical issue in the research of rotor dynamics. Empirical mode decomposition (EMD) has been introduced in fault diagnosis of rotor systems, which has proved to be usable and efficient in single fault diagnosis of a rotor system. However, in multi-fault diagnosis of a rotor system, because of the existence of a high-frequency fault signal, EMD is not as powerful as the diagnosis of a single fault in dealing with the decomposition of multi-faults. In this paper, differential-based empirical mode decomposition (DEMD) is introduced into multi-fault diagnosis of a rotor system. The analysis consequences show that the combination of any two faults among crack, rub-impact and pedestal looseness in multi-fault diagnosis can be decomposed successfully and efficiently under the application of the DEMD method, which is also more accurate and precise than the traditional EMD method.
Vibration suppression in harmonically forced viscously damped systems is considered using a new vibration absorber setup. The absorber is placed between the primary system and the supporting ground. The optimal absorber parameters are obtained with the aim of minimizing the maximum of the primary system frequency response. For a given damping ratio of the primary system and mass ratio of the system, the optimal stiffness and damping ratios of the absorber are calculated numerically. Two different numerical approaches are used in solving the problem; the first is based on the genetic algorithm technique and the second on the downhill simplex method. It is shown that an optimal mass ratio exists and it is calculated along with the corresponding absorber parameters for a range of the primary system damping ratio. The utmost optimal parameters associated with the optimal mass ratios are tabulated to be used for the design of such absorbers. The absorber efficiency is discussed and it is shown that this absorber becomes detrimental as the mass ratio is increased or when damping in the primary system is high. The proposed and classical absorbers efficiencies are compared.
This work concerns a two-level procedure for the global optimum design of hybrid elastomer/composite modular structures. The goal of the procedure is the maximization of the first Nf modal loss factors of the structure, satisfying mechanical constraints on the weight and on the bending stiffness, feasibility constraints on the admissible moduli for the constitutive laminates, along with geometric constraints on the positions of the viscoelastic patches. At the first level of the procedure, the optimization of the damping behavior of the structure is carried out: the optimization variables at this stage are the number of elastomer patches (modules), as well as their geometrical parameters (position, thickness and diameter), along with the material and geometric parameters of the composite laminated structure (elastic moduli, thickness of the laminate). The composite structure supporting the elastomer patches is thus optimized using a free-material approach, via the polar representation of 2D elasticity, and the second level of the optimization consists in finding the laminate stacking sequence satisfying the optimal elastic moduli and thickness issued from the first step. The method is able to automatically determine the optimal number of modules and it does not need the introduction of any simplifying assumption. The proposed approach relies on one hand, on the application of the well-known Iterative Modal Strain Energy (IMSE) method for the evaluation of the dynamic response of the structure, and on the other hand on the use of the polar formalism for the representation of the elastic anisotropic behavior of composite laminates as well as of a genetic algorithm as optimization tool to perform the solution search. We will illustrate the application of our approach to the optimization of the damping behavior of a rectangular composite plate with a discontinuous aperiodic distribution of viscoelastic material. The numerical results show the effectiveness of the proposed strategy.
In this paper, we consider the numerical resolution of a time and space fractional diffusion equation. The main purpose of this work is to construct an efficient accurate numerical solution by using spline function and then we analyze the stability of the obtained scheme for the time-space fractional diffusion equation. Numerical experiments are carried out to support the theoretical claims.
This article presents a baffle silencer with tunable resonators consisting of two superimposed and identically perforated plates associated with a partitioned cavity made of thermoplastic resin. One plate is fixed while the other is movable. Displacement of the mobile plate changes the internal shapes of the resonator necks and shifts the resonance frequency of the system to lower values. The contributions of this paper are firstly, the modeling of a panel with tunable resonators made of necks with a variable geometry and a partitioned cavity in resin and, secondly, the use of the model to elaborate a control strategy to attenuate variable tonal noise. All of the theoretical studies are validated by experimental measurements. Final results show the efficiency of the silencer in attenuating a tonal noise that varies between 2000 and 2800 Hz.
A novel method to solve the single-channel source separation problem is proposed, which is based on a morphological filter to remove noise and the optimal matching pursuit (MP) algorithm to create pseudo sources. The signal is first purified by the morphological filter. Then, the purified signal is decomposed by the MP method, the Gabor atoms of the MP are selected by genetic algorithm in order to be less time-consuming. The selected atoms and the purified signal are combined into multi-dimensional signals, and the underdetermined problem of single-channel source separation is solved. The singular value decomposition method is used to estimate the number of new constructed signals. Then, the fast independent component analysis algorithm is used to achieve the separation of the signals. The proposed method is applied to the separation of the simulated signals and the mixed faults of bearing, the results indicate that the method can well solve the single-channel signal separation problem.
This paper discusses chaos control and synchronization of the four dimensional Lorenz-Stenflo system based on passive control technique. Using passive theory, chaos control and synchronization of a four dimensional Lorenz-Stenflo chaotic system are realized with one input. The designed controllers ensure the stability of the controlled system and error dynamical system between two identical Lorenz-Stenflo systems. Also, the controllers ensure that the controlled system and error dynamical system converge to zero equilibrium. Numerical simulations show that the proposed method is effective for the Lorenz-Stenflo system.
One of the most critical issues in overhead cranes is the swing of a suspended load while the crane starts to move and accelerates, changes the movement direction, breaks or stops. This can lead to severe damage, and therefore several methods have been applied to damp the load swings. Most of these methods are based on information about the swing angle of a suspended load. In traditional methods, camera vision, acceleration or inclinometers sensors, simple pendulums and other types of sensors have been used. Generally, a method is desired if it can estimate the swing angle with the least equipment costs, while using an uncomplicated calculation method and the minimum sensitivity to environmental situations and industrial noises. In this paper, a new algorithm is proposed to estimate the swing angle. To do so, the supplied voltage and current of the induction motor which drives the trolley are measured, and then using a new proposed method based on a dynamic analysis of the mathematical dynamic model, the swing angle is estimated and is used in the controller system to damp the swings. The proposed method is verified by means of computer simulations.
The factors that are normally considered by customers for comfortable driving upon purchasing a car are acoustical comfort and exposed vibration. Keeping this in mind, the level of noise annoyance in reference to the vehicle acoustical comfort index is proposed. This index can be categorized by five states which are generally used in the computation that involve acoustical levels in the car cabin. This study is carried out in order to improve this index by classifying and categorizing these five states using the fuzzy set theory approach. Besides, identified sources of vibration are usually linked with engine transmission and tire-road interaction. This study includes the observation on the effects of the vibration due to tire interaction with the road, as well as the pattern of the trends toward the experienced noise against the engine speed [rpm] at both stationary and non-stationary positions. A combination of fuzzy set theory and nonlinear programming has been employed to develop a multi-objective model of hybrid fuzzy nonlinear weighted goal programming. This developed model adopts the results that have been provided in order to optimize the acoustics level by referring to the vibration level which is required at a certain value of the engine speed [rpm]. The proposed model has a significant impact towards a better environment, in the perspective of acoustics – a key factor in vehicle manufacturing process.
One of the characteristics that may influence customers in vehicle purchasing is the level of comfort of the vehicle’s sound vibration in the vehicle cabin. The basic principle suggests that the sound vibration discomfort level is affected by a few factors which are mainly based on magnitudes, frequencies, directions and also the exposed periods. Normally, the phenomenon of sound vibration disrupts the performance of the driver by affecting the driver’s vision and also inducing a certain degree of stress due to the sound and vibration to which the driver and his or her passengers are exposed. The sound vibration is generally contributed by a few sources originated from the transmission of the vehicle’s engine, tire interactions with the road surface and also the exposure of vehicle’s body vibration during the movement. The objective of this study is to propose an approach that clusters the level of sound and vibration into a few categories and classifies them into those categories without implementing the subjective test that normally involves human assessment. The study has observed the changes of the sound quality and the level of vibration at particular points in the vehicle cabin over the changes of engine speeds. In reference to the results, the study has successfully provided a technical procedure in order to cluster, and also to classify, the level of sound vibration by taking into account the correlation between experienced noise and exposed vibration in the vehicle cabin.
This paper is concerned with the modeling, nonlinear dynamic analysis and control design of an electrostatically actuated clamped-clamped microbeam. The model accounts for the mid-plane stretching and nonlinear form of the electrostatic force actuated along the microbeam span. A reduced-order model is constructed, using the method of multiple scales, to examine the microsystem static and dynamics behaviors. To improve the microbeam behavior, a nonlinear feedback controller is proposed. The main control objective is to make it behave like commonly known one-degree-of-freedom self-excited oscillators, such as the van der Pol and Rayleigh oscillators, which depict attractive filtering features in their dynamic frequency responses. For this, a review of the nonlinear dynamics of one of these oscillators is first provided to gain insight into its appealing filtering characteristics. We then present a novel control design that regulates the pass band of the considered microbeam and derive analytical expressions that approximate the nonlinear resonance frequencies and amplitudes of the periodic solutions when it is subjected to one-point then to fully distributed feedback forces. We apply Floquet theory to ascertain the stability of the limit cycles. We finally suggest an electronic circuitry made of six analog devices AD633JN for the implementation of the proposed feedback controller.
Attenuation of the adverse effects of vehicle vibrations on human health is a challenging problem. One common approach to solve this problem is to use various types of controllers in vehicle suspensions. In this study, in order to decrease the vehicle vibrations and hence improve the ride comfort, a fuzzy logic integrated sliding mode controller was designed. The performance of the controller was tested in a biodynamic human-vehicle combined model. The human body was considered as a lumped parameter model and incorporated into a full vehicle model. The biodynamic responses of a human body to vehicle vibrations were analyzed. Performances of the conventional sliding mode and fuzzy integrated sliding mode controllers were compared with those of a passive control strategy. According to the numerical results, the fuzzy sliding mode controller overcame both classic sliding mode and passive control approaches and decreased vehicle vibrations considerably. It can be deduced from the study that active suspension systems would play a key role in decreasing the negative effects of vehicle vibrations on human health, such as motion sickness, discomfort and spine injuries.
Dynamics of a longitudinally vibrating rod are analyzed from a wave standpoint, in which the motion of the rod is described in terms of waves that propagate through the uniform rod and are reflected and transmitted at structural discontinuities and boundaries. This study is based on the four engineering theories, namely, the elementary, Love, Mindlin–Herrmann, and three-mode theories. The propagation relations that are governed by the equations of motion are derived. The reflection and transmission relations, which are dependent upon the continuity and equilibrium conditions at structural discontinuities, are obtained. Waves generated by externally applied forces are found. The wave propagation, reflection, and transmission relations are assembled to provide a concise and systematic approach to vibration analysis of rods. Numerical examples are presented. Comparisons and recommendations are made for meaningful engineering practice.
The accuracy of the nodal patterns of combined degenerate mode shapes for a square membrane by previous researchers is investigated, and the nodal patterns of superimposed degenerate modes for square and non-square membranes and simply-supported plates are presented in a full range of amplitude ratios.
Envelope analysis is an effective technique of fault diagnosis for rolling element bearings (REBs). However, envelope analysis needs to select an appropriate frequency band of the signal. Numerous selection methods have been investigated, such as spectral kurtosis (SK) and wavelet packet kurtogram (WPK), which are based on kurtosis. Nevertheless, existing approaches are sometimes unable to identify bearing faults due to the contamination of discrete and random noises. In this paper, a novel method of fault diagnosis for bearings is proposed, which accumulates all or part of sub-band signals’ envelope spectrums at a given level in wavelet packet rather than demodulates one selected frequency sub-band signal. Two simulated signals and a real signal are analyzed to test the performance of the novel method. In the first case, stochastic impulses are added into the simulated outer race fault signal. The analysis shows that the novel approach is more robust to stochastic impulses than the other two methods such as SK and WPK. In the second case, the simulated signal containing two outer race faults from different REBs is analyzed using the three methods, respectively. The results show that the novel approach captures more useful information and detects the two different REBs’ faults contained in the same signal more effectively. Furthermore, the effectiveness of the novel method is validated by identifying the characteristic fault frequency of the real REB.
In this paper we present an analysis of the stability of a two-degree-of-freedom system, modeling a robotic arm connected to the actuator through an elastic joint and subject to digital position control. The system consists of two lumped masses connected to each other through a spring and a damper. In the model there is only one actuator, so the system is underactuated in a certain sense; two cases are considered, referring to a collocated and a noncollocated configuration. Stability analysis is presented using both a continuous and a discrete time approach. The discrete time approach is related to the case of a digital controller, typical in real applications. This samples the position and the velocity signals at discrete time intervals and, therefore, it generates a piecewise constant control force, introducing a delay in the control system as well. The stability charts are presented in the parameter space of the sampling time and the control gains. Their differences highlight the role played by the resonances between the finite sampling frequency and the natural frequency of the system in achieving robust stability with respect to parameter variations.
Semi-active isolation systems fill the gap between passive and active systems, delivering the versatility and adaptability of fully active systems, by expending a small amount of energy to change system parameters such as stiffness and damping. Magnetic suspension vibration isolation provides an excellent active isolation technology, and has shown useful characteristics including noncontact isolation, fast response, high reliability and long lifespan. However, because it is highly nonlinear and time variant, the control of magnetic suspension vibration isolation is an area that still requires further exploration. This paper presents a fuzzy control algorithm for a semi-active multi-degree-of-freedom vibration system. The fuzzy control is based on the minimization of the weighted sum of squared output forces. The output force response of the fuzzy, PID control semi-active vibration isolation system and passive system under the same excitation are simulated. The simulation results show that the fuzzy control system has much better performance in vibration isolation. An experimental platform is developed to test the performance of the magnetic suspension vibration isolation system and the proposed fuzzy control algorithm. The experimental results are found to be in good agreement with simulation.
In this study, as a state of the art testing method, real-time hybrid simulation (RTHS) is implemented and verified with a shake table for education and research. As an application example, the dynamic behavior of a tuned liquid damper (TLD)-structure system is investigated. RTHS is a practical and economical experimental technique which complements the strengths of computer simulation with physical testing. It separates the test structure into two substructures where part of the structure for which a reliable analytical model is not available is tested physically (experimental substructure) and coupled together with the analytical model of the remaining structure (analytical substructure). The implementation of RTHS involves challenges in accurate control of the experimental substructure as well as the synchronization of the signals. The details of the hardware and the software developed and the steps taken to improve the controller are discussed in this paper so that the implementation of RTHS is properly introduced. The accuracy has been verified using tracking indicators as well as using the response obtained from a spring-mass oscillator and TLD system. The shake table used in this study is available in over 100 universities around the world. In this paper, the implementation of RTHS is provided with sufficient details to enable easy introduction of this testing method wherever a similar shake table is available. This additional functionality will not only provide a new research tool, but it will also facilitate classroom demonstrations to improve how students understand new concepts in structural dynamics and earthquake engineering.
In this paper, we analyze the nonlinear magnetic-interaction forces in an electromechanical integrated toroidal drive and deduce the nonlinear electromechanically coupled dynamics equations of the drive system. Based on these equations, the bifurcation and chaotic vibrations of the drive system are investigated. The results show that chaotic vibrations occur in the drive system when the current in worm coils is relatively large. The current in worm coils, the ratio of the center distance to planet radius, the worm-coil inductance, and the support stiffness of the planet all have significant influence on the nonlinear vibrations of the drive system. We show the ranges for the system parameters that lead to a drive system with good dynamics. These results can be used to predict the dynamic load in a drive system and are useful for maximizing the power density of a drive system.
Shaking tables play a vital role in mechanical environmental simulation. Sinusoidal shaking tests are usually applied to specimens for simulating periodic motions. Due to the nonlinearities in the electro-hydraulic servo shaking table, its sinusoidal acceleration response contains higher harmonics, which lower the system control performance. To cancel those harmonics, the harmonic information should be firstly known. The paper proposes an acceleration harmonic identification scheme by using the extended Kalman filter. A nonlinear state space model of the acceleration response is then built for the extended Kalman filter. The harmonic information, including the amplitude and phase of each harmonic, is directly derived from the estimated states. The features of the algorithm are that the state transition equation is linear and the measurement equation is nonlinear. It also inherits the advantages of the traditional linear Kalman filter. Both simulation and experimentation are carried out to validate its efficiency and accuracy. The online estimated harmonic information can provide a basis for the further harmonic cancellation.
The purpose of this work is to increase the online availability of industrial gas compression installations. By prevention against the failures in gas turbines, used in this gas compression installation. In this work a new vibrations supervision approach based on parity space is used, this will guarantee us the optimal availability of this system. The obtained results show clearly how to ensure a reliable and safe operation in gas compression plants to economically recover the transported gas.
The disturbance propagation and active vibration control in complex space truss structures are investigated. Firstly, based on the advanced Timoshenko theory, the accurate dynamic responses of the space truss are obtained by the traveling wave method. Each structural member is treated as a waveguide, which transmits longitudinal, bending and torsional waves, and is connected by the junction. Secondly, the active power flow transmission of the space truss is suppressed by the feedforward active vibration control. Finally, the numerical simulation is implemented. The simulation results indicate that the dynamic responses of a space truss structure calculated by the traveling wave method are accurate and reliable in comparison with the results obtained by the finite element method. The dynamic responses are more accurate when using the Timoshenko beam model due to considering the effects of rotary inertia and shear distortion, especially in medium and high frequency ranges. Active control effects, attained by minimizing the active power flow, are compared with those achieved by minimizing the acceleration for suppressing the active power flow or the acceleration. It shows that active control effects achieved by minimizing the active power flow are much more effective than those reached by minimizing the acceleration, whether the error sensor is located in the far field or near field of the control source. In addition, the small error of the optimal control force has slight effects on the control results.
This paper reports a systematic investigation on the linear and nonlinear dynamics of a suspended cable, taking bending stiffness into account. Firstly, the linear dynamics features, for example, eigen frequencies and modes for in-plane and out-of-plane motions, are formulated. Secondly, parametrical studies are conducted to explore the effect of bending stiffness on the natural frequencies and mode shapes of the symmetrical/antisymmetrical in-plane and out-of-plane modes. Then, the three-to-one internal resonance between the first- and third-order in-plane symmetrical modes is analyzed by applying directly the method of multiple scales dealing with the nonlinear partial differential equation and boundary conditions. Finally, the frequency-response curves and force-response curves are obtained through solving the modulation equations using the Newton–Raphson method and the pseudo-arclength scheme. The results show that the bending stiffness plays a considerable role in changing the natural frequencies and mode shapes, shifting the conditions for the occurring of nonlinear interaction, saddle-node bifurcation and Hopf bifurcation of suspended cables.
Local vibration control systems of mechanical structures can be collocated or non-collocated. If a sensor is placed at the same location as an actuator the system is said to be collocated. Otherwise, the system is non-collocated. It is not always possible to collocate the vibration control actuator at the location of interest, e.g. in active magnetic bearings (AMBs) eddy current sensors are used to measure displacements of the supported shaft. Due to inevitable electromagnetic interferences the sensors cannot be placed exactly at locations of electromagnetic coils of the AMB. Non-collocation complicates the control problem because the dynamics of the structure between the control actuator and sensor disturbs the performance of the vibration control system. Non-collocated systems have non-minimum-phase zeros at the right half-plane, which may even destabilize the control system. Non-collocation effects were suppressed by several methods including phase shifting, time delay or passive vibration absorber methods. However, none of these methods ensured the required stability, nor a good performance. The present paper recommends the virtual (recalculated) collocation method for local control loops of the AMB. The idea is to calculate displacements at actuators' locations given the displacements at sensors' locations. The approach is illustrated with numerical results of the flexible rotor supported by AMBs and controlled with four proportional integral derivative (PID) controllers. The finite element model of the rotor is developed and transformed to the state-space. The model is reduced by the modal truncation technique. Then, an observer for the reduced system is developed. This way the shaft displacements at any discretization node along the shaft axis are simply estimated and introduced to the inputs of PID controllers. Calculation results demonstrate a good performance of the collocated PID control systems, confirming the potential of the method and giving a rationale for its further development.
Rolling element bearings are vital components in rotating machines, and it is important to diagnose bearing faults to avoid serious accidents in equipment. In this paper, singular spectrum analysis (SSA) is utilized to extract the bearing fault features. SSA is a non-parametric technique of time series analysis which decomposes the acquired vibration signals into an additive set of time series. Based on the selected singular features from SSA, a continuous hidden Markov model (CHMM) is introduced to diagnose the bearing fault. The detailed description and identification results of applying the proposed method to rolling element bearing fault diagnosis are shown in experiment 1. In experiment 2, a rolling element bearing accelerated life test is performed to simulate the performance variation of the bearing. The result demonstrates that the singular features and CHMM can reflect the performance degradation of the bearing from health to failure. A conclusion can be made that SSA and CHMM are feasible and effective in bearing fault diagnosis and performance assessment.
Vibration of a hollow circular plate subjected to a rotating peripheral force is analytically studied in this paper. Closed-form solutions are developed in a series form for the plate deflection as well as the distributions of the strain and stress. The Galerkin approach is adopted as the solution method and a finite element model has also been developed. Computer simulations were performed to verify the model and solution methods were adopted. Close agreement is observed when comparing the numerical results with those obtained from the analytical technique. The acoustic pressure field is eventually obtained in front of the vibrating plate surface using the Rayleigh integral method. The solution procedure presented and the numerical results obtained can be extensively utilized in the noise source separation. This has always been a significant challenge in many engineering applications such as the railway wheel-rail dynamics or that of the automotive gear trains.
This paper discusses the development of an active noise control (ANC) system to cancel compressor noise produced by a commercially available heating, ventilation and air conditioning unit enclosed within a closet. Feedback ANC architecture that requires no reference microphone is used for cost-effectiveness. A novel delayless subband adaptive filtering technique is used to reduce computational complexity of the algorithm and improve system performance. Finally, the system is extended to two-channel architecture in order to provide an additional zone of silence. Using an experimental setup, the noise from the compressor at two error microphone positions is recorded and all necessary secondary path measurements are taken. Noise attenuation levels of 11 dB and 21 dB are obtained at the two error microphones, resulting in an average attenuation of 18 dB.
In modern industry, milling is an important tool when a high material removal rate is required. Chatter detection in this situation is a crucial step for improving surface quality and reducing both noise and rapid wear of the cutting tool. This paper proposes a new methodology for the chatter detection in computer numerical control milling machines. This methodology is based on vibratory signal analysis and artificial intelligence. The methodology consists of five major steps: (1) data acquisition, (2) signal processing, (3) features generation, (4) features selection and (5) classification. As chatter components occur around system resonance frequencies, a multiband resonance filtering method is proposed at the processing step. The process is then followed by envelope analysis. This allows the signal-to-noise ratio to be increased and the sensitivity of generated features to be increased. Extracted features are then ranked based on their entropy in which only best features are selected and presented to the system for classification. At the classification step, the selected features are classified into two classes: stable and unstable utilizing neural networks. Two neural network approaches, radial basis function and multi-layer perceptrons, are tested. The developed approach is applied for chatter detection in a Huron K2X10 milling machine. This approach is tested on a milling machine at different depths of cut and various rotational speeds. Discussions are made and the results confirm the accuracy of the proposed methodology.
The purpose of this paper is to numerically investigate the influence of nonlinearities applied to vehicle powertrains equipped with a dual clutch transmission, including gear backlash, dual mass flywheel hysteresis, and torque pulses from the engine. To achieve this goal, a multi-body dynamic model of such a powertrain is constructed for transient vibration studies. Incorporated into this model is a combination of two nonlinear contact backlash models: for gear pairs a line-of-action force contact model is used to represent backlash in the mesh, and, for engaged synchronizer dog gears, a torsional nonlinear contact model is applied. This powertrain model is then used to study the response to shift transients under different conditions, including with and without engine torque harmonics, the variation of mesh damping and tooth clearance, and the impact of torsional vibration absorbers. Simulation results demonstrate that engine torque harmonics, mesh clearance, and external damping sources have a significant impact on duration of excitation, while the impact of mesh damping is less significant.
In this paper, a fuzzy rule-based system (FRS) has been used for optimal reliability-based robust controller design for a two-mass-spring system with probabilistic uncertainties in its parameters. In this way, a multiobjective uniform-diversity genetic algorithm (MUGA) is first used to find a Pareto front of two-mass-spring system in a deterministic approach. This paper considers a two-mass-spring system under an impulse input. Two conflicting objective functions in this model include settling time of the second mass and control effort exerted on the first mass. Consequently, such Pareto front is then obtained for a two-mass-spring system with probabilistic uncertainties in its parameters using the probabilities of failure of those objective functions through a Monte Carlo simulation approach. It is shown that the FRS system removes the difficulty of selecting suitable crisp values and obligation due to a defining limit state function. Besides, the multiobjective Pareto optimization of such robust controllers using MUGA unveils some very important and informative trade-offs among those objective functions. Consequently, some optimum robust controllers can be compromisingly chosen from the Pareto frontiers.
A tuned liquid damper (TLD), which consisted of two-layer hemispherical containers, partially filled with water, was investigated as a cost-effective method to reduce the wind-induced vibration of wind turbines. A 1/20 scaled test model was designed to investigate its performance on the shaking table. Three groups of equivalent ground accelerations were inputted to simulate the wind-induced dynamic response under different load cases. The influence of rotors and nacelle was assumed to be a concentrated tip mass. A series of free and forced vibration experiments were performed on the shaking table. The experimental results indicated that the spherical TLD could effectively improve the damping capacity of the test model. The standard deviation of the dynamic response could be effectively reduced when the excitation frequency was approximately equal to its fundamental frequency. For "overspeed" and "extreme operating gust" load cases, the standard deviations of the dynamic responses were reduced more than 40% when the liquid mass was about 2% of the generalized mass; for "parking" load cases, the corresponding standard deviation was reduced more than 50% when the liquid mass was only 1% of the generalized mass. That is to say, the spherical TLD can effectively improve the anti-fatigue performance of the wind turbine tower.
This paper presents the development of a biologically inspired method for topology optimization and its application to a vibration suppression problem. The proposed method is based on modeling the structure topology (distribution of stiffening ribs) by replicating the natural growth of dendritic structures, which are ramified branches as those e.g. in leaves or in insect wings. The test case is a plate excited by acoustic pressure. The multi-objectives topology optimization aims to reduce both the vibration amplitude and mass of the plate. Experimental tests are performed for baseline plate model validation and identification of acoustic excitation distribution. A set of solutions are designed by the proposed method and numerically compared with traditional optimization approaches, showing improved performances. Finally, in order to evaluate industrial applicability, the robustness of the solutions to uncertainty in branch widths is demonstrated.
Actuator placement has a significant impact on the dynamic response of actively controlled structures. Misplaced actuators and sensors often lead to controllability and observability problems, and the desired system performance may not be achieved with any choice of control law. This paper addresses the design of actively controlled structures wherein both the actuator placement and controller design aspects are addressed simultaneously. It is assumed that a hierarchical structure exists between the actuator placement and controller design objective functions with the actuator placement problem considered as being more important. The resulting multiobjective design problem is solved as a bi-level Stackelberg game. A computational procedure based on variable updating using response surface methods is developed for exchanging information between the two levels (leader and follower). The optimization problem has mixed discrete-continuous variables with discrete variables corresponding to actuator placement and continuous variables associated with the controller design problem. The solution approach includes a blend of genetic algorithms and sequential quadratic programming techniques and is applied to the design of a flexible truss structure. The proposed approach successfully designed an optimum controller while minimizing the weight of the structure and simultaneously maximizing the energy dissipated by the controller to bring the structure to its equilibrium position when subjected to an external disturbance.
This study focuses on the control of a novel active vibration isolator using an adaptive backstepping approach. The developed active isolator is introduced and its dynamic model is presented. It is shown that the unknown nonlinear restoring force and damping parameter pose control challenges. The nonlinear restoring force is approximated as a polynomial with unknown coefficients. Adaptive control is chosen as a suitable approach to tackle the control challenges. An existing lower-order adaptive backstepping controller is modified in order to include the actuator dynamics and avoid the zero convergence of the estimated parameter vector. An extensive experimental study is conducted to test the effectiveness of the modified controller. The performance of the controller is compared with that of the lower-order controller. The results from several testing scenarios are presented and interpreted, and the issues related to parameter estimation and control performance are addressed.
The condition for producing sustained oscillation during the placement of additional mass on a piezo sensed/actuated cantilever beam and diaphragm structure is derived. The phase condition for continuous oscillation of these structures is met automatically by adjusting the phase angle of the vibrating structure with a resistor–capacitor network in feedback. The concept is evaluated for the measurement of mass analytically, through numerical simulation, and is verified experimentally.
Using cross-ties is one of the effective countermeasures to suppress unfavorable bridge stay cable vibrations. It has been successfully applied in the field. However, dynamic behavior of cable networks is still not clearly understood, which hinders the development of a more efficient design. The current paper aims at extending the existing analytical studies on in-plane free vibration of cable networks by developing closed-form modal solutions for a wider series of cases, in particular for general cable networks consisting of n horizontally laid main cables interconnected transversely with a single line of rigid cross-ties. The validity of these analytical modal solutions is verified by independent finite element simulations. These closed-form modal solutions offer a clear elucidation of the mechanics underlying various modal behaviors observed in cable networks of different layout and structural properties. In addition, based on the proposed analytical formulation, the important system parameters of cable networks are identified. The unique features associated with cable networks of a number of specific configurations are investigated and discussed.
This paper presents a fast adaptive time-frequency method for analyzing stationary and nonstationary vibration signals with transients. The method is developed based on instantaneous frequency (IF) – variations in the time domain. The variable window length is determined by estimating the local IF in every window slice over time. The proposed method is tested using simulation signals and experimental vibration data. The results show that the proposed method can successfully retrieve transient signals at a 3 dB signal-to-noise ratio, and improve stationary and nonstationary signal resolution in time and frequency domains. The proposed scheme offers better resolution compared to the standard short-time Fourier transform (STFT), and the computing cost is only slightly greater than STFT scheme.
This paper presents an analytical investigation on the nonlinear dynamic analysis of functionally graded double curved thin shallow shells using a simple power-law distribution (P-FGM) with temperature-dependent properties on an elastic foundation and subjected to mechanical load and temperature. The formulations are based on the classical shell theory, taking into account geometrical nonlinearity, initial geometrical imperfection, temperature-dependent properties and unlike other publications, Poisson ratio is assumed to be varied smoothly along the thickness = (z) . The nonlinear equations are solved by the Bubnov-Galerkin and Runge-Kutta methods. The obtained results show the effects of temperature, material and geometrical properties, imperfection and elastic foundation on the nonlinear vibration and nonlinear dynamical response of double curved FGM shallow shells. Some results were compared with those of other authors.
The Rayleigh damping matrix formulation is a commonly implemented means for the representation of intrinsic damping in many finite element programs. However, methods for specifying the Rayleigh mass and stiffness-proportional coefficients based upon individual components’ unique dissipative properties are ambiguous and rely heavily upon engineering judgment. An alternative linear hysteretic constitutive modeling methodology is used to represent multiple dissipative properties in example base-isolated series frame structures; the resulting displacement data are verified against a second alternative method involving weighted modal time history analysis. A methodology for the determination of Rayleigh coefficients for series systems dominated by low-frequency behavior is then developed based upon a hybrid of the two independent alternative methods. The displacement data from the proposed Rayleigh damping methodology are calibrated against the linear hysteretic constitutive modeling methodology, with the results showing close agreement.
This paper has been framed to study the propagation of torsional surface waves in an inhomogeneous layer of finite thickness over an initially stressed inhomogeneous half-space. Rigidity, density and initial stress of the half-space are assumed to have linear variation, and in layers linear variation in rigidity and density are also considered. It has been observed that the inhomogeneity parameter and the initial stress play an important role for the propagation of the torsional surface wave. The method of separation of variables is applied to find the displacement field. The dispersion equation of phase velocity is derived. The velocities of torsional waves are calculated numerically as a function of kH and presented in a number of graphs, where k is the wave number, and H is the thickness of the layer. Graphical user interface has been developed using MATLAB to generalize the effect of the various parameters discussed. As a particular case it has been seen that the dispersion equation is in agreement with the classical result of the Love wave when the initial stresses and inhomogeneity parameters are neglected.
This paper addresses the design problem of a discrete controller with time delay and acceleration feedback. The delta operator is firstly used to describe the discrete acceleration signal and convert the delayed continuous-time state equation into the delayed discrete-time system. Then the delayed discrete-time system is transformed into the delay-free one by applying a discrete reduction method. Based on the delay-free discrete-time system, the optimal output delta state feedback controller is designed by minimizing a discrete non-standard quadratic performance index and the feedback gain of the controller is obtained by a convergent algorithm. On the basis of the optimal output delta state feedback controller, the discrete time-delayed acceleration feedback controller is achieved by using the inverse reduction method, and the corresponding recursive control algorithm is developed. The controller saves the process of performing numerical integration and eliminating direct current and trend term in designing the displacement or velocity feedback control, so as to make the closed-loop system become simpler. Moreover, it can solve the problem of phase shift of the measured signal caused by time delay. The proposed controller with a low order model-based control algorithm is implemented on a smart cantilever beam with an accelerometer and piezoelectric actuator for different controller gain-delay combinations, and the control performance is evaluated. Simulation and experimental results demonstrate that the controller can effectively reduce the free vibration response of the smart cantilever beam.
Minimal mass (ultra lightweight) and high packaging efficiency (stowage volume) are the most important factors associated with space technology and hence they become more attractive traits for getting larger bandwidth satellites on-orbit. Nowadays, maintaining the surface shape of pre-tension membranes to instrument precision has become a more challenging problem. Hence, membrane reflectors are receiving increasing attention for mission architectures that need extremely large in-space deployable antennas. This paper presents the finite-element investigation of a rectangular, flat thin membrane using polyvinylidene fluoride (PVDF) piezo-actuated material as an actuator/sensor. The passive effect of PVDF on the dynamics of an inflatable space-based rectangular shaped structure has been studied and trends in natural frequencies for various patch areas and thickness have been explored. Investigation shows that rather than using the various numbers of patches to the practical system for controlling their vibration behavior, the single patch with the appropriate thickness can easily control the desired vibration behavior. It can therefore be concluded that the discrete sensor/actuators devices are to be preferred to realize lower weight and effective control authority for the modest values of actuator voltages for active vibration control of practical structures.
Axially translating beams are widely seen in engineering applications. An active vibration control strategy based on a modified fuzzy sliding mode control is developed for controlling and stabilizing the motion of the beam. Geometric nonlinearity of the beam is considered. In the development of the control strategy, the governing equation of the beam is transformed into a multi-dimensional dynamic system with the Galerkin method of 6th order. An active control strategy is developed corresponding to the dynamic system, such that the control strategy can be used for multi-dimensional systems. Numerical simulations are performed with application of the control strategy developed. The effectiveness of the active control strategy is demonstrated in controlling and stabilizing the chaotic motion of the translating beam.
Skyhook technology is widely used in vibration control. However, it only attenuates vibration near the resonant frequency. To enhance the control performance of an isolation system, a new feedforward compensation control strategy, achieved by measuring base velocity with a geophone, is proposed in this paper. Firstly, the mathematical model of single degree-of-freedom pneumatic spring is derived in detail. Secondly, the feedback controller is designed experimentally, and an anti-windup proportion-integral controller is used. Thirdly, the feedforward compensation controller is designed using a finite impulse response filter, whose coefficients are updated on-line using the filtered-x least-mean-square algorithm with improved gradient estimate. At last, a series of experiments were conducted, and the velocity attenuation rate is calculated. The results of these experiments prove that the proposed method can greatly reduce base disturbance, and keep a high vibration velocity attenuation rate at all frequency points.
In this paper, an estimation is made to study the propagation of Stoneley waves in magneto-thermoelastic materials with voids and two thermal relaxation times in the context of a Green–Lindsay model. The basic governing equations have been formulated in the xz-plane and the magnetic field is considered in the y-axis, which acts perpendicular to the wave propagation. We applied Lame’s potentials method to solve the problem. The boundary conditions that the continuity of forces stresses, Maxwell’s stresses components, displacement components, heat flux, temperature and volume fraction field are illustrated at the interfaces between two dissimilar half-spaces to obtain the frequency equation of the Stoneley waves in the media. Some special cases neglecting: (i) the magnetic field, and (ii) the thermal relaxation times’ parameters are deduced as special cases from this study and the numerical results are displayed graphically.
Accurate formulas for obtaining the energy, velocity and displacement decay envelopes in purely nonlinear damped oscillators are presented here. These purely nonlinear oscillators have no linear stiffness components, and the new formulas derived in this paper are found to be highly accurate in determining the decay envelopes, regardless of the system’s physical parameters and its initial condition. The mechanism of these new formulas for obtaining the decay envelopes of the nonlinear oscillators is found to be exactly the same as the mechanism of the well-known amplitude decay formulas used for the linear oscillator. Finding such formulas is significant to many scientific applications of these nonlinear oscillators, such as the passive targeted energy transfer through the stiffness-based nonlinear energy sinks (NESs). In these types of NESs, these formulas can be easily applied for system identification and dynamic analysis. In addition, they are expected to have a significant application in different scientific fields for such oscillators.
In this paper, the fractional order of a new chaotic system was studied and the minimum effective dimension for which the system remains chaotic was calculated. We have presented the chaos synchronization of two identical and nonidentical fractional orders of the new system by using active control. Furthermore, the Laplace transform and the Niemann–Trouvaille fractional integral operator were used for synchronizing two system.
Tuned liquid dampers (TLDs) employ sloshing fluid to reduce the resonant response of structures. Existing structure-TLD models are limited to rectangular or circular tanks, shapes that may not always be feasible in practice due to geometric restrictions of the building floor plan. This paper utilizes an equivalent linearized mechanical model and a nonlinear multimodal model to predict the response of the structure-TLD systems where the TLD tank geometry is irregular.
Experimental structure-TLD system tests are conducted that consider two irregular tank shapes. Response history plots and frequency response plots of the structural displacement and TLD wave heights are created to evaluate the models using the experimental results. The parent distributions and 10-minute peak distributions of the structural displacements and TLD wave heights are created for the simulated and experimental results. These distributions indicate that both the linearized and nonlinear models can accurately predict the structural response; however, the linearized model substantially underestimates the peak wave heights. Since wave heights are required to establish the required tank free board, or roof impact pressures, it is concluded that nonlinear analysis of the structure-TLD system model is required before a TLD design is finalized.
This study deals with the development of displacement of the tool (amplitude of vibration), cutting temperature and tool wear prediction model for boring process using artificial neural networks (ANNs). The experiments have been conducted using full factorial design on an all-geared head lathes with the experimental setup. The adequacy of the developed model is verified by using the neural network model, which has been developed using the feed-forward back propagation algorithm using training data and tested using test data. To judge the ability of the model to predict displacement of the tool (amplitude of vibration), cutting temperature and tool wear values, the percentage deviation and average absolute percentage deviation have been used. The predicted ANN model values are very close to the experimental results.
This paper addresses identification and robust control of vibration of a flexible plate attached to the upper side of an enclosure. The frequency domain subspace methods and minimax-linear quadratic Gaussian (LQG) control are utilized to identify the model and to control the vibration of the flexible plate, respectively. In order to identify the model of the flexible plate, several frequency domain subspace identification algorithms with Instrumental Variable idea are used. Considering the fact that the flexible plate system is stable by nature, all identified unstable models are passed through a stabilized process using an iterative algorithm with different initial values. The first three modes of the plate are selected for control purposes, and the other modes are chosen as uncertainty term. To design the weighting function for the minimax-LQG controller, Chebychev and Yule–Walker filters are utilized to consider the effect of modeling uncertainty. These weights have a great effect on robust stability and performance of the control system. Simulation results are presented to show the effectiveness of the designed controllers for the reference model. Results confirm that some indexes that show the quality of the identified models can be used as suitable measures to predict performance of the designed controller.
In this paper, an adaptive control using the backstepping technique is applied for a supercavitating vehicle model to account for the unknown slope of the fin force with respect to fin angle of attack in the vehicle model. In the supercavitating-vehicle benchmark model, the fin force was modeled as a linear function with respect to the fin angle of attack, and the corresponding slope was considered to be a known constant for a fixed cavitation number. However, more realistic modeling for the fin force shows that the fin force slope is a function of the fin deflection angle, fin sweepback angle and fin immersion. In addition, noting that the cavity shape at the transom region determines immersion of the fins, the fin immersion and thus the slope of the fin force is also impacted by the so-called memory effect due to cavity–vehicle interaction. In this paper, we consider the fin effectiveness parameter relative to the cavitator, which is used to compute the slope of the fin force in the aforementioned benchmark model, to be an unknown parameter. Then a parameter estimation law is designed for this fin effectiveness parameter and an adaptive backstepping controller is designed for the supercavitating vehicle model. We prove the boundedness of all variables (and convergence of the vehicle state variables under certain conditions) via Lyapunov stability theory. In addition, if the bound of the fin effectiveness parameter is known, a projection of the parameter adaptive law can be used and the resulting modified controller will maintain the same properties. Evaluation results through simulation on both initial response and tracking performance of the closed-loop system show the effectiveness of the developed algorithm.
This paper presents a framework for model-based analysis of robust stability and performance for a multi-axis active vibration isolation system with constant but unknown payload and subject to modelling errors associated with structural flexibility. The theoretical treatment involves a linear time-invariant system subject to real parameter uncertainty associated with the unknown payload. A set of performance indices are formulated based on generalized H2 (Hg ) and H measures. A method for stability/performance verification is then developed using a parameter-dependent Lyapunov function that incorporates the kinetic energy of the uncertain payload mass. This allows nonconservative bounds on the performance indices to be established via numerical solution of a corresponding set of matrix inequalities. The approach is especially suitable, and computationally efficient, for multi-degree-of-freedom systems as the overall (symmetric positive-definite) properties of the system mass matrix are accounted for without involving information for each scalar parameter. The associated LMIs can therefore be solved in polynomial time with respect to the number of unknown parameters. Numerical examples for the case of sky-hook damping control and multi-objective Hg /H control are provided that demonstrate the effectiveness of the method as a tool for model-based controller evaluation and multi-objective optimization.
The problem under consideration relates to a model of a porous wall devoted to aircraft motor noise reduction. For such a medium, the parameters of the propagation equation depend on the frequency. Then, the corresponding time model involves nonrational convolution operators, which make the model complex from both the analysis and the simulation points of view. In this paper, based on the so-called diffusive representation of convolution operators, a time-local formulation of the porous wall model, well adapted to analysis and numerical simulation, is established and analyzed. Then its associated impedance operator is computed. Finally some numerical results relating to the simulation of the porous wall and to the one of its impedance operator are given to highlight the theoretical part.
A multi-dimensional earthquake isolation and mitigation device for long-span reticulated structures is a type of newly invented passive control device. In order to acquire the earthquake isolation and mitigation effect of the new devices on long-span reticulated structures under horizontal excitations, the pseudo-dynamic tests for a 1:3 modeled long-span reticulated structure with a size of 3 m x 3 m with and without the devices are carried out. Horizontal dynamic responses of the structure with and without the devices are compared, and the earthquake isolation and mitigation effect of the devices is evaluated under the horizontal excitations. It can be shown from the experimental and finite element numerical results that the proposed new devices have a good effect on earthquake isolation and mitigation on long-span reticulated structures under horizontal earthquake excitations.
In this paper free vibration of a Timoshenko beam with a tip payload, which is mounted on a cart (referred to as TBC) is studied. The cart (base) can only have lateral displacement and the tip payload has both mass and mass moment of inertia. The center of mass of the payload does not coincide with the point where the beam connects to the payload. Therefore, the tip of the beam is exposed to an extra bending moment due to the inertial force of the payload.
By employing Hamilton’s principle, the governing equations of motion and the associated boundary conditions for the TBC are first derived and then transferred into dimensionless forms. By using these governing equations and their associated boundary conditions, the closed-form frequency equation (characteristic equation) of the TBC is derived. This closed-form frequency equation is validated both analytically and numerically. The closed-form expressions for the mode shapes of the TBC and their orthogonality are also presented.
By using the closed-form characteristic equation, a sensitivity study is performed and the changes in the natural frequencies versus changes in the physical parameters are investigated.
The results presented in this paper are valuable for precise dynamic modeling and model-based control of flexible mobile manipulators; a flexible mobile manipulator is a flexible link manipulator with a moving base.
A nonlinear stochastic optimal control strategy for single degree-of-freedom viscoelastic systems with strongly nonlinear stiffness under Gaussian white noise excitation is proposed. First, the viscoelastic system is converted into an equivalent nonlinear non-viscoelastic system by replacing the viscoelastic force with amplitude-dependent stiffness and damping. Second, the partially averaged Itô stochastic differential equation for total system energy as one-dimensional controlled diffusion process is derived by using the stochastic averaging method of energy envelope. For the semi-infinite time-interval ergodic control, the dynamical programming equation is established based on the dynamical programming principle and is solved to yield the optimal control force. Finally, the variances of the responses of controlled and uncontrolled systems and that of the optimal control force are predicted analytically. Numerical results show that the proposed control strategy is very effective and efficient.
The main objective of the present work is to develop an algorithm consisting of the eigenvalue sensitivity and modal updating along with the mode tracking to analyze the dynamic behavior (i.e., vibrational properties) of a tensegrity structure. The optimum values of the design parameters including the pre-tension force, element section area, etc., are obtained to satisfy the desired vibrational properties of the structure. The optimum variables will be acceptable if the design constraints involving the buckling constraint for rod elements and the strength constraints for all components of the system are fully satisfied. The efficiency of the proposed algorithm for finding the optimum values of the design variables of the tensegrity structures is proved through the solution of three examples
This paper is concerned with a delayed non-fragile H control scheme for an offshore steel jacket platform subject to self-excited nonlinear hydrodynamic force and external disturbance. By intentionally introducing a time-delay into the control channel, a delayed robust non-fragile H controller is designed to reduce the vibration amplitudes of the offshore platform. The positive effects of the time delays on the non-fragile H control for the offshore platform are investigated. It is shown through simulation results that (i) the proposed delayed non-fragile H controller is effective to attenuate the vibration of the offshore platform; (ii) the control force required by the delayed non-fragile H controller is smaller than that required by the delay-free non-fragile H controller; (iii) the time delays can be used to improve the control performance of the offshore platform.
This paper first presents a review of very large scale integration signal processing applications using Q-format data representation, through field programmable gate arrays. Also, this paper presents a comprehensive review of Q-format-based applications, which include arithmetic computations in signal processing, linear time-invariant systems, finite impulse response filter, 3-D graphics system, personal digital assistant, and neural networks and power electronic converter control are discussed. Finally, a Q-format-based arithmetic logic unit (QALU) has been designed and developed using very high speed integrated circuit hardware description language. The QALU is used to develop the space vector pulse width modulation control, and the simulation and experimental results are presented.
The main hindrance in easy detection of bearing faults from vibration data is that the signal is noise ridden, and only an efficient method for noise reduction will effectively bring out the fault characteristics. This paper proposes a novel method for such noise reduction using Lucy–Richardson deconvolution, which is an iterative technique for deblurring images. Its application in signal processing more specially in bearing fault diagnosis is being studied in this paper. The characteristics of this deconvolution with different shapes of point spread function and their effectiveness are also shown.
Although various methods have been presented in the literature for rotating machine fault detection, it still remains a huge challenge to accurately extract features from non-stationary vibration signals with a high noise level, typically in the case of rolling element bearings faults diagnosis. Due to its random and non-stationary nature, fault related features are difficult to extract by common techniques and are usually overwhelmed by noise and macro-structural vibrations. In this paper, a new time series decomposition method based on a dynamic linear model is proposed, which provides time domain decomposition of a non-stationary signal into collections of latent components. The signal of a damaged bearing consists of exponentially decaying ringing that occurs periodically at the bearing characteristic defect frequency. Dynamic linear models with time-varying cyclical components provide a more generalized and adaptive description on rolling element bearings’ vibration signal with time-varying cyclical behavior. This allows the precise isolation of latent, quasi-cyclical bearing fault components via inferences on the time-varying parameters which characterize these components. An accelerated whole lifetime test of bearing has been performed to collect vibration data, which is utilized to validate the effectiveness of the proposed method.
The magnetically suspended control moment gyro (MSCMG) system is an actuator for attitude control of spacecrafts. It consists of a gimbal and a high-speed rotor suspended by magnetic bearings (MBs). The imbalance vibration due to the high-speed rotor can cause a velocity ripple to the gimbal and be transmitted to the spacecraft to decrease its attitude control precision. To suppress the imbalance vibration, this paper introduces an active control method in both the MBs and gimbal systems. Firstly, the structure and dynamics of the MSCMG system with the MBs and gimbal are described, and the transmission of the imbalance vibration is discussed. Then a notch filter with a phase shift and a feedforward controller are designed to prevent the MB system from generating the imbalance vibration by making the rotor rotate around its inertial axis. To correct the feedforward control errors resulting from power amplifiers, phase and gain compensations are made. Finally, another notch filter with a phase shift is employed to suppress the velocity ripple caused by the residual vibration from the MB system, and a constant-gain Kalman filter is adopted to obtain the best real-time estimate value of the gimbal velocity. Stabilities of the vibration control method and the Kalman filter are analyzed. Simulations and experiments have been performed to validate the proposed control method, which has a short computation time and can be used in many practical applications.
In this paper, the nonlinear dynamics equations of a pure rolling low-noise excavating system with one clearance are derived, and the characters and the factors affecting the response, such as rotating angular velocity, mass center of crank, elastic coefficient in the normal direction and the size of clearance, are discussed. The results show that, the larger the elastic coefficient is, the more stable the system is; the value of the elastic coefficient at clearance has almost no affect on the load torque, whether from the magnitude or fluctuation. When the size of clearance and rotational velocity are increased, the interactive forces will increase, and the maximum value of impact force is increased also. The results provide preference for the design of low-noise system in actual engineering.
This paper deals with finding the optimum parameters of a damped dynamic vibration absorber (DVA) to control chatter in metal cutting systems. The performance of conventional damped DVA is compared with the proposed skyhook damper in which the damper of the absorber system is connected between the absorber mass and an inertial reference in the sky, referred to as a skyhook damper. The damped DVA is optimized by reducing the magnitude in the positive side and increasing it in the negative side of the real part of the frequency response function of the main system. The optimum frequency ratio and the damping ratio of the damped DVA for the undamped and damped main system are obtained using analytical solutions and a numerical optimisation technique, viz genetic algorithm, respectively. The performance of the proposed skyhook damper is marginally better than the conventional type of damped DVA in controlling the vibration of the main system. This is verified by analyzing both the proposed and conventional models using finite element method-based commercial software ANSYS.
Adaptive suspensions can modify their filtering capacity to better accommodate excitations with different characteristics. The modification of stiffness (and, to a certain extent, damping) is particularly simple in pneumatic systems. The authors have proposed, modeled, analyzed, validated and tested a pneumatic suspension (composed of an air spring, an auxiliary tank and several connecting pipes) the transfer function of which can be modified simply by routing the air flow through the desired pipe. The method has been successfully tested in the case of unbalanced machinery. Procedures to estimate the input frequency have also been proposed for more general cases, but the question remains as to whether the adaptive scheme could be useful in the case of random excitations composed of a sizable range of frequencies. The focus of the work presented in this paper is to shed some light on this question. To this end, a suspension prototype is subjected to random inputs where the frequency content is tuned to increase the relative ‘weight’ of low frequencies, high frequencies or intermediate frequencies. The responses obtained using three different passive configurations, as well as an adaptive approach that can continuously choose among all three, are simulated, tested and compared. It will be shown that adaptation can minimize the root mean square displacement of the random response even in cases where there is significant overlap in the frequency content of the different types of input.
The utilization of structural control systems for alleviating the responses of civil engineering structures, under the effects of different kinds of dynamics loadings, has become a standard technology, although there are still numerous research approaches for advancing the effectiveness of these methodologies. The aim of this article is to review the state-of-the-art technologies in structural control systems by introducing a general literature review for all types of vibrations control systems that have appeared up to now. These systems can be classified into four main groups: (a) passive; (b) semi-active; (c) active; and (d) hybrid systems, based on their operational mechanisms. A brief description of each of these main groups and their subgroups, with their corresponding advantages and disadvantages, is also given. This article will conclude by providing an overview of some innovative practical implementations of devices that are able to demonstrate the potential and future direction of structural control systems in civil engineering.
We present a frequency-domain method to measure angular speeds using electrostatic micro-electro-mechanical system actuators. Towards this end, we study a single-axis gyroscope made of a micro-cantilever and a proof-mass coupled to two fixed electrodes. The gyroscope possesses two orthogonal axes of symmetry and identical flexural mode shapes along these axes. We develop the equations of motion describing the coupled bending modes in the presence of electrostatic and Coriolis forces. Furthermore, we derive a consistent closed-form higher-order expression for the natural frequencies of the coupled flexural modes. The closed-form expression is verified by comparing its results to those obtained from numerical integration of the equations of motion. We find that rotations around the beam axis couple each pair of identical bending modes to produce a pair of global modes. They also split their common natural frequency into a pair of closely spaced natural frequencies. We propose the use of the difference between this pair of frequencies, which is linearly proportional to the speed of rotation around the beam axis, as a detector for the angular speed.
In constructing a three-dimensional fractional derivative model for viscoelastic materials, difference of interpretation of strain in the fractional derivative results in many types of nonlinear models. In this paper, some nonlinear models are compared with experimental results of a polymer gel. In the experiment a weight was collided in the vertical direction on the upper free surface of a cylindrically shaped gel with the bottom side fixed. Then, the acceleration and the displacement of the contact surface between the weight and the gel are observed. In the models, deformation of the gel is approximated by the uniaxial compression of incompressible materials. Each model considered in this paper reproduces well the acceleration data in the early stage. However, differences between the calculated responses among the models begin to appear around the maximum point of the acceleration when the compression speed slows down. It is shown that incompressible models based on the weakly compressible approximations give good fits.
Higher order cumulant (HOC) is a new theory and method of modern signal analysis. Empirical mode decomposition (EMD) is a new time-frequency analysis method for analysis of non-stationary and nonlinear processes. This paper discusses the characteristics of both HOC and EMD, investigates their related technology and advantage in the process of dealing with nonlinear coupling characteristics of random and non-stationary signals. Then through combining with the merits of HOC and EMD, it proposes a new method for multi-damage feature extraction and fault diagnosis of gear systems. For restraining system noise and extracting the fault features of signals, the acquired signal is decomposed into a three-layer signal which has different frequency bands, and then every layer is given to a HOC analysis. Six kinds of signal are analyzed including signal without fault, signal with tooth root short crack, signal with tooth root long crack, signal with pitch circle short crack, signal with pitch circle long crack and signal with tooth wear, which were acquired at four different speeds: 300 r/min, 900 r/min, 1200 r/min and 1500 r/min. The results demonstrate that this method not only can be used to identify various faults (including multi-fault) in the low-speed and high-speed running conditions, but can also be used to identify the damage level of some faults. On this basis, combining the advantages of MATLAB and Visual C++ (VC++), a virtual instrument (VI) system of gear damage detection and diagnosis is developed through a mixed programming method. The interface is designed with VC++, the calculation of test data, signal processing and graphical display are completed by MATLAB. Using COM module technology, it calls the *.m file conversion program in VC++. A different kind and multifunctional gear fault diagnosis software system is successfully empoldered, which possesses some functions, including the introduction of gear vibration signals, signal processing, feature extraction, graphics display, fault detection and diagnosis. The system can be used to detect damage and diagnose faults in gear systems as proven by the results of the validation testing.
This paper analyzes the chaotic phenomenon of a permanent magnet synchronous motor (PMSM) when it is turned off and what effect research parameters of PMSM have on chaos in the PMSM. Linear feedback controller is designed based on the inverse optimal control method. This method is simple and avoids a great amount of computation. In theory, a chaotic system can be asymptotically stable to zero by the controller. Numerical simulations further test the effectiveness of the theoretical analysis.
The condition monitoring and fault diagnosis of rolling element bearings play an important role in the safe and reliable operation of rotating machinery. Feature extraction based on vibration signals is an effective means to identify the operating condition of rolling element bearings. Methods based on multi-scale mathematical morphology (MM) have recently been developed to extract features from one-dimensional (1-D) signals. In this paper, a new double-dot structuring element (SE) is constructed for multi-scale MM. A pattern spectrum, obtained from the multi-scale MM, is used as a feature extraction index. A correlation analysis gives the final identification result by utilizing information over a whole pattern spectrum. Compared with the most commonly used flat SE, the double-dot SE can extract more features of original signals at different scales. Vibration signals, measured from defective bearings with outer race faults, inner race faults and ball faults, are used to evaluate the fault detection ability of the proposed SE and bearing fault diagnosis method. Results show that faults at different levels can be identified, including ball fault; and the location of outer race fault can also be differentiated.
Planetary gearboxes are widely used in aerospace, automotive and heavy industrial applications that require compactness and high torque-to-weight ratios. Despite these advantages, tough operation conditions under which planetary gearboxes are typically used may lead to damage on their key components, for example, gears and bearings. Because of the unique behaviors of planetary gearboxes significantly different from fixed-axis gearboxes, the diagnostic features developed and working well for fixed-axis gearboxes will degrade when applied to planetary gearboxes. Therefore, there is a demand to develop features specifically for monitoring and diagnosing planetary gearboxes. To meet this demand, this paper proposes two features, namely, accumulative amplitudes of carrier orders (AACO) and energy ratio based on difference spectra (ERDS). The effectiveness of the proposed features is demonstrated using the vibration data acquired from a planetary gearbox test rig. The vibration data is measured under different motor speeds and various types of faults on gears and bearings. The proposed features are also compared with those reported in the literature. The comparison results show that the proposed features are more successful than others in monitoring and diagnosing planetary gearboxes.
The main aim of this paper is to introduce the operational matrices of integral and fractional integral using the flatlet oblique multiwavelets. The operational matrices of integral and fractional integrals for flatlet scaling functions and wavelets are presented and are utilized to reduce the solution of the Abel integral equations of the first and the second kinds to the solution of algebraic equations. The main characteristic behind our approach in using this technique is that only a small number of flatlet oblique multiwavelets is needed to obtain a satisfactory result. Illustrative examples reveal that the present method is very effective and convenient.
In this paper, analytical solutions for complex period-1 motions in a periodically forced, quadratic nonlinear oscillator are presented through the Fourier series solutions with finite harmonic terms, and the corresponding stability and bifurcation analyses of the corresponding period-1 motions are carried out. Many branches of complex period-1 motions in such a quadratic nonlinear oscillator are discovered and the period-1 motion patterns changes with parameters are presented. The parameter map for excitation amplitude and frequency is developed for different complex period-1 motions. For small excitation frequency, the period-1 motion becomes more complicated. For a better understanding of complex period-1 motions in such a quadratic nonlinear oscillator, trajectories and amplitude spectrums are illustrated numerically. From stability and bifurcations analysis of the period-1 motion, the analytical bifurcation trees of period-1 motions to chaos need to be further investigated.
The internal friction associated with the shaft hysteresis or with the possible release of some shrink-fit coupling exerts a destabilizing effect on the over-critical rotor running, but may be efficiently counteracted by other external dissipative sources or by a proper anisotropic configuration of the support stiffness. The present analysis considers a symmetric rotor-shaft system on viscous-flexible supports with different stiffness on two orthogonal planes containing the bearing axis. The internal friction of the shaft is described either by a linear hysteretic model or by a nonlinear Coulombian force contrasting the rotor motion relative to the shaft ends. The nonlinear equations of motion are solved using an averaging approach of the Krylov–Bogoliubov type, which yields the steady orbit depending on the support dissipation applied to damp the whirl motion, for various working conditions. The beneficial influence of the support stiffness anisotropy is clearly identified.
The dynamic reliability of the pipe conveying fluid was analyzed by a refined response surface method (RSM) in this study. In the refined RSM, a new response surface expression was proposed based on functional variables with the physical characteristics of basic random variables. The sampling points were located on Gauss Hermite integration points along the coordinate axes of standard normal random variables. The response surface was constituted via an iterative strategy, in which the information of the sampling points could be utilized richly. On the other hand, Hamilton’s principle for open systems was applied to formulate the motion equations of the pipe conveying non-uniform axial fluid. The proposed RSM was used to analyze the dynamic reliability and sensitivity of the pipe conveying non-uniform axial fluid. As shown in the numerical results, the refined response surface method leads to the better approximation of the nonlinear limit state function, higher precision and better stability of the failure probability estimation, especially for the dynamic reliability analysis of the pipe conveying fluid.
The direct torque control (DTC) technique of a permanent magnet synchronous motor (PMSM) has received increasing attention due to its simplicity and robust dynamic response compared with other control techniques. The classical switching table based DTC presents large flux, torque ripples and more mechanical vibrations in the motor. Several studies have been reported in the literature on classical DTC. However, the studies that actually discuss or evaluate the classical DTC are limited. This paper proposes, an alternative DTC method/switching table for PMSM, to reduce flux and torque ripples as well as mechanical vibrations. This is achieved by a simple modification in the classical DTC structure, by eliminating the two level inverter available in the classical DTC and replacing it with a three level neutral point clamped inverter. To further improve the performance of the proposed DTC, the available 27 voltage vectors are allowed to form different groups of voltage vectors such as Large - Zero, Medium - Zero and Small - Zero. Based on these groups, a new switching table is proposed. The proposed DTC is compared with the classical DTC and existing literature from the aspects of theory analysis and computer simulations. It can be observed that the proposed technique can significantly reduce the flux, torque ripples, and mechanical vibrations and improves the quality of current waveform compared with traditional and existing methods.
A dynamic vibration absorber (DVA) can be used as an effective vibration control device. It is essentially a secondary mass, attached to an original system via a spring and damper. The natural frequency of the DVA is tuned such that it coincides with the frequency of unwanted vibration in the original system. This results in absorption of the inertial energy transferred from the primary structure. This work aims at developing an adaptive-passive dynamic vibration absorber with the help of shape memory alloy (SMA) springs in order to attenuate the vibration for a range of excitation frequencies. In this paper, the unique property of SMAs temperature-dependent Young’s modulus has been used to change the stiffness of the spring actively to control the vibration. Experiments were carried out with an SMA-based dynamic vibration absorber to study the effect of reduction in amplitude of vibration of a cantilever structure. A microcontroller-based control system has been developed for timely actuation of SMA and to supply optimum current to the SMA springs connected in parallel. The experimental results show that the SMA-based dynamic vibration absorber is more effective in reducing the amplitude of vibration for a wider frequency range. The developed SMA-based DVA is used to damp out the vibration in piping applications. The effectiveness of adaptive-passive DVA in controlling the vibration for a range of excitation frequencies was proved.
In this paper, an adaptive backstepping sliding mode control approach is proposed to control the MEMS triaxial gyroscope. An adaptive backstepping controller that can compensate the system nonlinearities is incorporated into the sliding mode control scheme in the Lyapunov framework. First, a robust backstepping control system incorporated with sliding mode control technique is designed. Then, an adaptive law is derived to estimate the upper bound value of the lumped uncertainty in the backstepping sliding mode control. With the adaptive backstepping sliding mode controller, the chattering in control efforts can be obviously reduced. Numerical simulation is provided to verify the effectiveness of the proposed scheme.
This paper addresses the fractional sliding mode control of MIMO nonlinear noncommensurable plants, which does not seem to have been covered until this moment in the literature on fractional sliding mode control. It includes simulation results to confirm the feasibility of the solution presented.
Electrorheological fluids (ERFs) offer a rapid control of damping using very low power requirements. Different models have been proposed to simulate the hysteresis phenomenon observed experimentally in ERF. This paper describes the steps to be taken to extract measurements of an ERF in squeeze and shear mode. A novel modular test facility was designed to perform measurements of a specific ERF in squeeze and shear mode. This device allows the measurement of the dynamic response of the fluid under various excitation conditions. Dense measurement grids of fluid force and electrode displacement at harmonic excitation are collected in dependency of the excitation frequency, the displacement amplitude and the applied electric field. The main problems to be solved during the setup and execution of the measurements are discussed. The steps to be taken during signal processing to achieve high-quality measurements as inputs for material model fitting are described in detail. Example measurements for both squeeze and shear mode are presented. The fitting of the obtained results to a material model for ERF and discussion of the resulting extended Bouc–Wen model will be the topic of an accompanying paper.
In this paper, an adaptive controller is developed to suppress chaos and track the desired speed in an uncertain chaotic permanent magnet synchronous motor (PMSM) drive system. The controller consists of computational and supervisory control schemes. The computational controller, based on fuzzy neural networks, is used to approximate the unknown nonlinear control signal, while the supervisory controller is employed to attenuate the approximation error effects of the neural network and ensure the system is robust. Simulation results demonstrate that the proposed controller can successfully quash chaotic oscillation in a PMSM and allow speeds to follow the desired trajectory despite the existence of uncertainties.
This paper is concerned with iterative solutions to the generalized Sylvester matrix equation A1 V + A2 V + B1 W + B2 W = E1 VF1 + E2 VF2 + C. Two iterative algorithms are presented to obtain the reflexive and Hermitian reflexive solutions. With these iterative algorithms, for any initial reflexive and Hermitian reflexive matrices the solutions can be obtained. Some needed lemmas are first stated, then two theorems are stated and proved where the iterative solutions are obtained. Finally, we report two numerical examples to verify the theoretical results.
This study presents the application of vibration analysis in the determination of elastic constants (i.e. Young’s modulus in fiber direction, transverse Young’s modulus, and shear modulus) and modal damping ratios of a unidirectional composite beam. The frequency domain approach is used for the estimation of material constants, whereas modal damping ratios are predicted by the use of short-time Fourier transform (STFT). An analytical expression of the STFT for the free vibration response of a viscously damped system has been derived using the Hanning window. Analysis of a simulated vibration for a three-degree-of-freedom system has revealed that the STFT is capable of predicting the modal damping ratios accurately even when they are considerably large. For the experimental assessment of modal damping values of a composite beam, longitudinal, flexural, and torsional vibration responses are analyzed by both the STFT and well-known Q-factor approximation, and the obtained results show very good agreement.
Brushless direct current (BLDC) motors have advantages viz. high torque per weight, high torque per watt, increased reliability, reduced noise and a longer lifetime. A BLDC motor is an electronically commutated motor. Electronic commutation is sparkless because it does not involve any mechanical commutator and brush. It also eliminates electromagnetic interference. Because of these advantages, BLDC motors can also be used in hazardous environments. They find wide applications in industrial positioning and actuation. The wider usage of BLDC motors demands optimum position control in such applications for high efficiency, accuracy and reliability. A first order compensated BLDC drive is proposed in this paper to achieve effective position control. Simulation results at different loads clearly reveal that the proposed first order compensated BLDC drive system could yield comparable results with a proportional integral derivative controlled BLDC drive system. A proposed first order compensator is designed using analog components and the experimental results of compensated BLDC drive system are obtained to show the usefulness of the compensator for effective position control.
This paper deals with the problem of sliding mode control to achieve chaotic synchronization for the controlled driven system with an input nonlinear term – the term commonly ignored in the published literature. However, the problem does possess importance in practical applications while hardware limits imposed on the actuating devices need to be considered. The major contribution here is the development of a new adaptive control scheme instead of directly computing the magnitudes of overall nonlinear dynamics for compensation as that commonly adopted in the published literature. In the influence of control input nonlinearity, the adaptive sliding mode control scheme, possessing time-varying feedback gains, can compensate unmatched nonlinear dynamics without knowing their magnitudes. In addition, it is unnecessary to determine these time-varying feedback gains in advance but apply adaptive tuning according to suitably updated rules. Based on the Lyapunov stability analysis, a new condition ensuring stable synchronization is established. Case study and numerical simulations are given to verify effectiveness of the presented scheme.
An isolation system is not very effective when an inappropriate level of damping is used. This paper proposes a theoretical method which can be used to determine the optimal frictional coefficient of an isolation system. Only a one-dimensional isolation system and ground motion are considered. The frictional coefficient is optimized by minimizing the sum of squares of structural absolute accelerations, with the optimization results being validated graphically. Sensitivity studies were used to verify the feasibility of the optimal frictional coefficient, coupled with a practical example in Taipei under the conditions of the Hualien and El Centro earthquakes. Consequently, the feasibility and reliability of the proposed optimal design were verified.
In this paper an integrated circuit (IC) design of the fractional order proportional-integral-derivative (PID) controller is proposed. The development of the IC device is realized in Cadence environment, using the switched capacitors (SC) technology in order to reduce the area on the silicon wafer and to improve the electrical controllability. In order to obtain transfer functions that describe the fractional order of the differ-integral operator it is necessary to use interpolation methods, in particular, the choice in this work has fallen on the Oustaloup interpolation. This procedure is aimed at implementing a series of pole-zero blocks that approximate the non-integer order. The realized approach is able to guarantee a good approximation of the fractional order PID and simultaneously propose a detailed circuit analysis of the influence of the non-idealities, in particular the phenomenon of warping. This takes into account the distortion introduced by the s-domain to the z-domain transition, acting on the positions of poles and zeros, especially those at a higher frequency. Time and frequency domain result tests confirm the feasibility and reliability of the SC implementation.
This paper presents an improved fuzzy logic controller (FLC) for a permanent magnet synchronous motor (PMSM) for high performance industrial drive applications. The performance of the PMSM using proportional plus integral (PI) controllers and general fuzzy controllers are poor under load disturbances and transient conditions. The FLC is developed to have a smaller computational burden which makes it suitable for real time implementation, particularly at constant speed operating conditions. Hybrid control has the advantage of integrating a superiority of two or more control techniques for better control performances. A fuzzy controller offers better speed responses for startup and large speed errors. If the nature of the load torque is varied, the steady state speed error of the PMSM drive with an FLC becomes significant. To enhance the performance of the system, a new control method, hybrid fuzzy PI control and accelerated fuzzy PI control is proposed. The effectiveness of the proposed method is verified by a simulation based on MATLAB. The proposed hybrid fuzzy controller has good adaptability over load toque variation and can maintain constant speed.
Through the theoretical analysis and experiments on the test, the levitation control system stability of the MAGLEV vehicle on elastic track was investigated. Firstly, taking the single magnet coupled with elastic track as the object, the corresponding mathematical model and the real-time test platform based on dSPACE were founded. Secondly, two kinds of the state feedback controllers were developed based on Kalman filters, and their influences on the stability of the MAGLEV system were investigated, respectively. The research results show that, if the track has no damping, the controller treating the tracks as fixed cannot make the MAGLEV system steady. However a harder track stiffness enables the system, with a certain track damping, to stabilize. The control method considering the track’s flexibility can soundly maintain the system’s stability even if the track has a relatively soft stiffness and no damping effect. The tests on the real-time test platform verified the effectiveness of the latter control method.
In the first part of this paper, the theoretical and simulation analyses have been studied to prove the effectiveness of the pounding tuned mass damper (PTMD) to control the vibration of a traffic signal pole. In order to further verify the control effect of the PTMD, an experimental structure was prepared to test the novel approach in the lab. A horizontal and a vertical steel pipe are used to model the traffic signal pole. An L-shaped beam and a pounding collar covered on the interior with viscoelastic materials are used as the PTMD device. Both free and excited vibration tests were performed with and without PTMD control on the structure. It was found that the damping device was very effective in controlling the vibrations of the structure in both out-plane and in-plane vibrations.
In this paper, reflection and refraction phenomena are studied for a three-dimensional plane quasi-P wave incident at the interface between distinct triclinic half spaces. A method has been developed to find the analytical expressions of all the phase velocities of reflected and transmitted quasi-P (qP), quasi-SV (qSV), and quasi-SH (qSH) waves. Closed form expressions for the amplitude ratios of reflection and transmission coefficients of qP, qSV, and qSH waves are also obtained. These expressions are computed numerically for a given set of data and the velocity distributions and variation of reflection and transmission coefficients with polar and azimuthal angle of incidence are shown graphically using two-dimensional single and double axes graphs. Surface plots of velocity variations of different reflected and transmitted waves are drawn to analyze the combined effect of incident polar and azimuthal angle on velocity distribution. Numerical results presented indicate that anisotropy effects on the reflection and transmission coefficients are significantly different in the three-dimensional case compared to the two-dimensional case. Certain published work has been derived as special cases to illustrate the present technique. Software in MATLAB has been designed to analyze the reflection/transmission phenomena with present geometry in simpler elastic media, such as monoclinic, transversely isotropic, isotropic, etc.
In this paper an analytical, exact procedure for the reconstruction of simply supported bending vibrating beams having given values of the first N natural frequencies is presented. The results hold for beams in which the product between the bending stiffness and the linear mass density is constant. The analysis is based on the fact that this class of beams is spectrally equivalent to a family of strings fixed at the ends, and uses recent results on the exact construction of second-order Sturm–Liouville operators with prescribed natural frequencies. The analysis can be adapted to beams with pinned–sliding and sliding–sliding ends.
Rotor imbalance causes undesirable synchronous vibrations of displacement, force and torque. An active vibration control (AVC) method achieving the minimum vibration force and torque within a desired vibration displacement is presented in an active magnetic bearing (AMB) system. First, the dynamics of the AMB system with static imbalance and dynamic imbalance are introduced, and the dimensional displacement relationships of the rotation, geometric and inertial axes of the rotor are described. Demands of the AVC are analyzed, and the results indicate that the rotation axis has to be controlled to move along the center line and the inclination direction of the geometric axis and the inertial axis, respectively. Then the synchronous vibration displacement is identified with a general notch filter, and a feedforward controller is designed to control the rotation axis by providing a synchronous control current. A gain phase modifier (GPM) is proposed to achieve a precise synchronous control current and to compensate the gain and phase errors caused by the power amplifier. The GPM is incorporated into the feedforward controller to formulate two closed loops, which can adaptively tune the gain and phase of the synchronous control current, respectively. Finally, simulations and experiments have been carried out to indicate the effectiveness of the proposed approach, which can be widely used since vibrations of displacement, force and torque can be controlled simultaneously to satisfy various requirements.
This paper presents a first proposal to investigate the nonlinear dynamic response of imperfect symmetric thin sigmoid-functionally graded material (S-FGM) plate resting on an elastic foundation and subjected to mechanical loads. The formulations use classical plate theory taking into account geometrical nonlinearity, initial geometrical imperfection of the S-FGM plate and stress function. The volume fractions of metal and ceramic are applied by sigmoid-law distribution (S-FGM) with metal-ceramic-metal layers. The nonlinear equations are solved by the Runge-Kutta and Bubnov-Galerkin methods using stress function. The obtained results show the effects of material, imperfection and elastic foundations on the dynamical response of S-FGM plate.
The nonlinear vibration of a two-dimensional composite laminated plate in subsonic air flow with simply supported boundary conditions is investigated. Based on the von Karman’s plate theory, the equation of motion of the plate is established using Hamilton’s principle. The aerodynamic pressure induced by the coupled vibration of the plate and subsonic airflow is derived from the linear potential flow theory and compared with the existing model. The variable separation method is used to transform the equation of motion of the plate into nonlinear ordinary differential equations. The influences of the flow velocity, the length-to-thickness ratio and the ply angle of the plate on the nonlinear vibration behaviors of the plate are discussed. From the analytical and numerical results it can be seen that the critical instability velocity obtained from the present aerodynamic model is the same as the existing result. The first-order expansion of the transverse displacement can reflect the dynamic characteristics of the plate. With the increase of the flow velocity and the length-to-thickness ratio, the instability interval of the nonlinear vibration can be prolonged and the nonlinear resonance frequency can be increased. The composite laminated plate with smaller ply angle exhibits more stable dynamic properties than that with larger ply angles.
High-powered embedded computing equipment using air transport rack (ATR) form-factors are playing an ever-increasing role in critical military applications in air, land and sea environments. High power and wattage of the electronics and processors require large heat dissipation, and thus more sophisticated and efficient thermal cooling systems such as loop heat pipes or jet impingement systems are demanded. However, these thermal solutions are more susceptible to harsh military environments and thus, for proper performance of thermal and electronic equipment, they need to be protected against shock and vibration inherent in harsh environments like those in military applications. In this paper, an isolated ATR chassis including two jet impingement chambers is modeled as a three-degrees-of-freedom system and its response to random vibration and shock has been studied. Both finite element and experimental modal analysis is utilized to characterize dynamics of the components of the jet impingement system. The response of the model is compared to that of the traditional single-degree-of-freedom model, and the isolation system is optimized in terms of its damping.
In this article the fuzzy logic based closed loop chopper controlled permanent magnet DC motor drive is proposed for orthopedic surgical simulators. The proposed drive consists of an inner current control loop and an outer speed control loop. The fuzzy technique is used in the speed loop and the system is simulated using Matlab/Simulink. The steady state and transient state responses of the proposed fuzzy system are compared with conventional PI controlled system. The comparative analysis infers that the fuzzy system provides better performance.
Based on a step-by-step decoupling method, an inverse substructuring method is developed for the analysis of the dynamic characteristics of a single-coordinate coupled three-substructure system. The closed-form analytical solution to inverse substructuring analysis of the system is derived. The proposed method is validated by a lumped mass-spring-damper model, the predicted frequency response functions (FRFs) of substructures and the coupling stiffness; in addition, the most relevant system-level FRFs are compared with the direct computations, showing exact agreement. Finally, the sensitivity of the proposed method to measurement error is studied. The method developed offers an approach to extract the unknown substructure-level FRFs and coupling stiffness from system-level FRFs purely for single-coordinate coupled substructures.
The rolling element bearing is among the most frequently encountered component in a rotating machine. Bearing fault can cause machinery breakdown and lead to productivity loss. A bearing fault diagnosis method has been proposed based on multi-scale permutation entropy (MPE) and adaptive neuro fuzzy classifier (ANFC). In this paper, MPE is applied for feature extraction to reduce the complexity of the feature vector. Extracted features are given input to the ANFC for an automated fault diagnosis procedure. Vibration signals are captured for healthy and faulty bearings. Experiment results pointed out that proposed method is a reliable approach for automated fault diagnosis. Thus, this approach has potential in diagnosis of incipient bearing faults.
We propose an efficient method to study the (two-dimensional) in-plane nonstationary (transient) problem for a rigid rectangular structure above the oscillating foundation. A massive structure is perfectly coupled with the foundation, whose oscillations are caused by an oblique plane seismic wave incoming from below to the boundary surface. The structure is assumed to be considerably more rigid than the foundation. The mathematical formulation admits application of the Laplace transform over time and Fourier transform along the horizontal coordinate. By satisfying the boundary conditions over the contact zone between the rectangle and the foundation, the problem is reduced to a system of two integral equations for normal and tangential contact stress, which contain the Laplace parameter. To solve this system, we apply a numerical method to arising Volterrà–Fredholm integral equations. Then the dynamic properties of the structure is studied for various combinations of physical and geometrical parameters.
A multi-level partial blocks excitation system was proposed to meet the special requirement of vibration equipment. The dynamic mechanical model was analyzed using Lagrange equations to obtain angular displacement equations of higher level partial block. The instantaneous vibration intensity and amplitude were also found. The simulation test was performed using MATLAB in order to obtain the motion curves, phase-trajectory and Poincare maps of higher level partial block. Due to the fact that the existence of the initial sensitivity, nonrepeatability and complexity of the phase trajectory, and flake points set and many discrete points in Poincare maps, the vibration system exhibited many characteristics of chaotic vibration. It was found that the chaotic excitation system with a strongly nonlinear and wide frequency band could achieve some special exciting vibration properties, such as intermittent high vibration intensity, transient super-high vibration intensity and large vibrating amplitude. Based on these analyses, the vibration mill was developed. The research showed that these measured vibration intensity K - t and amplitude A - t curves were consistent with theoretical analysis and the simulation of the motion curves, phase-trajectory and Poincare maps. In the field of vibration engineering, the special inertial properties are important to overcome work barriers and solve current technological bottlenecks.
In a shrink-fitted joint, the interface pressure plays an important role as it is the main source of the joint and it keeps the joining components together. However, time-variation of the interface pressure causes parametric instability in the system. In this paper, the effect of time-variant interface pressure on the dynamics of two shrink-fitted rings has been studied. Deriving a dynamic equation of motion of the joint of two shrink-fitted rings and substituting time-variant interface pressure in the equation, the problem extends to nonlinear vibration. The obtained equation of motion, which contains parametrically excited terms, is a general form of Mathieu’s equation. A perturbation method, to determine the instability regions of motion, is applied to obtain the transition curves. To validate the obtained stability regions, an experiment has been performed. Both the analytical and experimental results demonstrate that by increasing the value of the interface pressure, the natural frequencies of the joint increase.
A C0 finite element (FE) formulation based on higher order shear deformation theory (HSDT) is developed for free vibration analysis of composite skew cylindrical shells. The problem of C1 continuity associated with the HSDT has been overcome quite efficiently in the present FE model. The curved isoparametric element used in the model consists of nine nodes with seven nodal unknowns per node. Use of shear correction factor is avoided by assuming a realistic parabolic variation of transverse shear strain through the shell thickness. The transverse shear stresses are taken as zero at the shell top and bottom. Sander’s approximations are considered in the FE formulation to include the effect of three curvature terms in the strain components of composite shells. Since there is no result available in the literature on the problem of skew composite cylindrical shell based on HSDT, the present results are validated with some results available on composite plates/shells. Many new results are presented on free vibration response of laminated composite skew cylindrical shells considering different geometry, boundary conditions, ply orientation and skew angles.
A maximum principle is derived for the optimal control of a beam with Kelvin–Voigt damping subject to an external excitation with the control exercised by means of piezoelectric patch actuators. The objective functional is defined as a weighted quadratic functional of the displacement and velocity which is to be minimized at a given terminal time. A penalty term is also part of the objective functional defined as the control voltage used in the control process. The maximum principle makes use of a Hamiltonian defined in terms of an adjoint variable and the control function. The optimal control problem is expressed as a coupled system of partial differential equations in terms of state, adjoint and control variables subject to boundary, initial and terminal conditions. The solution is obtained by expanding the state and adjoint variables in terms of eigenfunctions and determining the optimal control using the maximum principle. Numerical examples are given to demonstrate the applicability and the efficiency of the proposed method.
This paper deals with the study of the parametric instability characteristics of delaminated composite plates subjected to periodic in-plane load. A first order shear deformation theory (FSDT) based on finite element method (FEM) is developed for studying the instability region of mid-plane delaminated composite plate. A detailed parametric investigation is carried out to study the influence of the delamination area, number of layers, degree of orthotropy, aspect ratio and static in-plane load on the dynamic stability characteristics of delaminated cross-ply plates. The results of vibration and buckling of delaminated composite plates are compared with previous numerical studies in the literature and the authors’ experimental investigations. The boundaries of instability regions are obtained by using Bolotin’s method and are represented in the non-dimensional load amplitude-excitation frequency plane. It is observed that the natural frequencies and the critical buckling load of the plates decrease with an increase in delamination size. The increase in delamination size also causes dynamic instability regions to be shifted to lower excitation frequencies.
This paper presents the experimental results of online self-tuning pole placement control for active vibration of a flexible beam. The vibration is controlled using a piezoelectric actuator bonded on a flexible beam. An online computer control that runs on a PC-based control and its graphical user interface have been developed in such a way that the user can perform online monitoring and manipulation of control parameters of the active vibration control algorithm for a flexible beam system. The parameters of the pole placement controller have been self-tuned based on autoregression with an exogenous terms model of a bonded piezoelectric actuator beam identified via a recursive least square algorithm. A PC-based control system was implemented using a peripheral component interconnect data acquisition card and LABVIEW software. Results show that the online self-tuning pole placement control offers better transient performance over the fixed controller when tested at different tip loads. The control parameters have converged to a new value as the physical parameter of a flexible beam is changed.
This paper deals with a sliding mode control for a class of fractional uncertain chaotic systems under perturbations of parameters. A fractional integral (FI) sliding surface is proposed for fractional-order systems and then the sliding mode control technique is carried out to realize the control of the given systems. Based on Lyapunov stability theory, we theoretically verify that the controller is effective, and the designed control scheme can go against the system’s uncertainty to guarantee the property of asymptotical stability in the presence of parameter fluctuations. Later, two typical examples are illustrated numerically to show that the control approach in this paper is capable for any form of fractional-order uncertain systems.
Shaft/bearing rubbing systems may undertake a number of quite different responses. Recent experiments on shaft/bearing rubbing have revealed that two or three different responses may exist under the same frequency ratio with different initial conditions and system parameters. In the present paper, the rubber bearing/shaft system is simplified into a general bearing/shaft system with nonlinear elastic support of bearing, which is established based on the classic impact theory and is analyzed by the modern nonlinear dynamics and bifurcation theories. The boundaries for the existence of the no-rub responses are determined analytically, and the synchronous full annular rub solution are derived and the stability is analyzed to determine the region of the synchronous full annular rub response. The results provide an opportunity for a better understanding of the dynamical characteristics, such as the synchronous full annular rub motion, the jump phenomena as well as the transition between the partial rub motion, the dry whip and the full annular periodic rub motion. A systematic study on the influence of the system parameters on the dynamics characteristics is carried out. An overall picture of the response characteristics of this model is then obtained by drawing the existence boundaries in the parameter space. The present results provide a good understanding of the relationship between the different rubbing responses and the system parameters.
To optimize the trajectories of the sun tracking system, the dual-axis sun tracking control method for a photovoltaic power system is discussed in this paper. The optimization goal is maximization of an electric energy production in the photovoltaic system considering the tracking system’s consumption. Firstly, the elevation angle and azimuth angle trajectories are described as a nonlinear and bounded optimization problem. Then the predictable trajectories of elevation angle and azimuth angle are derived by using the known formulas and knowledge. However, many factors affect the tracking trajectories, such as machine accuracy, formula error, the partial shading due to the shadow of clouds, trees, birds, dirt, and buildings, etc. Firstly, a novel system structure is introduced to improve the electrical energy consumption. Then, the perturbation and observation (P&O) control method is proposed to improve the tracking trajectories by decreasing the errors of machine and formula by combining with the conventional predicted method. The tracking efficiency of the dual-axis sun tracking system using the predicted method is compared with that using the predicted method combined with the P&O method. The simulation results presented in the paper show that the proposed method has excellent tracking characteristics compared with the fixed title, single-axis tracking, and dual-axis tracking using the single predicted method.
This paper develops intelligent control schemes for a diaphragm-type pneumatic vibration isolation system. The active-control schemes are applied to the pneumatic isolator to enhance isolation performances in the low-frequency range where passive techniques usually have difficulties in remaining effective, especially at the resonance frequency. The functional approximation technique (FAT) is integrated with a sliding-mode control (SMC) design to capture unknown system dynamics and release the requirement of mathematical modeling. To deal with approximation error and system dynamics variation, an adaptive fuzzy sliding-mode controller (AFSMC) is employed as a compensator of the FAT-based SMC. Lyapunov stability theory is used not only to ensure the closed-loop stability, but also to formulate the updating laws for weighting coefficients of expansion basis and fuzzy tuning parameters. To validate the proposed method, a composite control scheme using pressure and velocity measurements as feedback signals is implemented. Experimental explorations indicate that isolation performances obtained using the proposed FAT-based sliding control augmented with AFSMC compensation (FA + AFSMC) are evidently better than those of the traditional proportional integral-derivative control and solely AFSMC scheme.
A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies of hemi-ellipsoidal shells of revolution with eccentricity having uniform thickness. Unlike conventional shell theories, which are mathematically two-dimensional, the present method is based upon the 3-D dynamic equations of elasticity. Displacement components ur, u, and uz in the radial, circumferential, and axial directions, respectively, are taken to be periodic in and in time, and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the hemi-ellipsoidal shells of revolution with eccentricity are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to three or four-digit exactitude is demonstrated for the first five frequencies of the shells of revolution. Numerical results are presented for a variety of hemi-ellipsoidal shells of revolution with eccentricity.
A compound track-absorber model with multiple wheels on the rail is employed to study the effects of a rail absorber on the normal wheel–rail contact forces in the frequency domain. Two different absorber models, which are the piecewise continuous absorber and the discrete absorber installed in the middle of the sleeper span, are presented. It can be seen from the calculation results that there are more peaks occurring in the frequency range of 500–1200 Hz due to the wave reflections between the wheels than that of a single wheel–rail interaction. However, these peaks are all suppressed due to the effects of the rail absorber, and there are new peaks appearing at other frequencies while the amplitude of these peaks is relatively small. The peaks in contact force at low frequencies are higher, whereas the peak at pinned-pinned resonance is suppressed.
The sunbeam can be converted into electricity via photovoltaic solar cells, and sun trackers are such devices for efficiency improvement. In this paper, different types of sun-tracking systems are reviewed, such as fixed tilt-angle, dual-axis, single-axis with East-West direction, and single-axis with North-South direction. The captured irradiation using different sun trackers are compared, and different influence factors are analyzed to gain the optimal orientation of the sun, such as time error, latitude, azimuth angle and tilt-angle of a photovoltaic module, reflectivity, and composite transparent coefficient. These results are very important to improve the tracking efficiency of the sun tracker.
Fluid viscous dampers have been widely applied to reduce the effects of vibrations in civil engineering structures. A good understanding of the dynamical behavior of these devices is required to analyze structures equipped with fluid viscous dampers. The simple Kelvin–Voigt and Maxwell rheological models do not have enough parameters to suitably capture the frequency dependence of device parameters, so other models representing some generalizations of the basic Kelvin–Voigt and Maxwell models have been developed. This paper deals with parameter identification for basic and generalized Kelvin–Voigt and Maxwell models for fluid viscous dampers. The identification procedure gives the best mechanical parameters by minimizing a suitable objective function that represents a measure of difference between analytical and experimental applied forces. For this purpose, the particle swarm optimization is adopted. Results are obtained under various test conditions, comparing the agreement of various models with experimental data. Finally, a numerical investigation is performed on a simple one degree of freedom structure, equipped with fluid viscous dampers and subject to a real seismic motion.
This paper deals with frequency optimization of symmetrically laminated angle-ply annular sector plates. The design objective is the maximization of the fundamental frequency and the design variable is the fiber orientation in the layers. The first order shear deformation theory is used for the finite element solution of laminates. Nine-node Lagrangian rectangular plate element which have five degrees of freedom per node is used for the finite element solution of the laminated annular sector plates. The modified feasible direction method is used for the optimization routine. For this purpose, a program based on FORTRAN is used. The numerical analysis is carried out to investigate the effects of annularity, boundary conditions and sector angle on the optimal designs and the results are shown in tabular and graphical forms. Finally, the obtained results are compared. It can be shown that the parameters have a key role on the optimum design of laminated annular sector plates.
This paper reports an investigation of the active vibration control of a piezoelectric flexible cantilever plate. The bending and torsional vibration of the flexible plate can be measured and actuated by distributed bonded piezoelectric sensors and actuators, after conducting optimal placement. To suppress the vibration, a kind of composite nonlinear controller is proposed and implemented. The control gain of the developed nonlinear control algorithm can be adjusted according to the measured vibration amplitude and the corresponding parameters. The advantage of the nonlinear controller is the ability to regulate the control value online to suppress both the larger and the smaller amplitude vibrations effectively, without allowing excessive saturation or insufficient phenomenon of the control effect. An experimental setup characterizing a thin, cantilever square plate bonded with piezoelectric patches was developed to verify the proposed controller. Experimental comparison studies were carried out for suppressing both the bending and torsional vibrations, and the control performance of the nonlinear controller is analyzed and discussed. The experimental results demonstrate that significant vibration suppression can be achieved by using the presented control schemes.
Space robots are a kind of coupling system with a rigid body and flexible structures, in which harmonic drive gears are usually used as speed reducers. Thus, the vibration problem is unavoidable due to maneuvering and external disturbances. This paper is concerned with the design and implementation of a fuzzy sliding mode control (FSMC) algorithm and a composite controller to dampen the vibration of a flexible manipulator with a flexible link and a harmonic drive gear (flexible joint). The designed controllers are used to dampen the end-point vibration of the flexible link and flexible joint manipulator, to compensate for unknown and time-varying nonlinear uncertain parameters, such as friction torque and flexible joint characteristics of a harmonic drive gear, etc. The experimental comparison research was conducted, including set-point active vibration control and vibration suppression under resonant excitation. The experimental results demonstrate that the FSMC and the composite algorithms can significantly enhance the performance of vibration suppression for flexible manipulator.
The article presents an aircraft wireless communication (AWC) model that replaces existing indoor wired sensor communication in aircraft with wireless sensor architectures to reduce electrical wiring issues. In the proposed system for radio reception of signals from multiple wireless sensors, the space division multiple access technique escalates the strength of transmission power and condenses electromagnetic signal interference. The performance of proposed AWC model is investigated and validated for safe indoor propagation and enhancement of the overall capacity of the AWC system.
This paper presents the simulation and hardware implementation of a hill-climbing (HC) modified fuzzy-logic (FL) maximum power point tracking (MPPT) control scheme used in photovoltaic (PV) power systems with the direct control method. The conventional HC method is used to improve the FL search method and eliminate their drawbacks. The main difference of the proposed method to the existing MPPT control method includes that it offers fast and accurate tracking to the maximum power point under uniform radiation or partial shading conditions as compared to the conventional FL method, and it eliminates the proportional-integral control loop. Contributions are made in several aspects such as converter design, simulation, controller programming, and experimental setup. Simulation and experimentation results are provided to demonstrate the validity of the proposed hill-climbing modified fuzzy-logic controller.
Influences of system parameters on dynamic behavior of the vehicle shimmy system with consideration of clearance in the steering linkage mechanism are analyzed. The kinematic pair of steering linkage mechanism with clearance between the steering tie rod and left trapezoidal arm is modeled based on Hertz’s law, and a four-degree-of-freedom dynamic model of a vehicle shimmy system with consideration of clearance in the steering linkage mechanism is presented. Based on this model, numerical analysis is carried out, and the influences of the parameters, such as clearance, contact surface stiffness of the kinematic pair, wheel alignment parameters, and vehicle speed on the dynamic response of the vehicle shimmy system are discussed. It is shown that, considering the clearance in the steering linkage mechanism, these parameters can make a coupled contribution to the dynamic response of the vehicle shimmy system, and some effective measurements for vehicle shimmy attenuation are available. The conclusions will provide theoretical basis for effective vehicle shimmy control, especially for vehicles which are in use.
In this paper, the nonlinear dynamical characteristics of the Duffing–van der Pol oscillator subject to both external and parametric excitations with time delayed feedback control are analyzed. Using the multiple scale method, the primary and principal parametric resonances are discussed. Both the periodic and chaos dynamical behaviors are presented by numerical solutions. From the results, it can be seen that the frequency and amplitude responses for the primary and principal parametric resonances can be affected by the time delayed control. Moreover, it is not only the external and parametric excitations that have an influence on the periodic and chaotic motions, but also the control parameters.
This paper considers the optimal placement of actuators for vibration control of tensegrity structures using different control strategies. The problem is formulated as a multi-objective optimization problem where the objective functions are the control energy and the residual or spillover energy which are minimized. The optimization problem is solved by genetic algorithm. The tensegrity structure of class 1 comprising of two modules with three actuators is considered as an example.
This paper investigates the suppression of vibration and noise radiation in a flexible raft system through the use of periodic structure theory. A floating raft isolation system is constructed. The transfer matrix method, the finite element method and periodic structure theory are combined to calculate the dynamic response of the system and the dispersion relations of the periodic structure. The effects of substructure resonances on vibration and noise radiation are analyzed. Next, the periodic isolation structure is used to suppress the vibration and noise radiation in the floating raft system. The isolation performance of the combination of periodic structures and continuous isolators are investigated. Additionally, the influences of the parameters of the floating raft system on vibration and noise are discussed. The numerical results demonstrate that vibration and noise are significantly suppressed in stop bands and are not worsened in pass bands.
This paper deals with the study and comparison of the dynamic response of aircraft with passive and active landing gears due to runway irregularities while the aircraft is taxying. This paper develops a detailed full aircraft mathematical vibration model to describe an active landing gear system. The derived dynamic equations are used to analyze the active landing gear system using proportional integral derivative (PID) controllers. The performance of this system is compared with the passive landing gear system by numerical simulations. The active landing gear system is able to increase the ride comfort and good track holding by reducing the fuselage acceleration, vertical fuselage displacement caused by landing and runway excitations.
A parametric study for post-buckling analysis of an axially moving beam is conducted considering four different axial speeds in the supercritical regime. At critical speed, the trivial equilibrium configuration of this conservative system becomes unstable and the system diverges to a new non-trivial equilibrium configuration via a pitchfork bifurcation. Post-buckling analysis is conducted considering the system undergoing a transverse harmonic excitation. In order to obtain the equations of motion about the buckled state, first the equation of motion about the trivial equilibrium position is obtained and then transformed to the new coordinate, i.e. post-buckling configuration. The equations are then discretized using the Galerkin scheme, resulting in a set of nonlinear ordinary differential equations. Using direct time integration, the global dynamics of the system is obtained and shown by means of bifurcation diagrams of Poincaré maps. Other plots such as time traces, phase-plane diagrams, and Poincaré sections are also presented to analyze the dynamics more precisely.
This paper investigates the performance of an improved fuzzy logic controller (FLC) with a reduced rule base vector controlled permanent magnet synchronous motor (PMSM) drive. The FLC is developed with minimum rules to provide high performance operations due to less computational burden. Hybrid control has the advantage of integrating a superiority of two control techniques for better control performance. To enhance the performance of the PMSM drive system, a new control method, hybrid fuzzy logic controller, using minimum rule base is proposed. The proposed hybrid fuzzy logic controller based on accelerated fuzzy proportional plus integral and fuzzy proportional-integral-derivative is suitable for constant speed applications of a PMSM drive.
This paper highlights several misinterpretations that arise in the field of fractional systems analysis using a representation known in the literature as "state space description". Given these misinterpretations, some results already published and based on this description are questionable. Thus alternative descriptions are proposed.
This paper presents a novel adaptive active control method, which is used for the flutter suppression problem in hypersonic flow. First, the system’s stability is analyzed and the Hopf bifurcation points are obtained. Then, fuzzy systems are employed to approximate the system’s nonlinear dynamics. Furthermore, in order to increase the robustness of the system, a sliding surface is designed by introducing an integral operator. Thirdly, by Lyapunov theory, the proposed fuzzy sliding mode active control guarantees the convergence of flutter and the global boundedness of all the signals in the closed-loop system. The simulation results demonstrate the effectiveness of the proposed method.
Coupled bending and axial vibrations in a planar multi-story frame structure are controlled from a wave vibration standpoint, in which vibrations are described as waves that propagate along uniform waveguides, and are reflected and transmitted upon structural discontinuities. The bending vibrations are modeled using a Timoshenko model, which takes into account the effects of rotary inertia and shear distortion. The axial vibrations are modeled using elementary theory, as it is typically valid for frequencies up to twice the cutoff frequency of Timoshenko bending waves. Regardless of the complexity of a structure, when it is modeled from a wave point of view, it consists of only two basic types of structural components, namely, structural elements and joints. In this paper, both structural element and structural joint controllers are designed based on various control strategies such as optimal damping and optimal energy absorbing. Numerical examples are presented. Results are compared to those obtained based on the classical Euler–Bernoulli model that are available in the literature. As was expected, good agreement between the results of the models at low frequencies was obtained.
In this paper the authors analyze various structures of proportional–integral–derivative (PID) regulators in the control system of the electro-hydraulic strength machine for determination of material characteristics under the controlled stress, strain and energy parameters (strain energy density). The aim of this work is to determine the appropriate structure of the PID controller, so as the control system can accurately follow up the reference signal. Changes of the controller settings, depending on amplitude and frequency of the reference signal, have been presented.
In this study, the large-amplitude vibration of a functionally graded (FG) truncated conical shell with an initial geometric imperfection has been investigated using large deformation theory with a von Karman–Donnell type of kinematic nonlinearity. The material properties of an FG truncated conical shell are assumed to vary continuously through the thickness. The fundamental relations, the modified Donnell-type nonlinear motion, and compatibility equations of the FG truncated conical shell with an initial geometric imperfection are derived. The relation between nonlinear frequency parameters with the dimensionless amplitude of imperfect FG truncated conical shells is obtained. Finally, the influences of variations of the initial geometric imperfection, compositional profiles, and shell characteristics on the dimensionless nonlinear frequency parameter and frequency–amplitude relations are investigated. The present results are compared with the available data for a special case.
A finite element model of large amplitude free vibrations of thin functionally graded beams with immovably supported ends is developed in this paper. The material properties of functionally graded beams are assumed to vary according to the power law distribution through the thickness direction. The finite element model is formulated in a variationally correct way based on Euler-Bernoulli beam theory and von Karman geometric nonlinearity. The linear exact displacement fields of the static case are used as the shape functions. The time response of each node is assumed to be a harmonic function, and the error residuals due to this assumption are minimized by employing the Galerkin method. Together this assumption and method transform the finite element equations to an eigenvalue equation that can be solved using a direct iterative method in tandem with the principle of energy conservation. The accuracy of the proposed method is demonstrated by comparing the frequencies and amplitudes with those of other methods presented in the literature. Finally, the relation between the frequencies of functionally graded beams and those of the homogeneous beams at various initial amplitudes is also examined.
A whole-spacecraft vibration isolation platform can improve the dynamic environment during satellite launches. In this paper, the dynamic characteristics of a whole-spacecraft vibration isolation platform with uncertain parameters are investigated. The governing equation of the platform is derived and the non-probabilistic reliability theory is utilized to analyze the dynamic characteristics. Then, the numerical results are carried out and compared with the experimental data. It is found that non-probabilistic reliability theory is a powerful tool to reveal the dynamic characteristics, which may lead to a new design of the platform with enhanced security and reliability.
A procedure for designing a feedback control to asymptotically stabilize, with probability one, quasi-generalized Hamiltonian systems subject to stochastically parametric excitations is proposed. First, the motion equations of controlled systems are reduced to lower-dimensional averaged Itô stochastic differential equations by using the stochastic averaging method. Second, a dynamic programming equation for the averaged system with an appropriate performance index (with undetermined parameters in cost function) is established based on the dynamic programming principle, and the optimal control law is derived from a minimization condition with respect to control. Third, the Lyapunov function method is adopted to evaluate the stability boundary of asymptotic stability with probability one for the uncontrolled/controlled systems. Finally, the parameters in cost function are selected to guarantee the sufficient stability of the controlled systems. Numerical results for a nine-dimensional mathematical system and a three-dimensional practical system, which describes a structure including viscoelastic element, illustrate the effectiveness of the feedback control strategy, and stability domains can be obviously enlarged when imposing the feedback controls on the original systems.
This study deals with sound radiation of a vibrating body in a half space. Half space may be formed by a rigid, anechoic or specifically by an impedance surface. The practical application of the impedance surface may be the sound field determination of a machine sitting on a floor, coated with an isolation material, for passive noise control. The study is based on the solution of Helmholtz integral equation by the boundary element method (BEM). A BEM code developed for general vibro-acoustic applications is used for numerical solutions. Examples include sound sources taken from theory and daily life. Some benchmark studies and real life applications are involved.
The simulation study of particle damping in microgravity or zero-gravity environments is carried out using the Discrete Element Method in this paper. The results show that the damping particles in zero-gravity environments have a reasonable damping performance only when the particle container is almost fully filled with particles and at large displacement amplitude. The damper will have little effect because the particles will come together and form a floating cluster in the middle of the container, if the vibration amplitude is less than half of the gap between the particle bed and the ends of the container. To break that floating cluster, a cross-shaped spoiler is introduced and fitted inside the container, which greatly raises the damping performance in zero-gravity environments.
Flywheels are widely used on-board spacecraft for attitude control or energy storage. However, micro-vibrations generated by flywheels will influence the performance of high-sensitivity instruments on-board the spacecraft. This study addresses the dynamic modeling and analysis of the micro-vibration isolation of flywheel assemblies. Firstly, an analytical model was developed to describe the coupled multiple flywheel system (MFS) and multi-axis isolation system, with equations in state-space form presented for control purposes. This analytical model properly reflects the mass and inertia properties, the gyroscopic effects and the flexible modes of the coupled system, which can be generalized for isolation applications when multiple flywheels are mounted together. Secondly, the analytical model was validated using the MSC.NASTRAN software based on finite element techniques. Finally, using the proposed model, we investigated the coupled dynamics of the MFS and the isolation system. The results show that the mass and inertial properties and the gyroscopic effects of the MFS will induce couplings between the structural modes. The gyroscopic effects of one flywheel interact with or counteract the effects of the others, which will produce complex vibrational modes and affect the isolation performance accordingly. Thus, the coupled dynamics within the system should receive attention during isolation design for the MFS.
The effect of temperature change on dynamic performances of planar 3-RRR flexible parallel robots is studied in this paper. In general, the strain and stress are produced not only by the external exciting force, but also by temperature change. The strain energy that is caused by temperature change should not be ignored. Based on the Hamilton principle and the finite element method, the general equations of motion of 3-RRR systems are determined, in which the effect of temperature change is taken into consideration. The equations of motion of planar 3-RRR flexible parallel robots are solved using Gear’s algorithm. The commercial Ansys 13.0 software is used to confirm the validity of the theory model. The effect of the daily temperature change of different cities on the performance of 3-RRR flexible parallel robots is investigated. Numerical results show that a small temperature change will cause a significant change in the stress of the flexile links of planar 3-RRR flexible parallel robots. The effects of temperature change should not be ignored when analyzing the dynamic performances of planar 3-RRR flexible parallel robots.
In this paper a new hybrid vibration damping technique as a combination of the semi-active pulse switching technique and passive constrained layer damping is proposed as an effective vibration control method for all frequency ranges. The semi-active pulse switching technique is an effective method to damp any type of vibrations with no need for external energy sources. However, its performance in high-frequency ranges decreases. In addition, passive techniques are not so effective in low-frequency ranges, but have significant effects in high-frequency ranges. The proposed hybrid damping technique as a combination of these two control methods is a new effective control technique for all frequency ranges. It covers the weakness of the semi-active method and provides significant damping in both low and high-frequency vibrations.
In this paper, accurate frequency solutions of tapered vibrating beams and plates using a simple and efficient displacement based unified beam theory in lieu of computationally expensive and rather complex two-dimensional plate theories are presented. The results are given in the form of Euler-Bernoulli/Timoshenko to quasi three-dimensional (3D) solutions. Lower frequency bending and axial modes, as well as torsional and biaxial bending modes corresponding to higher frequency values, are predicted which are in very good agreement with 3D finite element results as well as the published literature. The effects of different parameters like taper ratio, thickness and beam/plate-aspect ratios on the vibration frequencies of tapered structures are studied. It can be seen that due to taper, bending vibration modes become asymmetric along the longitudinal axis of the structure. Further, it can also be noticed that the vibration behavior of thicker beams and plates is characterized by the appearance of a significant number of axial modes at lower frequency values as compared to that of relatively thinner beams/plates.
The solid and liquid mixture (SALiM) vibration isolator is a relatively new passive vibration control technology, especially for the vibration isolation of heavy equipment with low frequency. The isolator contains liquid and elastic solid elements as working media, and its axial stiffness property approximates to bilinear stiffness in certain ranges. This paper focuses on the dynamics design of the isolator and the theoretical analysis of its nonlinear frequency response function (NFRF). The nonlinear dynamic model of a vibration system with a SALiM isolator, i.e. the equation of motion (EOM), is at first established. Then the average method, a classical analytical tool, is employed to estimate the approximate solution of the nonlinear EOM. However, the symmetrical first-order solution obtained with the above method may not be adequate due to the asymmetry of the stiffness of the SALiM isolator. Therefore, the modified average method with a trial expression including a direct current term is introduced. In order to verify the approximate results, a numerical reference based on the Runge-Kutta method is provided for comparison. Moreover, from plots of the resulted NFRFs, it is found that there exists a jump phenomenon induced by bilinearity, which may have harmful impacts on the equipment which is supposed to be protected from vibrations and shocks. To avoid the downside of the bilinear stiffness, the NFRF is analyzed, which allows the determination of the critical values of the isolator parameters to avoid the jump points.
In a rotor-bearing system running with uniform angular acceleration, after running through the resonance, typical beat vibrations occur because the response of the system consists of the natural and excited motion. Shortly after resonance both are vibrations with frequencies close to each other. The present study explains a method for estimating damping of rotor-bearing systems from transient beat characteristics observed during the run-up stage. A mathematical justification is provided that the transient response of the rotor-bearing system consists of a beat response when the system crosses resonance. It is also clear from the mathematical model that the beat phenomenon observed depends on the level of damping in the system. The beat time period is also dependent on the angular acceleration of the system. This beat response is considered for wavelet analysis and the damping is estimated. Angular acceleration (α) of the rotor often increases the damping effects. This paper investigates how the damping ratio changes with respect to different angular acceleration values of the rotor-bearing system. Experimental validation of the beat phenomenon and damping identification is done for a rotor-bearing system. Validation for the above proposed method is done by the half-power bandwidth method of the run-up response and logarithmic decrement method of the beat response. A damping estimation from the impulse response of the stationary rotor by using wavelet transforms is also presented and validated using the logarithmic decrement method.
In this paper, we use the fractional Laplace decomposition method (FLDM) to solve fractional chaotic systems that have various applications in engineering. The FLDM is simple to apply and, moreover, has advantages of manipulating the series solution in an efficient way. We have used the obtained series solutions to generate chaotic sequences.
This paper deals with the reduction of vibrations caused by wind load in slender structures. The structure is modeled as a Single-Degree-of-Freedom system and the wind load is estimated through the pre-filter technique: the aerodynamic force is a function of White Noise filtered by a simple oscillator. Two optimization criteria to calculate the best values of the frequency and the damping ratio of the Tuned Mass Damper (TMD) are compared here. The aim of the first criterion is the reduction of the displacement of the top end of the structure, while the aim of the second criterion is the reduction of the inertial acceleration of the top end of the structure. The comparison of the two criteria is carried out through sensitivity analyses for different environmental conditions and system configurations. The comparison shows that the acceleration criterion is more attractive only for some conditions. Moreover, it is plain that the different efficiencies of the TMD optimized through each of two criteria are related to the mass ratio. Finally, the optimization criteria are applied to estimate the TMD design parameters to reduce the vibrations due to wind load in a lighting tower.
In this work we present the construction and evaluation of recursive Bayesian estimation algorithms for human motion tracking using fractional order models. The presented schemes include both fixed fractional order as well as variable order models with implicit and explicit model order estimation schemes. The performance of the designed techniques is compared to a set of conventional integral order methods using several measurements of human hand and head motions.
The bearing is the key component in a rotating machine. It is important to assess the performance degradation of bearings for realizing proactive maintenance and near-zero downtime. In this paper, a methodology based on the zero crossing characteristic features and a coupled hidden Markov model is introduced for estimating bearing performance degradation. Zero crossing features are time domain representations of the vibration signature in the spectrum domain. They discover the change of bearing performance. When zero crossing features are extracted, a coupled hidden Markov model is employed to assess the performance degradation quantitatively. Results from a bearing accelerated life experiment validate the feasibility and effectiveness of the proposed method.
Sunroof buffeting noise is annoying to drivers and passengers. The conventional method for suppressing sunroof buffeting noise is to use passive deflectors. A recent trend has been large sunroof openings, such as panoramic sunroofs, in accordance with customer preferences for a feeling of openness. Since sunroof buffeting noise tends to become louder as the sunroof opening area becomes larger, a conventional passive deflector may not be a solution in this case, and a new effective method for reducing the sunroof buffeting noise is required. Previous work showed that a strong, self-sustained tonal noise, generated from a Helmholtz resonator exposed to a grazing flow, could be significantly reduced by closed-loop control of an active deflector installed near the upstream edge of the resonator opening. The active deflector system is a cascade of a microphone sensor mounted inside the cavity, controller, power amplifier, and deflector mechanism vibrated by a voice coil actuator. Since the acoustic pressure inside the cavity is influenced by the shear layer modified by the active deflector, the active deflector and acoustic response of the cavity form a closed-loop control system. The main objective of the present study is to implement this technology on a real vehicle and evaluate whether the technology can be utilized to suppress sunroof buffeting noise. A simple active deflector system was assembled and installed in a compact-sized hatchback car with a sunroof opening length of 460 mm. The active deflector system was tested both in a wind tunnel and on a proving ground. The test results showed that the active deflector reduced the sunroof buffeting noise by as much as 25 dB. The active deflector was shown to be stable and robust regardless of changes in the wind speed and wind yaw angle.
Vibration-sensitive equipment mounted on a building structure can be severely damaged by a moderate earthquake, due to the dynamic amplification effect of the primary structure. To alleviate this problem, the seismic protection of such equipment using a fuzzy-controlled piezoelectric equipment isolation system (PEIS) is investigated experimentally in this study by conducting a shaking table test. In the test, the PEIS is placed on top of a full-scale steel frame that is used to simulate the dynamic effect of the primary structure, while the mass of the equipment on the PEIS is simulated by rigid mass blocks. Through controlling the driving voltage of the embedded piezoelectric actuator, the friction damping and motions of the PEIS are attenuated by the fuzzy controller. The implementation of the proposed fuzzy-controlled system requires only one displacement sensor, and thus the system is very easy to implement and less costly than comparable systems. The results of the experiment suggest that, for earthquakes with high intensities or strong near-fault characteristics, the studied system is able to substantially reduce the demand for isolation displacement while maintaining superior isolation efficiency. This implies that the proposed system is particularly desirable for cases of equipment isolation in which the installation space is limited.
In this study, the resonance frequency behavior of a functionally graded beam under viscoelastic boundary conditions is investigated. Nondimensional frequency parameters of the beam are analyzed using the finite element method. The system of equations of motion is derived by using Lagrange's equations under the assumption of Euler–Bernoulli beam theory. The material properties of the beam are assumed to vary through thickness according to the power-law distribution. Different boundary conditions are attained by applying various stiffness and damping coefficients to viscoelastic support elements. The model is validated by comparing the results with a previous study. The effects of various material distribution and boundary conditions are discussed in detail.
In this paper, the mechanical sensitivity of a vibration sensor is investigated by developing a mathematical model with the function of a relative movement modulus and measurement error. This model enables mechanical sensitivity to be improved by enhancing the performance of the vibration sensor. The purpose of the present work is to reduce measurement error by choosing the right damping rate that enables vibration sensor sensitivity to be optimized. The presented model is validated by computer simulation and experimental tests. The obtained results have shown that correct choice of damping rate and frequency range keeps the mechanical sensitivity constant.
The characteristic of a zero stiffness isolator is given first and the stiffness difference between the zero stiffness isolator and a linear one is discussed. Three different types of displacement shock excitations are applied to the base of the zero stiffness isolator and the linear isolator. Three indices are defined to analyze the characteristics and evaluate the performance of the nonlinear isolator. The absolute displacement shock responses in time domain and the maximum absolute displacement ratio for the undamped linear and nonlinear systems are presented for different shock severity parameters. The performance of the damped nonlinear isolator is studied and compared with that of the linear isolator. Results show that the performances of the nonlinear isolator are related to the parameters of the nonlinear isolator and the type of the shock excitation. It is beneficial to introduce a zero stiffness isolator for shock excitations, but the performance is limited by certain conditions. Some useful conclusions which can be used to design this kind of isolator for considering shock isolation are given.
In this study, an optimal nonlinear tracking control law is analytically developed for the semi-active suspension system by the response prediction of the quarter car model, which includes the nonlinear magneto-rheological (MR) damper model. Before this, the skyhook model optimized by the genetic algorithm is presented as a desired model to be tracked by the controller. The optimum parameters of the skyhook reference model are found by minimization of the difference between the root mean square values of acceleration obtained by the power spectral density of an actual random road excitation, and the boundary values specified by the ISO2631 standard at different effective frequencies. The effectiveness of the proposed control system is investigated in the presence of model uncertainties through simulation studies conducted by random road excitations in the time domain. The optimal property of the control law provides the possibility of limiting the input current to the MR damper, as the control input, to the physically admissible range by compromising with other conflicting objectives, that is, ride quality and handling performance. The results indicate that a satisfactory dynamic performance for the suspension system through a reduced input current to the MR damper can be achieved by the proposed control law.
A conventional vibration absorber is valid when the external excitation frequency falls into the neighborhood of a specific value. It is not feasible for vibration suppression applications subject to frequency-varying excitations. In this paper, an adaptive controller is proposed to learn the disturbance spectrum in real time so that output vibration suppression can be achieved regardless of the variations in the excitation frequency. The Lyapunov-like analysis is used to verify the closed-loop stability and ensure boundedness of internal signals. Simulation cases show that the proposed strategy can give satisfactory performance.
In this paper, an intelligent control approach based on neuro-fuzzy systems performance is presented, with the objective of counteracting the vibrations that affect the low-cost vision platform onboard an unmanned aerial system of rotating nature. A scaled dynamical model of a helicopter is used to simulate vibrations on its fuselage. The impact of these vibrations on the low-cost vision system will be assessed and an intelligent control approach will be derived in order to reduce its detrimental influence. Different trials that consider a neuro-fuzzy approach as a fundamental part of an intelligent semi-active control strategy have been carried out. Satisfactory results have been achieved compared to those obtained by means of vibration reduction passive techniques.
Based on the model predictive control (MPC), the soft switching method, and the observer/Kalman filter identification (OKID) method, this paper presents the decentralized fault-tolerant trackers for a class of unknown interconnected large-scale multi-input multi-output sampled-data nonlinear systems with input constraint, actuator failure, and closed-loop decoupling properties. The off-line OKID method is utilized to determine decentralized appropriate (low-) order discrete-time linear models for the class of unknown interconnected large-scale sampled-data systems by using known input–output sampled data. Then, to overcome the effect of modeling error on the identified linear model of each subsystem, an improved observer with the high-gain property based on the digital redesign approach will be presented. So, decentralized multiple MPC controllers are designed beforehand by using the identified linear models. Once a fault is detected in each decentralized controller, one of the backup control configurations in each decentralized subsystem is switched to using the soft switching approach. Thus, the decentralized fault-tolerant control with the closed-loop decoupling property can be achieved through the above approach with a high-gain property decentralized observer/tracker.
In this study, free in-plane and out-of-plane bending vibrations of frame structures have been analyzed together with torsional vibration. Axial extension, rotational inertia and shear effects have also been considered. The frame structure has been designed to have two beams with doubly symmetric cross sections that are connected at various angles to each other. Natural frequencies have been obtained analytically by solving simultaneous linear equations of complex coefficients. Finite element and experimental modal analysis have also been conducted to verify the analytical results. The agreement among the results from the various methods has been found to be good.
In this work, we study the stabilization of a pendulum system by coupling with a heat equation through the left boundary observation of the heat equation, while a velocity feedback of the pendulum system is designed to affect the same side heat flux of the heat equation. Based on the semigroup approach and Riesz basis method, the well-posedness and exponential stability of the system is deduced. Finally, some numerical simulations are presented to show the effectiveness of this feedback control design.
This paper proposes a robust adaptive finite-time controller for stabilization of a non-autonomous electromechanical gyrostat system in the presence of model uncertainties and external disturbances. The effect of the dead-zone nonlinearity in the control input is also taken into account. Moreover, all parameters of the system are assumed to be fully unknown in advance. To deal with the system's unknown parameters, some adaptation laws are introduced. Subsequently, based on the finite-time control theory, an adaptive robust controller is proposed to stabilize the non-autonomous gyrostat system in a given finite time. Then, Lyapunov's stability theory is applied to prove the finite-time stability of the designed control scheme. Finally, a numerical simulation is given to demonstrate the efficacy and robustness of the proposed finite-time control approach.
Viscous dampers have demonstrated their value for vibration control of civil engineering structures subjected to seismic excitations due to their effective energy dissipation capabilities and excellent durability characteristics. In most existing designs of practical applications on structural control with viscous dampers, just several ground motions with different risk levels are included. Logical treatment on the randomness inherent in the occurrence and propagation of earthquakes has still not received sufficient appeal. In this paper, stochastic seismic response analysis and reliability assessment of passively damped structures are carried out through experimental investigations and numerical simulations. Complete shaking-table tests on a framed structure with viscous dampers are involved, where the base excitation is represented by a physical stochastic ground motion model. For the numerical analysis and reliability assessment, the probability density evolution method and the theory of extreme value distribution are employed. Experimental and numerical investigations indicate that the seismic performance of the controlled structure with viscous dampers is significantly improved compared with that of the uncontrolled structure, and the structural safety is essentially enhanced.
The multi-dimensional earthquake isolation and mitigation device (MEIMD) for long-span reticulated structures is a newly invented passive vibration control device. In order to explore the vertical earthquake isolation and mitigation ability of the device, vertical pseudo-dynamic tests on a 1:3 scaled long-span reticulated structure with and without devices are carried out. In the tests, dynamic responses of the structure with the devices are compared with those without the devices under different earthquake waves. It can be seen from experimental results that the devices can obviously reduce the displacement, acceleration, and members’ strain responses of a long-span reticulated structure. Moreover, the finite element analyses are also performed to verify the seismic reduction effect of MEIMD. The numerical results fit well with the experimental results and this indicates that the finite element analysis has high simulation precision.
In this paper, the dynamic behavior of a high-speed rotating shaft under the combined localized defects on outer race, inner race and rolling element has been analyzed. An adaptive algorithm based on wavelet packet decomposition and Hilbert transform is used to extract the bearing fault characteristic component from the vibration signals. The reverse Biorthogonal wavelet 5.5 is considered as the most appropriate wavelet for decomposing the bearing vibration signal, on the basis of the maximum energy-to-Shannon entropy ratio criterion. The imperial trend suggested in diagnosing the combined localized defects of rolling bearing is based on experimental analysis at various rotor speeds. The results are presented in the form of envelope analysis, bifurcation diagrams and Poincaré maps that show the appearance nonlinearity in the dynamic response due to the rotor speed and the presence of combined localized defect. Significant peaks are reported at BPFO, BSF, FTF and modulation of BPFI with rotational frequency in envelope spectrum. Fundamental train frequency also shows noticeable excitation. A modified mathematical model shows good agreement with experimental results.
This paper presents a study of a quasi-zero-stiffness (QZS) isolator. A unique relationship between the geometry configuration and the stiffness of the spring elements is obtained in order to design the property of high-static-low-dynamic stiffness. Analytical solutions of the nonlinear QZS system are derived with the harmonic balance method for the characteristic analysis of the force transmissibility and critical conditions for occurring jump-down and jump-up phenomena. The effects of damping and excitation force on the system behaviors are discussed. A series of experimental tests demonstrate that the QZS system greatly outperforms a corresponding linear isolation system. The former enables vibration to be attenuated at 0.5 Hz, while the latter can only execute attenuation after 4.2 Hz. The QZS system is especially effective for vibration isolation in the low-frequency range.
This paper considers identification problems of Hammerstein finite impulse response moving average (FIR-MA) systems and presents a gradient-based iterative algorithm and a least-squares-based iterative algorithm to estimate the parameters of the Hammerstein systems by using the data filtering technique. The analysis and simulation results show that the gradient-based iterative algorithm has a higher computational efficiency than the least-squares-based iterative algorithm.
It is well known that seal force has a great influence on dynamic coefficients of the rotor-seal system and Muszynska’s model is employed by many scholars to research the seal system. But the rotor-seal system has larger eccentricity ratio, Muszynska’s model will not describe the characteristics of the rotor-seal system well. So a more accurate model is critical for describing the seal force. An improved nonlinear model of a rotor-seal system is proposed for describing seal force of the rotor-seal system based on the two-control-volume model and rotor motion equation. This model can not only solve the larger eccentric problem but can also bring a simple calculation through the numerical methods. Dynamic coefficients of the rotor-seal system are also researched based on the new nonlinear model under the condition of the tooth-on-stator and tooth-on-rotor. In order to verify that the equation-control model is correct, Childs and Scharrer's experiment and two-control-volume model are employed and there is a comparison between theoretical results and experimental results. The result shows that theoretical results from the improved model are in better agreement with Childs and Scharrer's experiment than two-control-volume model. The proposed model in this paper provides a theoretic reference for further research on the rotor-seal system.
The 3D piezoelasticity theory and the spatial state-space approach are used to study the steady-state non-axisymmetric sound radiation and scattering characteristics of an infinitely long, arbitrarily thick, orthotropic functionally graded hollow circular cylinder, coupled with an inner (actuator) layer of functionally graded piezoceramic material. The method of stationary phase is employed for evaluation of the radiated far-field pressure integral. Numerical simulations include water-submerged air-filled steel-PZT4 composite cylinders driven by harmonic electromechanical loads or insonified by an obliquely incident plane sound wave. Also, when the actuator layer is operating in the active vibration mode, the effects of the number of control modes on the input voltage required for partial or complete cancellation of the far-field and internal radiated pressures as well as on the backscattering form function and noise reduction amplitudes are examined. Limiting cases are considered and validity of formulation is established by comparison with available data as well as with the aid of a commercial finite element package.
In the transportation domain, on-board rotors in bending are subjected not only to rotating mass unbalance but also to several movements of their base. The main objective of this article is to predict the dynamic behavior of a rotor in the presence of base excitations. The proposed on-board rotor model is based on the Timoshenko beam finite element. It takes into account the effects corresponding to rotary inertia, gyroscopic inertia, and shear deformation of shaft as well as the geometric asymmetry of disk and/or shaft and considers six types of deterministic motions (rotations and translations) of the rotor’s rigid base. The use of Lagrange’s equations associated with the finite element method yields the linear second-order differential equations of vibratory motion of the rotating rotor in bending relative to the moving rigid base which forms a non-inertial frame of reference. The linear equations of motion highlight periodic parametric terms due to the geometric asymmetry of the rotor components and time-varying parametric terms due to the rotational motions of the rotor rigid base. These parametric terms are considered as sources of internal excitation and can lead to lateral dynamic instability. In the presented applications, the rotor is excited by a rotating mass unbalance combined with constant rotation and sinusoidal translation of the base. Quasi-analytical and numerical solutions for two different rotor configurations (symmetric and asymmetric) are analyzed by means of stability charts, Campbell diagrams, steady-state responses as well as orbits of the rotor.
An innovative μ-disc-type inductive micro-motor is proposed and studied in this paper. The novel 3D solenoid-type electromagnetic poles are designed and fabricated by dry isotropic etching technique so that the output torque of the inductive motor can be greatly increased even though a simpler fabrication procedure is employed. On the other hand, the order-reduced dynamic model for the proposed micro-motor is established by using the singular perturbation theory. Based on the order-reduced model, a composite controller is synthesized to prevent potential collision between the disc and the center bearing by sliding mode control strategy and successfully suppress the unfavorable periodic oscillation, due to eccentricity of the disc, by an anti-swaying policy. Eventually, a few comparisons on several typical operational conditions, such as various vacuum levels, van der waals force and periodic disturbance, are also addressed and presented. The efficacy of the composite controller and the performance of the proposed micro-motor are verified by intensive simulations undertaken via the commercial software, Matlab/Simulink, and the interface module dSpace DS 1104 Board. Finally, the superior performance for the proposed micro-motor is assured, e.g., the collision between the disc and the center bearing can be successfully prevented and a constant spinning speed can be retained even if a certain degree of disturbance and uncertainty abruptly occurs.
This study focuses on performance evaluation of an active vibration controller in a closed loop finite element (FE) environment for piezoelectric smart structures by integrating a reduced-order-model-based controller into the FE model. Based on the first-order shear deformation theory, a coupled piezoelectric-mechanical FE model with electric potential variables is developed for the piezoelectric smart structure to provide a platform for vibration analysis and controller design. A system identification technique known as subspace identification method is employed to obtain a multi-input multi-output state space reduced-order model which can with sufficient accuracy predict the behavior of the piezoelectric smart structure under consideration from the inputs and outputs of FE simulations. A linear-quadratic regulator controller together with a Luenberger observer is designed based on the reduced-order model for the purpose of vibration control. The reduced-order-model-based controller is then integrated into an FE environment by updating the actuator voltages according to the controller at each time instant during the transient analysis of FE simulations. Eventually, the performance robustness characteristics of the proposed vibration controller are evaluated in case of structural parameter variations and taking the sensor or actuator offline in a closed loop FE environment. Numerical examples are presented to demonstrate the efficiency of the proposed scheme for evaluating the vibration controller performance of piezoelectric smart structures in a closed loop FE environment.
This paper presents an image encryption scheme based on complete shuffling algorithm: limited in the skew tent-map-predicated image cryptosystem and chaotic substitution box transformation. The proposed image encryption algorithm provides extra confusion due to the inclusion of a chaotic S-box. It is well known from the literature that simple image encryption based on a total shuffling scheme is not secure against a chosen cipher text attack. We then projected an extended algorithm which does well against a chosen cipher text attack. Furthermore we analyze the proposed technique for unified average changing intensity (UACI) and NPCR analysis to determine its strength.
Tuned vibration absorbers have been shown to reduce the forced vibration response at a specific frequency for many applications. This paper presents a novel absorber using fluidic flexible matrix composites (F2MC). Fiber reinforcement of the F2MC tube kinematically links the internal volume with axial strain so that fluid flows in and out of an axially vibrating tube. Coupling of an F2MC tube through a fluid port to a pressurized air accumulator produces a novel absorber that can suppress vibration at the tuned absorber frequency. A 3-D elasticity model for the tube and a lumped model for the fluid mass produce a fourth-order F2MC-mass model. The analytical closed-form isolation frequency is derived and shown to depend primarily on the port inertance, orifice flow coefficient, and the tube parameters. Viscous damping in the orifice can be adjusted to reduce the resonant peak and broaden the isolation bandwidth. With a fully closed orifice, the zero disappears and the system has a single resonant peak. For a constant port inertance, variations in the primary mass do not change the isolation frequency, making the F2MC absorber robust to mass variations. Experimental results validate the theoretical predictions by demonstrating a tunable isolation frequency that is insensitive to primary mass variation as well as a 94% reduction in forced vibration response relative to the closed-valve case at the isolation frequency.
The use of cartridge valves with high pressure and large flow rates in a hydraulic system usually causes serious vibration and noise issues. In this paper, a type of cartridge valve with silencing grooves was presented and its mathematic model was built up. Four types of silencing grooves were selected for the cartridge valve, and they were optimized separately based on the actual application system for testing the safety valve in hydraulic support. Through simulation, their silencing effects were analyzed. The U-shaped groove has been found to be dominant among all the investigated groove types and it can significantly reduce the peak pressure gradient of the tested valve compared with no grooves. This research not only provides a new solution for reducing the vibration and noise of a hydraulic system, but also presents an effective method for the design of silencing grooves on a cartridge valve.
In this paper, a stable reinforcement learning control approach using neural networks (NNs) is developed for the trajectory tracking of an n-link rigid robot manipulator. The considered systems are in discrete time form. The proposed controller design consists of two NNs. One is the critic network that is used to approximate the long-term cost function, whereas other is that the action NN is employed to generate the system input. Then, an optimal control input can be obtained compared with other robot manipulator systems. Using the Lyapunov approach, the tracking error and weight estimates are proven to be semi-global uniformly ultimately bounded. A simulation example is employed to illustrate the effectiveness of the proposed controller.
In order to realize equipment’s near-zero downtime and maximum productivity a rolling bearing performance degradation assessment is proposed, which is one of the most important techniques. The traditional feature extraction methods based on stationary and Gauss characteristics were unfit to handle non-stationary and non-Gauss signals when the rolling bearing performance begins to degrade. The higher-order statistics (HOS) are fit for handling the non-stationary and non-Gauss signals. Bispectrum not only possesses all the properties of HOS but also has a higher computational efficiency because of a lower order compared with other types of HOS. The support vector data description (SVDD) is a single value classification method which can overcome the problem of a lack of samples in the degradation process of the rolling bearing. A method is proposed in the paper which is based on the bispectrum and SVDD. Firstly, the rolling bearing data of normal state is collected and handled by bispectrum. Based on feature vectors extracted from normal data an SVDD model fitting a tight hypersphere around them is trained. The general distance of test data handled by the bispectrum to this hypersphere is used as the degradation index. In the end, through simulation and a rolling bearing’s accelerated life test, the effectiveness and feasibility of the proposed method is verified.
The dynamic properties of vibration control systems pose unique requirements and challenges on the implementation of model predictive control (MPC) algorithms with stability and feasibility guarantees. This article presents a comprehensive experimental comparison of computation timing and damping performance for various MPC methods; analyzing their offline and online properties in active vibration control and their impact on practical implementability. Optimal and sub-optimal MPC algorithms providing guaranteed stability and constraint feasibility have been applied to the real-time active vibration attenuation of a lightly damped mechanical test structure. Based on the experiments presented in this paper, the standard and sequential quadratic programming-based, optimal and sub-optimal minimum time multi-parametric programming-based and the sub-optimal Newton–Raphson’s algorithm-based MPC methods demonstrate closely comparable vibration attenuation performance. The offline and online timing analysis indicates that the underlying difference between the investigated MPC algorithms lies mainly in practical implementability difficulties caused by inherent algorithm efficiency, rendering certain variants of MPC more suitable for vibration control than others.
The optimal active flutter control of supersonic composite laminated panels is studied using the distributed piezoelectric actuators/sensors pairs. The supersonic piston theory is used to calculate the unsteady aerodynamic pressure, and Hamilton’s principle with the assumed mode method is employed to develop the equation of motion of the structural system. The controllers are designed by the proportional feedback control method and the linear quadratic Gauss (LQG) algorithm. The optimal locations of the actuator/sensor pairs are determined by the genetic algorithm (GA). The aeroelastic properties of the structural system are mainly analyzed using the frequency-domain method. The time-domain responses of the structure are also computed using the Runge–Kutta method. The influences of ply angle on the flutter bound of the laminated panel with different length–width ratios are analyzed. The optimal design for the locations for different numbers of piezoelectric patches used in the proportional feedback control is carried out through the GA. Meanwhile, the control effects using different numbers of actuator/sensor pairs are investigated. The flutter suppression by the LQG algorithm is also carried out. The control effects using the two different controllers are compared. Numerical simulations show that the optimal locations obtained by the GA can increase the critical flutter aerodynamic pressure significantly, and the LQG algorithm is more effective in flutter suppression for supersonic structures than the proportional feedback controller.
This paper presents a novel refined bacterial foraging algorithm (RBFA) to solve a multi-objective optimal power dispatch (MOOPD) problem incorporating multiline flexible AC transmission system (FACTS) devices in modern power systems and to seek optimal parameters of the same. This paper also deals with the concept of the interline power flow controller (IPFC) for providing better power flow management in a multiline transmission system. The optimal control parameters thus obtained are used to enhance the stability of the system and minimize transmission losses. The stability of modern power systems is improved by installing fast reacting devices such as IPFC together with the optimal parameters of IPFC. The optimal location of IPFC and solving optimal power dispatch (OPD) problems are required to employ the introduction of multi-objective based optimization techniques. This paper proposes a new algorithm based on the bacterial foraging algorithm (BFA) with a proposed multi-objective optimization technique. The proposed approach is tested with standard IEEE 30 bus system and comprehensive simulation results show better in constraint handling, finding optimal control parameters of IPFC, handling of voltage profile, minimize the transmission losses and quality of solution.
The main purpose of this paper is to provide an efficient numerical approach for the fractional differential equations (FDEs) on the half line with constant coefficients using a generalized Laguerre tau (GLT) method. The fractional derivatives are described in the Caputo sense. We state and prove a new formula expressing explicitly the derivatives of generalized Laguerre polynomials of any degree and for any fractional order in terms of generalized Laguerre polynomials themselves. We develop also a direct solution technique for solving the linear multi-order FDEs with constant coefficients using a spectral tau method. The spatial approximation with its fractional-order derivatives described in the Caputo sense are based on generalized Laguerre polynomials Li(α) (x) with = (0, ) and i denoting the polynomial degree.
A novel vibration source separation and identification method using the denoising source separation (DSS) technique is proposed for the mixed mechanical vibration signals from engines in ships. Denoising source separation enables us to extract the source signals from the mixed signals without prior knowledge of sources and their mixing mode, and thus the important source information extracted by DSS can be used to monitor or actively control engine noises. Different denoising functions such as energy, skew, kurtosis, and tangential functions in DSS are applied to both simulation studies and experimental data to evaluate their separating performances. The tangential function provides the best outperformance with both numerical study and engineering application. In addition, the effectiveness of the proposed DSS method is validated by correlation analysis and the frequency marker tracking method.
The issue of passively controlling aeroelastic instability of general nonlinear multi-degree-of-freedom systems, suffering from Hopf bifurcation, is addressed. The passive device consists of an essentially nonlinear oscillator (nonlinear energy sink [NES]), having the task of absorbing energy from the main structure. The mathematical problem is attacked by a new algorithm, based on a suitable combination of the multiple scale and the harmonic balance methods. The procedure is able to furnish the reduced amplitude modulation equations, which govern the slow flow around a critical manifold, on which the equilibrium points lie. The method is applied to a sample structure already studied in literature, consisting of a two-degree-of-freedom rigid airfoil under steady wind. It is shown that NES, under suitable conditions, can shift forward the bifurcation point and, moreover, it can reduce the amplitude of the limit cycles. Relevant asymptotic results are compared, for validation purposes, with numerical simulations.
An active unbalanced vibration compensation scheme with built-in force actuator for a flexible switched reluctance motorized spindle (SRMS) is proposed. The force actuator is a set of windings, which are wound on the stator pole of the switched reluctance motor (SRM). The equivalent unbalance identification method is proposed to indentify online the unbalanced vibration caused by the grinding wheel’s mass imbalance. The equivalent reference unbalance compensation signal is produced by the identification method, which is used to obtain the compensation current of a force actuator, so a controlled, non-contact electromagnetic compensation force on the rotor of the SRMS is produced by the force actuator to compensate the actively unbalanced vibration of the flexible SRMS. The dynamic flexible SRMS is modeled by means of finite element method (FEM). The inductance of main and control windings, the coefficients of the compensation and the unbalanced magnetic pull force are identified by the FEM, and then the active unbalanced vibration compensation scheme for the flexible SRMS is designed in Matlab, in which inductance of main and control windings, the coefficients of the compensation and unbalanced magnetic pull force are obtained by the Look-up table method. The results show that the proposed active unbalanced force compensation scheme has an obvious compensation effect and the coefficients indentified by the FEM have been closer to an actual effect on compensating the unbalanced vibration of the flexible SRMS.
This paper is concerned with the problem of robust state feedback controller design to suppress fractional-order chaotic systems. A general class of fractional-order chaotic systems is considered and it is assumed that the systems’ equations depend on bounded uncertain parameters. We transform the chaotic system equations into linear interval systems, and a sufficient stabilizability condition is derived in terms of linear matrix inequality (LMI). Then, an appropriate feedback gain is introduced to bring the chaotic states to the origin. Such design will result in a simple but effective controller. Several numerical simulations have been carried out to verify the effectiveness of the theoretic results.
Electrorheological fluids (ERFs) offer rapid control of damping using very low power requirements. Different models have been proposed to simulate the hysteresis phenomenon of ERFs. A modular test facility was designed to perform measurements of a specific electrorheological fluid in squeeze and shear modes in Part I. Based on these measurement cycles, material models for squeeze and shear modes are proposed and corresponding model parameters are identified within this parameter space. The fitted models are benchmarked against the measurement data and are capable of resembling the fluid’s dynamic properties at harmonic excitation, including transitions between Bingham-like and visco-elastic material behavior. Once model parameters are identified, the dynamics of an ERF are resembled excellently by phenomenological models. However, clear trends within the parameter space cannot be stated for all model parameters which prevents the derivation of analytical statements for the model parameters. Since the identification of model parameters is not transferable, a new adaptation is necessary for every application. Nevertheless, the presented procedure can be applied directly in these cases and is robust.
In this article, the magneto-thermo analysis problem of an infinite functionally graded (FG) hollow cylinder is studied. The radial displacement, mechanical stresses and temperature, as well as the electromagnetic stress, are all investigated along the radial direction of the infinite cylinder. Material properties are assumed to be graded in the radial direction according to a novel power-law distribution in terms of the volume fractions of the metal and ceramic constituents. The inner surface of the FG cylinder is pure metal, whereas the outer surface is pure ceramic. The equations of motion and the heat-conduction equation are used to derive the governing second-order differential equations. A finite element scheme is presented for the numerical purpose. The system of differential equations is solved numerically and some plots for displacement, radial and electromagnetic stresses, and temperature are presented.
In this study, modal testing and finite element model calibration of in-filled reinforced concrete (RC) frames are studied. For this purpose a full-scaled, one bay and one-story RC frame is produced and tested for plane and brick in-filled conditions. Dynamic characteristics, such as natural frequencies, mode shapes and damping ratios, of plane and in-filled RC frames are determined using the Operational Modal Analyses method under ambient vibration. The RC frame is vibrated by natural excitations with small-impact effects and the response signals are measured using sensitive accelerometers during ambient vibration tests. Measurements of time-frequency range and effective mode number are determined by considering similar studies and literature. To obtain experimental dynamic characteristics, enhanced frequency domain decomposition and stochastic subspace identification methods are employed. Analytical modal analysis is performed on a two-dimensional finite element model of the frames using SAP2000 software to provide analytical frequencies and mode shapes. The results of ambient vibration tests show that dynamic characteristics change significantly depending on the existence of an in-fill wall. The first five natural frequencies are obtained experimentally between 16.64 and 179.20 Hz, and 63.56 and 226.12 Hz for plane and brick in-filled, respectively. Dynamic characteristics obtained by analytical and experimental methods are compared with each other and the finite element model of the frames is updated by changing some uncertain modeling parameters, such as material properties and boundary conditions, to reduce the differences between the results. At the end of the study, maximum differences in the natural frequencies are reduced on average from 39% to 8% and a good agreement is found between analytical and experimental dynamic characteristics after finite element model updating. This result shows the importance of finite element model updating to reflect the current behavior of the structures. In addition, it is seen that material properties are more effective parameters in the finite element model updating of the plane frame. However, for the brick in-filled frame, changes in boundary conditions determine the model updating process.
The combination model of the vehicle and ladder track system that accounts for the wheel–rail interface has been developed to analyze the wheelset and ladder track vibration characteristics in the frequency and time domains. In the wheel–rail interface, the vertical contact is represented by contact stiffness derived from the Hertz theory of normal elastic contact, and lateral contact is idealized by linear contact used Kalker linear rolling contact theory. The considerable noise and vibration frequency of the ladder track is determined by experimental investigation results. Then the effect of the most significant ladder track parameters on the track vibration is analyzed in time domain using the vehicle–track coupling model. Based on the results of the parametric study, an optimization of the mechanical properties of the ladder track to reduce the track vibrations is performed using the multipoint approximation method. The results of the optimization are presented and discussed.
Natural porous materials have a large area of usage, from micromechanical designs to medical applications, due to their geometrical forms and chemical properties. Mechanical properties of porous materials are usually performed after several homogenized applications because of their complex geometric forms. It is known that usage of homogenized details of microarchitecture in macro structural analyses provides savings in terms time and computational effort. However, realistic analyses are performed by including microarchitectural details in models, due to advancing technology and reverse engineering techniques.
In this study, modal properties of a porous structure are investigated by taking microstructural details into consideration according to the voxel-based finite element model, and significant modal behavior properties, which cannot be observed in routine modal analyses, are determined. In addition, analyses using the homogenized model of porous structure are performed, and it is seen that the obtained results are not only different numerically but also have different modal behavior from the porous model. Special modes, defined as local modes, which are not seen in homogenized models, are observed in models by using the voxel-based finite element method and analyses are comprehensively performed.
This paper proposes a refined bacterial foraging algorithm (RBFA) for solving the multi-objective based optimal power dispatch with optimal placement of distributed generation (DG) to minimize the total real power loss, generation cost, the environmental emission and considering various controls and limits. The RBFA is based on the social foraging behavior of the Escherichia coli bacteria and its improved version of the basic bacterial foraging algorithm. The RBFA provides natural selection to eliminate poor foraging strategies for bacteria and to propagate other successful foraging strategies where foraging is proceeded using a position updating process, step length, search dimension and search direction with adaptation of basic foraging principles. Initially, the algorithm randomly generates the particle positions representing the size and location of DG and its proposal to solve the simultaneous optimization of the multi-objective problem. The proposed RBFA is used to determine the optimal sizes and locations of multi-DGs; the different types of DG are considered and the load flow is used to calculate the exact loss and to minimize simultaneously the economic cost and the emission of thermal units by changing the location and varying the sizes of the DG units. The test results indicate that the RBFA method can obtain better results than similar social behavior algorithm method on the IEEE30-bus system. The results are compared with and without DG units. The proposed method found the optimal location and sizing of DG units with control of the voltage profile, control of the cost of generation and control and reduction of environmental pollution and transmission losses.
Control of structural vibration due to wind and earthquake forces has been extensively researched. However, studies on vibration control of structures against underground blasts are limited. It is thereby important to study the usefulness of established vibration control technologies in the blast resistant design of structures. In the present work, an attempt is made to study the effectiveness of the New-Zealand (N-Z) type base isolator (BI) in mitigating structural vibration effects due to blast induced ground motion (BIGM). The BIGM is modeled by an exponentially decaying function representative of a typical rock blast, and the isolator by a bilinear model. The influence of the various BI parameters on its performance is examined in the time domain by considering a single-degree-of-freedom structural model and a realistic five-story building. Numerical studies reveal that the N-Z base isolation system is highly effective in reducing both the underground blast induced structural acceleration as well as the displacement. It is noted that the peak displacement and permanent deformation of the BI may be crucial design criteria. These may, however, be restricted by selecting a proper combination of the BI parameters without significantly compromising the response reductions obtained by it.
Vibration absorbers are frequently used to control and minimize excess vibration in structural systems. Dynamic vibration absorbers are used to reduce undesirable vibration in many applications such as pumps, gas turbines, engines, bridges, electrical generators, etc. To reduce the vibration of the system, the frequency of the absorber should be equal to the excitation frequency. The aim of this paper is to investigate the use of a variable stiffness type magnetic vibration absorber to control the vibration of beam structure. This study will aim to develop variable stiffness of a magnetic vibration absorber to adapt to the change in a vibratory system; its stiffness can be varied by changing the distance between magnets. The absorber system is mounted on a cantilever beam acting as primary system. The objective is to suppress the vibration of the primary system subjected to a harmonic excitation whose frequencies vary. This can be achieved by varying the stiffness by changing the distance between the magnets. The advantage of a magnetic vibration absorber is that it can be easily tuned to the excitation frequency, so it can be used to reduce the vibration of a system subjected to variable excitation frequency.
The nonlinear oscillatory motion of an elastic sphere in contact with a rigid flat surface to different loads is clearly dominated by the damping mechanism of the system. However, the damping power law is unable to be identified using the decrement method due to the almost identical free vibration responses. In this paper, a procedure which allows identification of the nonlinear viscous damping from the free response data is presented. The procedure is based on the figure relating the damping restoring force and the velocity which is distinguishable for different damping laws. A dynamic experiment is described, and from the free vibration data obtained the damping restoring forces are extracted for spheres with different materials being steel and low density polyethylene (LDPE). Subsequently, based on the models and observations the characteristics of the damping law are estimated. The results show that a linear viscous damping model is a good representation for the steel sphere contact, which confirms earlier studies; whilst the LDPE sphere contact follows a nonlinear power law for the viscous damping function, which is newly obtained. The validity and accuracy of the proposed method are supported by the good agreement between numerical results and experimental results.
The problem of reflection of plane waves due to an incident longitudinal wave at a plane free fibre-reinforced thermoelastic half-space has been investigated. There exist three types of plane waves which are longitudinal, transverse and thermal waves in the thermoelastic medium. The analytical expressions of their velocities are obtained and it is observed that they depend on the angle of propagation. Using appropriate boundary conditions, the amplitude and energy ratios for the reflected waves are derived and computed numerically.
The focus in this paper is on investigating the influence of hinge friction on the steady-state dynamic response of a transversally base-excited shallow arch. Two semi-analytical models are derived by applying an assumed-modes approach based on sinusoidal modes and Craig–Bampton modes respectively. It is shown that both models give qualitatively and also to a great extent quantitatively similar response results. Hinge friction induces the presence of equilibrium sets rather than static equilibria. Furthermore, the influence of friction on the load-path for a quasi-static acceleration loading is illustrated. In the steady-state analysis of the semi-analytical models, amplitude–frequency diagrams are presented. These plots are obtained by solving two-point boundary value problems in combination with a path-following technique. Local stability and bifurcation analysis of periodic solutions is carried out using Floquet theory for systems of Filippov type. Especially for low excitation amplitudes, the responses dramatically change due to hinge friction, since these responses are dominated by hinge stick. Near resonances and in the case of high-amplitude excitation, the frictional hinge will only slip and the influence of hinge friction is significantly reduced. When hinge friction is relevant, the Craig–Bampton model is expected to predict responses more accurately.
Character recognition has been an active area of research and, due to its diverse applicable environment, it continues to be a challenging research topic. The data entry form is a convenient and successful tool for collection of information by filling the sheets with handwritten characters. For many purposes, such as documenting and archiving, extracting the handwritten characters is important. One of the most important fields in these forms is the data-filled boxes. The extraction process is important in processes of handwritten recognition techniques. Feature extraction plays an important role in different classification-based problems, such as face recognition, signature verification, optical character recognition (OCR), etc. The performance of OCR highly depends on the proper selection and extraction of a feature set. Different feature extraction methods are designed for different representations of the characters. The holistic approach is focused on feature extraction of the entire image and recognition using a neural network. This work proposes a subspace approach that regularizes and extracts Eigen features from handwritten numerals. Extracted Eigen features are recognized using a neural network. The proposed algorithm has been successfully implemented and has the added advantage of obtaining the extraction and recognition result at the same time.
A particle damper (PD) is a device that can attenuate mechanical vibrations thanks to the dissipative collisions between grains contained in a cavity attached to the vibrating structure. It has been recently suggested that, under working conditions in which the damping is optimal, the PD has a universal response in the sense that the specific dissipative properties of the grains cease to be important for the design of the device. We present evidence from simulations of PDs containing grains of different sizes, shapes and restitution coefficients, that the universal response is also valid when fragmentation of the grains occurs (generally due to intensive operation of the PD). In contrast, the welding of grains (caused by operation under high temperatures) can take the PD out of the universal response and deteriorate the attenuation. Interestingly, we observed that even at working conditions off the optimal damping, the shape of the grains remains unimportant for the response of the PD.
The complex shear modulus of an electrorheological (ER) adaptive sandwich beam is optimally estimated to model the system for vibration control. In the composition of a three layered beam, the ER fluid layer is embedded between two constraining layers. Using finite element (FE) method, the governing equations of the composite viscoelastic beam are derived. The developed model is compared with the results found in the literature. In addition, for a fabricated ER sandwich beam, the ASTM E756 standard is employed to estimate the complex shear modulus of the viscoelastic layer in different electric fields. An optimization procedure is conducted based on particle swarm optimization (PSO). In this process, the rough estimation of complex shear modulus extracted by ASTM E756 is modified to correlate the results of the FE model and the experimental tests. The updated FE model is mapped into an appropriate form that can be used for control objectives. Finally, a semi-active sliding mode control is utilized to attenuate the vibration of the adaptive sandwich beam by tuning its electric field dependent characteristics.
We investigate the validity and accuracy of using assumed modes methods to estimate the effective nonlinearities of vibration modes. For this purpose, a problem concerning the nonlinear response of a linearly tapered cantilever beam is considered. Since, in the selected example, the linear eigenvalue problem cannot be solved analytically for the exact mode shapes, an approximate set is required to discretize the partial differential equation governing the beam's motion. To approximate the mode shapes, three methods are utilized: (i) a crude approach, which directly utilizes the linear mode shapes of a regular (untapered) cantilever beam; (ii) a finite-element approach wherein the mode shapes are obtained in ANSYS, then fitted into orthonormal polynomial curves while minimizing the least square error in the modal frequencies; and (iii) a Rayleigh–Ritz approach which utilizes a set of orthonormal trial basis functions to construct the mode shapes as a linear combination of the trial functions used. Upon discretization, the modal frequencies, the geometric and inertia nonlinearity coefficients, as well as the effective nonlinearities of the first three vibration modes are compared for eight beams with different tapering. It is shown that, even when the modal frequencies are well-approximated using the three methods, a large discrepancy is observed among the estimates of the inertia, geometric and, thereby, effective nonlinearities of the structural modes. In fact, when using the modal frequencies as a convergence measure for assumed modes methods, inaccurate, and sometimes, erroneous predictions of the effective nonlinearities can be obtained. As a result, this paper recommends that a stricter measure based on the convergence of the nonlinear coefficients be implemented for discretizing a nonlinear system using approximate mode shapes.
Flexible rotor systems supported by angular contact ball bearings display very complicated nonlinear behavior due to clearance and nonlinear Hertzian contact force. In this paper, a nonlinear vibration theoretical model for a flexible rotor-bearing system is derived in which the dynamic model of the shaft element, disk, coupling, nonlinear contact deformations and forces of the ball bearing are established. Nonlinear responses and orbits analysis of a flexible rotor angular contact ball bearing system are studied using the numerical integration method and maximal Lyapunov exponent. Bifurcation and stability of periodic motion of the flexible rotor-bearing system are studied using the continuation-shooting method and Floquet multipliers. Influences of initial contact angles, unbalance, damping factor, axial preloads, bending moments, stiffness ratio and rotating speed on stability and the bifurcation of periodic motion of the rotor-bearing system are analyzed. Finally, the theoretical model for a flexible rotor-bearing system is experimentally verified.
In this paper, a discretized multi-freedom-degree (DMFD) model is presented to predict the lowest locally resonant (LR) band gap in phononic structures. The DMFD model is adopted to improve the accuracy and the application of previous conventional prediction models. Firstly, the model is applied to the one-dimensional ternary LR structure to show the improvement in precision that is independent of the decrease of the density of the scatterer. Then, the model is extended to the evaluation of the resonance frequencies in a two-dimensional binary LR structure, and the estimates from the present model, which are in good agreement with the previous results, verify our model. Each parameter in the DMFD model allows a clear physical insight into the band-gap mechanism. This model could provide a pre-estimation of the lowest gap of binary and ternary LR structures.
This paper develops general theoretical results about an input–output model-following methodology for linear systems, as an optimal control problem. A control law is obtained by minimizing a quadratic index that takes into account the matching errors and the control inputs. The control is obtained from the Lagrange multiplier method and can be interpreted as an extension of the linear quadratic regulator, with finite and infinite horizon formulations. The major contribution of the paper is the development of solutions involving plant output feedback. The method is illustrated with an application to a nonlinear flexible aircraft with nonstationary aerodynamics and nine flexible modes. Simulations compare state and output feedback solutions. In the proposed example, when taking into account unmodeled flexible dynamics and parametric uncertainties, the best results are given by the proposed output feedback.
In this article, a novel synchronization scheme, modified function projective lag synchronization (MFPLS), between identical and nonidentical hyperchaotic complex systems with fully uncertain parameters, is proposed. In the proposed general method, the states of two hyperchaotic complex systems with unknown parameters are asymptotically synchronized up to a desired scaling function matrix with time delay, and all of the unknown parameters are identified. The adaptive controller and laws of parameters are designed to achieve MFPLS between the drive and response systems. Theoretical proof and numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.
The closed form of the sensitivity of modal flexibility for a real undamped system is derived based on the algebraic eigen sensitivity method. The formula is then adopted to detect the damage location and severity. The merit of the proposed approach over many other exiting modal flexibility sensitivity-based schemes is that it eliminates the adverse effect of the truncating higher-order modes. Moreover, the proposed approach could identify results with sufficient accuracy by employing one mode or multiple modes. To tackle the operational mode shape normalization problem ascribed to the unknown ambient excitation, the scaling factors are employed. A number of assumed damage scenarios in beams has been used to demonstrate the applicability of the proposed damage detection method. It is demonstrated that the proposed method is not sensitive to noise, and it can effectively identify single and multiple damage.
Up to now, many advanced signal processing methods have been developed for machine condition monitoring and fault diagnosis. One assumption for the use of these methods is that one vibration source is isolated from other irrelevant sources in advance. In some practical cases, when a transducer is installed in the vicinity of closely arranged components of a machine, it is inevitable to obtain a vibration signal mixture generated by multiple sources. As a result, the isolation of the desired vibration source from other vibration sources becomes a challenging problem if only one transducer is employed to sample the single-channel signal mixture. Blind equalization based methods, such as the eigenvector algorithm (EVA), are potentially capable of recovering each of the vibration sources through setting different equalizer lengths. However, selection of an appropriate equalizer length is rarely reported by a systematical method. To determine the appropriate equalizer length, an improved EVA for extracting sparse equalized signals, such as a cyclic impulsive signal, is developed in this paper. The improved EVA is able to automatically select an appropriate equalizer length for the EVA and adaptively recover the cyclic impulsive signal from multiple vibration sources. Two multi-fault signal mixtures, including a simulated signal and a real vibration signal collected from an industrial machine, are employed to verify the effectiveness of the improved EVA. Comparisons between the original EVA and the improved EVA are done. The results demonstrate that the improved EVA is effective on automatic selection of the appropriate equalizer length and adaptive recovery of the cyclic impulsive signal of interest from the single-channel multi-fault signal mixture. Finally, the improved EVA is generalized to extract different kinds of signals.
Early damage detection not only improves the safety and reliability of structures but also reduces maintenance cost. However, damage detection is difficult to implement in large structures under ambient excitation because of the limitation of sensors, the uncertainty of ambient excitation, and the global properties of modal frequencies and displacement modes. This paper proposes a new damage detection method that employs the real encoding multi-swarm particle swarm optimization algorithm and fitness functions evolved from strain modes to find the optimal match between measured and simulated modal parameters and to determine the actual condition of structures. The proposed method requires low-frequency modes and incomplete modes and does not require mass normalization of parameters, thus making the method suitable for nondestructive dynamic damage detection of large structures under ambient excitation. Taking a concrete guide wall structure as an example, this paper studied the global searching performance and the sensitivity of the proposed method. The efficiency of the proposed method was analyzed by using different noise levels and sensor numbers. Results show that the proposed method is effective and can be applied in many types of large structures.
This paper presents the position control of a shape memory alloy (SMA) wire actuator by measuring the load generated by the SMA and using a neural network as an estimator for displacement. The experimentation facility is designed and developed for the position control of the SMA. Gain scheduled proportional integral (GSPI) and pulse width modulated GSPI controllers are designed and implemented. The closed-loop performance of the position control system using the displacement estimated from the load measurement is the same as the performance obtained with the direct position feedback. The position control of the SMA actuator using the SMA load with the neural network estimator is an easily implementable method that does not affect the frequency of operation of the SMA actuator.
This paper deals with irrational transfer functions having monotonic nondecreasing step responses. Firstly, some results on the monotonicity of step responses in irrational transfer functions describing fractional- or distributed-order systems are presented. Then, some conditions guaranteeing the existence of monotonic nondecreasing step responses in more general forms of irrational transfer functions are found. Various examples are brought to show the usefulness of the obtained results in time response analysis of fractional/distributed-order systems. The achievements of the paper can be used in the design of control systems having monotonic step responses.
To suppress unbalanced vibrations of low-speed rotors suspended by magnetic bearings, such as a magnetically suspended flywheel, an autobalancing control method based on elimination of synchronous force has been applied. But its precision may decrease for high-speed rotors such as magnetically suspended control moment gyros. The reason is that the low-pass characteristic of an amplifier in a magnetic bearing control system causes errors in the force elimination. Moreover, this low-pass characteristic increases with rotational speed. To resolve this problem, we propose an autobalancing control scheme using adaptive feedforward compensation based on a least mean square (LMS) algorithm. In this LMS algorithm, two input signals are synchronous displacement and its orthogonal signal. The weights of the input signals are introduced into the algorithm. They are updated in the principle of least mean square to minimize the error between actual and reference values of synchronous current. In simulation and experiments, this method reduces synchronous vibration to less than 40% of that with conventional proportional feedforward. The results demonstrate that this method counteracts the negative effect of low-pass characteristics of an amplifier adaptively and suppresses the synchronous vibration force more precisely. Accordingly, high-precision autobalancing of high-speed rotors can be achieved.
This paper introduces a new Matlab toolbox for the numerical solution of power law frequency-dependent damped vibration and dissipative wave equations involving the positive fractional time derivative. The classical integer-order derivative models have long encountered huge difficulty in describing such complex thermoviscous behaviors, particularly if a broadband excitation is involved. Recent decades have seen a growing interest in the fractional derivative modeling of such anomalous viscosity. Among various time fractional derivative models, the positive fractional derivative model has clear advantages to hold causality of wave problems thanks to its positive definition. However, the numerical methods and software available today are mostly for the standard fractional derivative equations. This paper will present a finite difference method for positive fractional vibration and acoustic equations, and then focus on a new Matlab toolbox of its implementations, which is very easy to use with a friendly graphical user interface. The toolbox is freely available as an open source software and will help promote the application of the positive fractional derivative models to diverse dynamic problems where the viscosity plays an essential role.
This paper presents a theoretical and experimental investigation on a flexible robotic arm. The dynamic processes of the arm involve flexible and rigid motion components. The associated dynamic equations can be decomposed into two corresponding subsets that form the basis for the proposed decomposed dynamic controller for a flexible robotic arm. One-link and two-link manipulators are used in experimental investigations to examine the accuracy of the theoretical analysis of the robotic arms. Finally, a comparison between the experimental and calculated results is made to verify the effectiveness of the proposed controller.
Information technology (IT) literacy is associated in current society by collecting the latest information from the internet. Learning how to use IT tools for practical applications is becoming a basic part of engineers’ literacy. Results reveal that most engineers are capable of using and operating IT facilities, and few engineers are willing to use them frequently. Perceived ease of use reveals that there is a distance between ease of use and practical activities. The general capacity of information of engineers correlates with perceived usefulness. Engineers with IT experiences tend to be more willing to accept IT facilities. Subjective norms show a considerably low relationship with use intention. Other people barely affect a person’s intention to use IT facilities. For perceived behavioral control (PBC), IT resources and the ability of a computer also affect the intention to using IT facilities.
In conventional displacement-based finite element formulation, the nodal transverse deflections and slopes of a beam element are used to approximate its transverse deflection distribution. In this paper, a curvature-based finite element formulation is presented for dynamic modeling of planar multi-link flexible manipulators. This formulation approximates the curvature distribution of the Euler-Bernoulli beam element by using its nodal curvatures. Therefore, in the curvature-based finite element formulation, fewer numbers of total elastic degrees of freedom for the system are needed. In addition, while the displacement-based finite element formulation yields discontinuous bending stresses at the inter-element nodes, this modeling provides continuous bending stress at those nodes. The proposed modeling will be verified and the dynamic behavior of the flexible planar manipulators will be studied.
A theoretical model of a base system consisting of two isolators and a beam is established. To improve the isolation performance of the base system, distributed dynamic vibration absorbers (DDVA) are attached to the beam to reduce at each single frequency in the frequency range of interest. A transfer matrix method which uses mobility or impedance is adopted to calculate the force transfer rate of the base system. Detailed expressions of the mobility formulae are given for isolators, for DDVA and for the Euler beam on which only a flexural wave propagates. The dynamic transfer matrixes of each substructure are obtained and the force transmitted to the foundation is calculated. The effects of DDVA and the isolators’ parameters on the force transfer rate of the base system are discussed in detail. Experiment results of the base system and the combined base system are presented to validate the theoretical results.
This study employs the digital signal processor control dsPIC30f4011 fabricated by the Microchip Company to be a control for a DC motor and a stepping motor. With DC motor control we obtain the potential of the variable resistor by a high speed digital to analog dsPIC converter for the input rotational speed setup. Through a dsPIC input trapping module and a pulse wave for the circuit breaker in the read DC-motor-end, we can acquire the actual motor rotational speed. After comparing the actual rotational speed with the setup rotational speed, a proportional-integral-derivate control mode and module for motor control of the pulse width modulation (PWM) to the dsPIC30f4011 can be employed to quickly adjust the rotational speed to the steady setup rotational speed. While loading, the actual rotational speed will descend. A program repeats the above action, quickly adjusting the rotational speed to again steady the setup rotational speed, voluntarily. This would reach the goal of pacing to finish control of a close/loop circuit in the DC motor. For the stepping motor control we apply basic I/O control in the dsPIC30f4011 to the output forward/reverse rotation to control the pulse wave. The rotational speed and forward/reverse control of the stepping motor, the single step and continuous modes in the control mode, and the status of the stepping motor represented in the LCD allow users to realize the current running condition of the stepping motor.
In this paper, we bring attention to synchronization between a fractional-order chaotic system and an integer order chaotic system, which is very challenging because it can form a bridge between a fractional-order chaotic system and an integer order chaotic system. More specifically, we present a general form of a class of chaotic system, which can be synchronized between a fractional-order chaotic system and an integer order chaotic system. Furthermore, an example is carried out to verify and demonstrate the effectiveness of the proposed control scheme. Simultaneously, our work is supported by logical theorems and intuitive numerical simulation.
The acoustic spectra of noise radiation from a turbulent non-premixed inverse diffusion flame were measured and the effect of the point of observation, air jet Reynolds number and overall equivalence ratio on the spectra were examined. The tests were conducted in a wide range of air and fuel flow rates and both the non-reacting and reacting cases were considered and discussed. For the non-reacting case, the noise emitted from the cold flow is mainly generated by the central air jet, with only a small role played by the fuel jets. The dominance of the noise produced by the air jet is confirmed by the observation that the cold flow noise is a strong function of the air jet flow rate or air jet Reynolds number. The spectral features of the noise from the combusting flames differ significantly from those of the cold flow noise due to the chemical reactions. Upon combustion, the noise radiated from the flames significantly overwhelms the corresponding cold flow noise in the range of frequency under consideration (80–3000 Hz). The distance of the point of observation only affects the magnitude of the sound pressure level while both the shape and magnitude of the sound pressure level are influenced by the azimuth of the point observation. The total sound pressure level increases with Re, while the effect of FE on the total sound radiation level indicates that the highest level of noise occurs as complete combustion is approached.
Using the procedure suggested by Dafermos, we are expanding the classical and known Visik's result and prove the existence and uniqueness of a finite energy solution, in the context of the thermoelasticity of porous materials. Also, some additional smoothness assumptions required for the controllability of this solution are investigated.
The present investigation is concerned with interaction due to a mechanical source in transversely isotropic micropolar elastic media, determined using the finite element method. A particular type of normal force has been taken to illustrate the utility of the approach. The components of displacement, stress and microrotation are obtained and depicted graphically for a specific model. A special case of interest is also deduced from the present investigation.
A new method, namely Impact-synchronous Modal Analysis (ISMA), utilizing the modal extraction technique commonly used in Experimental Modal Analysis performed in the presence of the ambient forces, is proposed. In ISMA, the extraction is performed while the machine is running, utilized Impact-synchronous Time Averaging prior to performing the Fast Fourier Transform. The number of averages had a very important effect when applying ISMA on structures with dominant periodic responses of cyclic loads and ambient excitation. With a sufficient number of impacts, all the unaccounted forces were diminished, leaving only the response due to the impacts. This study demonstrated the effectiveness of averages taken in the determination of dynamic characteristics of a machine while in different rotating speeds. At low operating speeds that coincided with the lower natural modes, ISMA with a high number of impacts determined the dynamic characteristics of the system successfully. Meanwhile, at operating speeds that were away from any natural modes, ISMA with a moderate number of averages taken was sufficient to extract the modal parameters. Finally for high-speed machines, ISMA with a high number of impacts taken has limitations in extracting natural modes close to the operating speed.
Starting from the kicked equations of motion with fractional derivatives, we obtain the fractional discrete maps. Then, we mainly show the chaotic vibration of the fractional discrete maps, the Zaslavsky map and logistic map, and their chaotic behaviors.
Dynamic vibration absorbers are efficient devices used in vibration and noise control of several mechanical systems. In recent years, some studies about these control devices comprising systems with nonlinear characteristics have emerged. In those cases, either the primary system or the dynamic absorber, or even both, can be nonlinear in terms of their stiffness. On the other hand, the absorber damping is generally modeled as viscous. The viscous damping model is widely used in numerical simulations but is very difficult to achieve in real situations. An alternative is the use of viscoelastic damping models, which brings flexibility for vibration control actions. In this work, a methodology to optimally design a viscoelastic dynamic vibration absorber when attached to a nonlinear single-degree-of-freedom system will be presented. The mathematical formulation of the problem is based on the generalized equivalent parameters concept along with the harmonic balance method. The cubic nonlinearity is considered in the primary system and the viscoelastic material is represented by the four-parameter fractional derivative model. Numerical simulations to find the optimal parameters of the absorber are performed for three different types of viscoelastic materials using nonlinear optimization techniques. For some conditions, the results show that the viscoelastic absorber "linearizes" the compound system when this device is properly designed and attached to it. This is mainly due to the reaction forces introduced by the absorber and the large dissipation of vibratory energy introduced by the viscoelastic material. A study of the stability of the compound system reveals that, for most of the time, the periodic solution remains stable for the whole frequency range of concern.
In this study, shimmy of a nose landing gear model with torsional degree of freedom is analyzed. Equations governing the torsional nose landing gear model and the stretched string tire model are presented. Freeplay is incorporated into the model. A magnetorheological (MR) damper modeled using the current–dependent Bouc–Wen model is introduced to the torsional landing gear model with and without freeplay. Parameter identification of the Bouc–Wen model is accomplished using genetic algorithms. Incorporation of an MR damper into the landing gear model with and without freeplay is the advantage in this study. Implementation of the current–dependent Bouc–Wen model in such a landing gear model is another brand new concept.
The effects of railway car-body flexibility on the dynamic analysis of high-speed trains traveling on bridges are studied. The flexible car-body is modeled as a uniform beam supported by the primary and secondary suspensions. A parametric sensitivity study is carried out to examine the effects of different parameters, namely the track irregularity, rail joint, traveling speed and the wheel flat, on the dynamic responses of the car-body and bridge. The rail surface roughness is regenerated by its power spectral density. Different types of rail joint geometries and wheel imperfections are mathematically modeled and included in the numerical simulation. It is found that the flexural mode shapes of the body structure can remarkably affect the calculated ride comfort index especially in the low frequency range.
The purpose of this study is to describe a practical Blackboard system that can be applied by schools; users can manage their own information and access via the internet. The Blackboard system can help users to manage tasks quickly and share data conveniently through simple steps that are implemented in tools of this information system. In addition, this Blackboard system offers a simple communication interface through Email and a quick searching function to establish contact with other members. Such a system could provide several functions designed to increase the users’ conveniences and efficiency.
An ideal engine mount should provide a dual behavior. It needs to be soft to reduce the transmitted force, and to be hard to limit the relative displacement. The constant parameter linear mounts are unable to provide a good isolation when the excitation frequency is variable. Hydraulic engine mounts were invented as smart isolators to passively produce a soft isolator at low amplitude and a hard isolator at high amplitude. Having a dual behavior puts the mounts in the domain of nonlinear systems which in turn causes many new phenomena which have never appeared in linear analysis. The dual behavior hydraulic engine mounts were introduced around 1980 and passed through many analytic and technical improvements. This article will review these improvements up to 2012 and discusses the technical problems and methods of remedy.
This paper presents a new global terminal sliding mode control (GTSMC) methodology for the simultaneous positioning and vibration suppression of slewing a flexible-link manipulator. The proposed control scheme is realized using only a joint actuator without an extra actuator (for example, the widely used piezoelectric zirconate titanate), and the non-minimum phase vibration control problem is solved. Firstly, based on the differential geometry method, the initial dynamic system is decomposed into two subsystems, namely an input-output subsystem and a zero-dynamics subsystem. Secondly, a continuous GTSMC strategy without chattering phenomenon is designed for the input-output subsystem, and the limited convergence time is deduced. Moreover, the eigenvalues of the zero-dynamics subsystem can be pointed by setting proper controller parameters for Lyapunov asymptotical stability. Finally, simulation and experimental results demonstrated the efficacy and feasibility of the proposed control methodology.
Active vibration control of cable net structures is becoming significant when large-size cable net structures are widely applied in various engineering fields, especially in satellite antennas. The placement of actuators and sensors will have a major influence on the control efficiency. This paper develops an H2-norm strategy for the optimal placement of sensors/actuators in controlled flexible cable net structures with active cables constructed by incorporating piezoelectric actuator into flexible cables. The dynamic model of cable net structures with active cables is established using a finite-element method. The optimization indexes for actuator and sensor locations are unified to an H2-norm of the closed-loop transfer matrix from the disturbance to the controlled output. A genetic algorithm is used to solve the resulting nonlinear optimization problem. The numerical examples of the flexible cable net structure widely applied to the parabolic reflectors of space antennas have been analyzed, and the results show that the proposed computational scheme is effectiveness for the optimal sensors/actuator placement problem of cable net structures with active cables.
In this paper, a novel modified function projective lag synchronization (MFPLS) for fractional-order chaotic (hyperchaotic) systems is proposed. Considering fractional derivatives do not satisfy the Leibniz product rule, as it is known in integer-order calculus, it is difficult to achieve the synchronization with a scaling function between the drive and response systems in the time domain. In this paper, we construct the equivalent integer-order systems based on the Laplace transform and make numerical calculation. By means of the Lyapunov stability theory, an adaptive controller is designed to achieve MFPLS for the transformed systems. According to the mapping relationship between the original and transformed systems, MFPLS for the fractional-order chaotic systems is achieved. Theoretical proof and numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.
The nonlinear motion of the Spar platform hull is studied by numerical simulation and model experiment in this paper. The nonlinear differential equation for a coupled heave-pitch of a platform hull is established in a regular wave. The bifurcation pictures of response amplitude with wave frequency variation, Poincare’ maps and time histories are calculated to study the nonlinear dynamical behaviors of the platform hull. The parameters domain for unstable pitch motion is calculated numerically. It is found that the platform motion is sensitive to wave frequency. With the changing of wave frequency the platform exhibits harmonic motion, twice super-harmonic motion, 1/2 sub-harmonic motion, quasi-periodic motion and chaotic motion. The nonlinear 1/2 sub-harmonic motion and the parameter domain for unstable pitch motion are qualitatively verified by the model experiment.
At present, owing predominantly to advances in measurement technology and microprocessor control, development of a new generation of smart materials may lead to widespread adoption of semi-active damping systems into everyday life. An important class of such materials includes so-called "intelligent" magneto-rheological. A dominant feature of these materials is that their physical properties can be altered relatively easily under the influence of an external magnetic field. In this paper, a simplified model of a vehicle equipped with in-time controlled semi-active magneto-rheological suspension system is presented. Moreover, simple algorithms employed to control it are described and their efficacy studied by computer simulation and direct experiment.
Torsional as well as reciprocating vibration magneto-rheological dampers (MRD) were used as in-time semi-active controls. In addition, a magneto-rheological rotary brake (MRB) was employed as a torsional vibration damper. As a result of direct experiments and simulations we were able to obtain characteristics of both devices showing dissipative features and relationship between model parameters.
The main goal of this paper is to present methods for assessing the impact of changes in properties of MRD and MRB dampers for a reduction in variations in vertical wheel forces. These properties are controlled by demonstrated optimization algorithm responsible for an optimal selection of friction in magneto-rheological dampers. Also, an optimization criterion has been proposed.
A control algorithm presented in this paper has been verified by means of conducting an extensive experimental investigation employing a Ford Transit van. Based on the results of our numerical and experimental studies it has been proved that through properties changes in MRD and MRB dampers it had been possible to reduce the variations in vertical wheel forces. Thus, an increase in the safety of the vehicle is possible.
Leaves are mainly responsible for food production in vascular plants. Studying individual leaves can reveal important characteristics of the whole plant, namely its health condition, nutrient status, the presence of viruses and rooting ability. One technique that has been used for this purpose is Electrical Impedance Spectroscopy, which consists of determining the electrical impedance spectrum of the leaf.
In this paper we use EIS and apply the tools of Fractional Calculus to model and characterize six species. Two modeling approaches are proposed: firstly, Resistance, Inductance, Capacitance electrical networks are used to approximate the leaves’ impedance spectra; afterwards, fractional-order transfer functions are considered. In both cases the model parameters can be correlated with physical characteristics of the leaves.
This paper presents a stability study of linear time-invariant and periodic systems with time delay. The methods of semi-discretization, continuous time approximation and Lyapunov stability theory are used to study the stability of two benchmark systems. It is found that for linear time-invariant systems, the Lyapunov method is usually conservative leading to a much smaller domain of stability in a parameter space than the true solution, with the exception of the complete Lyapunov functional due to Gu, which gives highly accurate predictions with little conservatism. For periodic systems, it is difficult to find appropriate Lyapunov–Krasovskii functionals. Numerical methods such as semi-discretization and continuous time approximation are more appealing, and can compute geometrically complex stability boundaries in the parameter space with high accuracy.
A novel method is developed incorporating a special input sequence for a general class of observable and reachable bilinear system identification. An order reduction scheme is introduced to determine the system matrices. This method makes a significant improvement to its predecessors by removing the observability requirement for the linear part of the bilinear systems. Numerical examples are given to demonstrate the method developed in this paper.
Aeroelastic instability may occur in aircraft during flight, therefore their prediction represents an important issue within aerospace engineering. Experimental aeroelasticity is still an important field in providing the tools to validate and understand instability phenomena analysis. As many industrial practices require fast evaluations of critical conditions, e.g. flight flutter testing, there exists a natural demand for on-line aeroelastic identification. A number of different methods have been proposed to characterize systems, but recently those showing most success for on-line identification have been based on subspace approaches. The eigensystem realization algorithm (ERA) represents one of the first subspace methods for identification, with the advantage of dealing with multi-input, multi-output data. However, its need for repeated application of the singular value decomposition and a dependence on impulse response functions implies limitations to on-line identification. Generalization studies of the ERA method have led to recursive forms of that algorithm. A recursive form closely related to ERA has been developed in terms of a modified batch estimation approach, and it is denoted as the extended eigensystem realization algorithm (EERA). This work presents results on the application of extended EERA method viewing on-line aeroelastic parameters identification of an experimental apparatus in the wind tunnel. Designed to reproduce the conditions for typical section aeroelastic behavior, an apparatus has been used to show the EERA capabilities in identifying on-line aeroelastic frequency and damping parameters. Results have shown that the approach is robust and adequate for aeroelastic characterization during experimental activities.
Blasting is still an economical and viable method for rock excavation in mining and civil works projects. Ground vibration generated due to blasting is an undesirable phenomenon which is harmful for the nearby inhabitants and dwellings and should be prevented. In this study, an attempt has been made to predict the blast-induced ground vibration and frequency by incorporating rock properties, blast design and explosive parameters using the general regression neural network (GRNN) technique. To validate this methodology, the predictions obtained were compared with those obtained using the artificial neural network (ANN) model as well as by multivariate regression analysis (MVRA). Among all the methods, GRNN provides excellent predictions with a high degree of correlation.
In this paper, a novel particle swarm optimization maximum power point tracking (MPPT) control method is presented to gain the maximum power point of photovoltaic (PV) power, which is based on the direct current voltage superposition principle to predict the output characteristic of a PV array at partial shading. The proposed control method conveniently can be used in the real-time MPPT control strategy for large-scale PV systems, and with the implementation of the collect circuit it is easy to gain the global peak of multiple PV arrays, thereby resulting in lower cost and higher overall efficiency. The proposed method is proved by using simulation results.
The integrated optimization of structure and control systems is investigated for n interconnected building structures subjected to earthquake. The vibration control model is established for the interconnected building structures, and optimal stiffness and damping parameters of assigned passive controllers are calculated based on LQR algorithm and an equivalent control effect strategy in the frequency domain. The integrated optimization model of structure and control, including design variables, the objective function and constraint function, is built. The design variables are size parameters of structural elements, the parameters of the weighted matrix, and the number and locations of passive controllers. The maximal displacement of the controlled system in the time domain and the energy index in the frequency domain are introduced as the optimized objective functions. A genetic algorithm is adopted to solve this kind of optimization problem with discrete and continuous design variables. The results of a numerical example show that the proposed method is reasonable and effective.
This paper is concerned with the design of vibration absorbers for the reduction of the transient vibration in systems. The classical absorber setup is considered first where the absorber is attached to the primary system. Then, a modified setup is proposed where the primary system is attached to the absorber and the latter is attached to the ground. The objective is to reduce the transient vibration of the system, which can be achieved by minimizing its time constant. First, the problem is solved numerically and several observations are made to facilitate the analytical derivation of the optimal parameters. Then, the analytical expressions of the optimal parameters are written in terms of the system damping and mass ratios. It is shown that for both setups, an optimal mass ratio exists for which the absorbers reach their utmost performances. However, the optimal mass ratio of the classical setup is too large to be considered a feasible solution and therefore it is ignored. For highly damped systems, both absorbers proved to have low performances. The two setups are compared and it is shown that the proposed absorber can achieve time constants lower than those attained with the classical setup. Numerical examples are considered to illustrate the effectiveness of the designs.
This research investigates people’s willingness to use LEGO Mindstorms robotics by synthesizing the task-technology fit, the theory of planned behavior, the technology acceptance model, and the flow theory. The results indicate that task characteristics, technology characteristics, individual characteristics, and task-technology fit have significantly positive relationships. Subjects in the technology acceptance mode indicated that perceived usefulness, perceived ease of use, attitude and intention to use have a significant positive relationship. Meanwhile, subjective norms, intrinsic and extrinsic satisfaction and perceived enjoyment indicate a positive intention for learners to use LEGO Mindstorms robotics. Overall, relevant factors using LEGO Mindstorms robotics are found. Therefore, educators should develop prospective subjects through the use of LEGO Mindstorms robotics courses, which are an effective support in learning.
The issue of impulsive stabilization and Hopf bifurcation of a new three-dimensional chaotic system is investigated. This paper derives some sufficient conditions for the stabilization of the system via impulsive control with varying impulsive intervals. By choosing an appropriate bifurcation parameter, we prove that a chaotic system undergoes Hopf bifurcation under certain conditions. Some numerical examples are given to support the analytic results.
In recent years, many studies on bipedal walking robots and control algorithms have been conducted. However, different conditions and circumstances that have to be taken into account make the control of biped walking robots a big challenge. This paper proposes the implementation of a new hybrid intelligent control approach for a seven-link biped walking robot to track the specified trajectory based on a compensatory neurofuzzy network and fuzzy controller. This algorithm consists of two main parts: the feedforward compensator includes an integrated compensatory neurofuzzy network for identification of the inverse dynamics model which attempts to cancel the dynamics of the robot, and the feedback controller which includes a Mamdani-type fuzzy controller to compensate the modeling error and the effect of noise on the system. Moreover, a new style of membership functions distribution for fuzzy controller with noise reduction capability is proposed and its influence on the performance of the robot under noise-free and noisy conditions is investigated. Simulations performed on a biped robot illustrate the methods and their performance. The results confirm the high tracking capability and effectiveness of the proposed control approach.
This paper deals with the problem of multiple crack identification for beam-like structures from a natural vibration mode. A simplified expression for natural vibration modes of a beam with an arbitrary number of cracks has been obtained explicitly in terms of the crack parameters. The obtained solution allows not only a new form of the eigenvalue problem for a multiple cracked beam to be derived, but it is also straightforward to formulate the standard inverse problem of multi crack identification from measured mode shape. The proposed procedure in combination with the well known regularization method enables both location and size of multiple cracks to be consistently identified from the sparsely and noisy measured data. The robustness of the technique that can be called the crack scanning method has been illustrated and validated by the numerical simulation results.
To overcome the limitations of conventional fuzzy logic control strategies, an adaptive fuzzy logic control based on a hybrid Taguchi genetic algorithm is proposed to control the vibration of the magneto-rheological suspension in order to promote ride comfort. A half-car model equipped with two telescopic magneto-rheological dampers is first developed. An adaptive fuzzy logic control based on a hybrid Taguchi genetic algorithm is then formulated on the basis of the developed model. The hybrid Taguchi genetic algorithm is applied to tune the linguistic variables and control rules of the fuzzy logic control. Finally, a road test is carried out to validate the proposed control scheme. For comparison purposes, a conventional fuzzy logic control is also implemented on the test car. The results show that the magneto-rheological suspension system with two control strategies can improve ride comfort, and the proposed control algorithm has better ride improvement than conventional fuzzy logic control.
A numerical method for solving optimal control problems is presented in this work. The method is based on radial basis functions (RBFs) to approximate the solution of the optimal control problems by using collocation method. We applied Legendre–Gauss–Lobatto points for RBFs center nodes to use numerical integration method more easily, then the method of Lagrange multipliers is used to obtain the optimum of the problems. For this purpose different applications of RBFs are used. The differential and integral expressions which arise in the system dynamics, the performance index and the boundary conditions are converted into some algebraic equations which can be solved for the unknown coefficients. Illustrative examples are included to demonstrate the validity and applicability of the technique.
An active control method is proposed to reduce the wind-induced vibration of laminated plates by use of a velocity feedback control strategy. A piezoelectric fiber-reinforced composite sensor and actuator are used to achieve effective active damping in the vibration control. The displacements in the time and frequency domains, as well as the power spectral density and the mean-squared value of the transverse response, are formulated under wind pressure at variable control gain. It is observed in the numerical results that the damping performance of the laminated plate can be significantly improved by using an outside active voltage on the constraining layer. The effects of the fiber orientation angles, both in the base laminated plate and the active piezoelectric fiber-reinforced composite constrained layer, are also discussed.
This paper focuses on an electro-hydraulic servo system, which is derived from a shaking table. It proposes a control scheme based on a back propagation (BP) neural network, whose weights are trained by the particle swarm optimization (PSO) according to the fitness, which is determined by the input and the feedback signals. Each particle of PSO includes weights and thresholds of BP. The movement of each particle is adjusted by its local best-known position and the global best-known position in the searching space. With the update, a satisfactory solution can be achieved. In order to show the performance of the proposed control scheme, the designed network is also trained and tested by BP only. The comparisons between the PSO-BP and BP networks demonstrate that the PSO-BP one has better performance than that of BP, both in convergence speed and in convergence accuracy.
Surface Electromyography (sEMG) is widely used in evaluating the functional status of hands to assist in hand gesture recognition in many fields of treatment and rehabilitation. Multi-channel parallel interfaces (MCPIs) or time-division multiple access (TDMA) interfaces are the main technologies for the man–machine communication medium of sEMG recognition instruments. However, they can also result in a complex circuit connection and noise interference. A hand gesture recognition model based on sEMG signals by using single-mixture source separation and flexible neural trees (FNTs) is a breakthrough model of hand gesture recognition designed to conquer the above defects. It distinguishes itself from the traditional MCPI or TDMA interfaces by more accurate and reliable measurements of signals. Single-mixture source separation by use of ensemble empirical mode decomposition (EEMD), principal component analysis (PCA) and independent component analysis (ICA) is a novel single-input multiple-output (SIMO) blind separation method, which can simplify the two interfaces described above. The FNT model is generated and evolved based on the pre-defined simple instruction sets, which can solve the highly structure dependent problem of the artificial neural network. The testing has been conducted using several experiments conducted with five participants. The EEMD-PCA-ICA algorithm can blind separate single mixed signals with higher cross-correlation and lower relative root mean squared error. The results indicate that the model is able to classify four different hand gestures up to 97.48% accuracy.
A passive and adaptive control method for stabilizing a pipe conveying fluid is presented. Owing to fluid–pipe interactions, pipes are subjected to excessive vibrations. Classical passive control methods are only valid for stabilizing the pipes over a narrow range of flow velocities. In this paper, the theory of nonlinear targeted energy transfer (TET) is applied to suppress the excessive vibration of a pipe by using an essentially nonlinear attachment, which is called a nonlinear energy sink (NES). Numerical evidence for a passive TET between the pipe and NES is proposed. Results show that the NES can robustly absorb and dissipate a major portion of the vibrational energy of the pipe.
Slab tracks are widely used worldwide in high-speed railways. In order to investigate the dynamic behavior of the train and slab track coupling system, a new approach, based on conceptions of the vehicle element and track element, is developed with finite elements in a moving frame of reference. By discretizing the slab track subsystem into track elements that flow with the moving vehicle, the proposed method eliminates the need for keeping track of the vehicle position with respect to the track model. The governing equations are formulated in a coordinate system traveling at a constant velocity, and the associated stiffness matrix, mass matrix and damping matrix for the track element in a moving frame of reference are derived. The vehicle element is introduced to model a car with primary and secondary suspension systems, which has 26 degrees of freedom, where 10 degrees of freedom are used to describe the vertical movement of the car, and 16 degrees of freedom are associated with the rail displacements. In the numerical study, four cases of application examples are presented taking into consideration the effects of track roughness, train speed and track parameters. The numerical solutions compare favorably with the results obtained by alternative methods. The method is shown to work for varying train speed and track parameters, and has several advantages over the conventional finite element method in a fixed system of reference.
This paper proposes robust loop-shaping techniques for a two-axis nano-positioning piezoelectric stage. Piezoelectric transducers are usually used to drive precision mechanisms because of their favorable properties, such as high resolution, high accuracy, and large driving force. However, the nonlinear characteristics of piezoelectric materials can degrade system performance. Therefore, we model a piezoelectric stage as a linear system, and regard its nonlinear factors as system uncertainties. Because robust control can guarantee stability and performance for systems with uncertainties and disturbances, we apply loop-shaping techniques and design standard robust controllers for the stage. In addition, we consider fixed-order robust control for the system in that controllers with lower orders are preferred for hardware implementation. Lastly, the designed controllers are implemented for experimental verification. The results demonstrate the effectiveness of these robust controllers in tracking reference signals and suppressing high-frequency vibrations.
Modern machinery and manufacturing systems are committed to be more accurate and punctual in delivery, which in turn requires a perfect machining and maintenance system. Maintenance has many indispensable tasks, of which vibration control is one of the most challenging for maintenance engineers. Majorly in rotating machinery like gears and turbines, vibration is the predominant factor to be controlled. Hence this paper deals with a novel way of controlling the vibration in spur gears. Generally gear vibrations can be reduced by profile modification or by decreasing the pressure angle or dynamic load and also by means of increasing the contact ratio. In this work, a profile modification is considered. A groove has been generated at the bottom land of the gear in order to increase the thickness and height of the gear tooth at the root. Due to this, the stiffness of the gear tooth at the bottom land of the gear increases which in turn reduces the radial load deflection and the vibration amplitude in the vertical direction (shaft bending direction). Two spur gears (gear A and gear B) having the same gear parameters are selected. In gear B, a groove has been generated at the bottom land. Both the gears are discretized and analyzed by FEA software. The analysis is made under frequency response to identify the amplitude of vibration of the gears due to transmitted (tangential) load and radial load for the existing gear (gear A) and the modified one (gear B). The result shows that the modified gear has a better control in the radial load direction. Hence an increase in the tooth depth within a limit ensures that the control of magnitude of the vibration is effective. Finally, experimental analysis has been done to validate the computational data and the results are in good agreement.
Impact models of two colliding bodies are usually generated by fundamental physical and geometrical principles. Initially, the number of unknown variables is not the same as the number of equations expressing the principles, so the models should be complemented with an appropriate set of constitutive equations which contain enough information on the physical properties of the system and therefore allow accurate predictions of its behavior. Along these lines we here discuss a problem when a block, moving along a line on a dry surface, impinges against another block being at rest, through a deformable straight rod of negligible mass. Among the variety of all possible choices that can be used, we suggest the constitutive model of the viscoelastic body with fractional derivatives of stress and strain, restrictions on the coefficients that follow from Clausius–Duhem inequality, and the Coulomb friction law given in the set-valued form. Owing to the presence of dry friction and the proposed fractional model, known as the fractional Zener model, the problem belongs to the class of set-valued fractional differential equations (or multivalued differential equations of arbitrary real order) leading to the equivalent Cauchy problem given in terms of two coupled integro-differential inclusions, for which the existence result ensuring the contractible solution set exists. By use of the combinatorial analysis of the problem, we identify 11 imaginable scripts and separate 10 feasible ones that were confirmed numerically by a procedure that combines nonlocal and nonsmooth modules.
In order to solve a structural multi-damage identification problem, a two-stage damage identification method based on evidence fusion and improved particle swarm optimization (IPSO) is presented. First, structural modal strain energy and frequency are considered as two kinds of information sources. Then, evidence fusion theory is utilized to integrate the two information sources and preliminarily identify structural damage locations. After the damaged locations are determined, particle swarm optimization (PSO) is used to identify the extent of structural damage. Considering that the search efficiency of a basic PSO is still not very good, some improved strategies are presented, such as mutation position iteration formula, micro-search of an elitist, two convergence conditions, etc. The simulation results demonstrate that the proposed two-stage method can estimate the damage locations and extent with good accuracy.
The effects of rotary inertia, shear deformation, and joint model on vibration characteristics of single-story multi-bay planar frame structures are studied in this paper. An exact analytical solution is obtained using a wave vibration approach, in which vibrations are described as waves propagating along uniform structural elements and being reflected and transmitted at structural discontinuities. Both bending and longitudinal vibrations in the multi-bay frames are taken into account. It is found that rotary inertia and shear deformation play an important role in accurately predicting natural frequencies of multi-bay frames at higher frequencies. It is also found that the choice of joint model affects the predicted natural frequencies.
Controlling the lateral movement of buildings under earthquake effects is very important to prevent total collapse and therefore reinforced concrete (RC) shear walls are used to obtain the lateral stability of such buildings. In this study, the usability of partial RC shear walls to strengthen buildings with weak earthquake behavior was investigated. The basic parameters of the study were determined to be the ratio of shear wall height to shear wall length (Hw/Lw) and whether the upper inflection point of the bent bar, a steel bar commonly used in the beams of RC buildings in Turkey, is integrated into or bent outside of the partial shear wall section. Three units of two-story, double-span weak RC frames were produced at a one-third scale. Two of these three frames were then strengthened by partial shear walls integrated on both sides of the central column. Strengthened and non-strengthened specimens were tested under reversed-cyclic lateral loading. The frame systems strengthened via partial RC shear walls showed significant improvement in strength and stiffness. No debonding was observed in the anchorage rods used in the shear wall-foundation connection.
Real-time substructuring is a hybrid technique in which the critical component of the structure is tested, while the remainder is numerically analyzed based on a suitable model. The synchronization between the testing and the analysis is maintained by a controller. This paper proposes a new controller based on fuzzy logic for real-time substructuring applications. The advantage of a fuzzy-logic-based controller is that it is rule based and involves far less computations. The performance of the proposed controller is verified through numerical simulations of a substructured linear and nonlinear single-degree-of-freedom system for two different damping ratios. The performance of the controller is compared with that of conventional controllers which are used in real-time substructuring on the basis of a nondimensional error index. The fuzzy logic controller is found to have the least error index for the chosen nonlinear system and performs satisfactorily for a linear system. Furthermore, the effectiveness of the proposed fuzzy logic controller is demonstrated by numerically evaluating the response of a portal frame pinned at one of the beam column joints for the El-Centro earthquake. The displacement time history response was found to closely match that of the emulated system.
This paper presents a method to identify the root cause of the axial vibration of crankshafts for high speed diesel engines based on an auto-regressive and moving average model and the analytic hierarchy process. Through determining initial moving average variables and measuring axial/bending/torsional vibrations of a crankshaft at the free-end of a four-cylinder diesel engine, auto-regressive spectrum analysis is applied to the measured vibration signal. In an investigation of the root cause of the vibration, the hierarchy tree and judgment matrix are given to identify the main vibration root causes. The results show that the axial vibration of the crankshaft is mainly coupled and excited by the bending vibration at high speeds. But at low speeds, the axial vibration in some frequencies is coupled and excited primarily by the torsional vibration. Through investigation of the root cause of the axial vibration of the engine crankshafts, calculation accuracy of the vibration can be improved significantly.
Based on Reissner’s mixed variational theorem (RMVT), finite cylindrical layer methods (FCLMs) were developed for the three-dimensional (3D) free vibration analysis of simply supported, functionally graded material (FGM) sandwich circular hollow cylinders. The FGM sandwich cylinder consists of a thick and soft FGM core bounded with two thin and stiff homogeneous material face sheets, in which the material properties of the FGM core are assumed to obey an exponent-law varying exponentially with the thickness coordinate. In this formulation, the FGM sandwich cylinder is divided into a number of equal-thickness cylindrical layers, where the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-surface variations of the field variables of each individual layer, respectively. An h-refinement process instead of a p-refinement one is adopted to yield the convergent solutions in this study, and the layerwise linear, quadratic or cubic function distribution through the thickness coordinate is thus assumed for the related field variables. The accuracy and convergence of the RMVT-based FCLMs developed in this article are assessed by comparing their solutions with the exact 3D solutions available in the literature.
This paper mainly analyzes the chaotic phenomenon of a permanent magnet synchronous motor (PMSM) when the PMSM is turned off and the research parameters of PMSM identify the effect of chaotic phenomenon of PMSM. Hamilton-Jacobi-Bellman (HJB) equation is introduced and a proposed optimal control technique based on HJB equation to control chaos in PMSM. Based on HJB equation, the problem of the design optimal controller is summarized as that of partial differential equations. And then the optimal controller is got by constructing Lyapunov function. In theory, a chaotic system can be controlled to any expected state using this scheme. Applying this scheme to control the chaos of PMSM when the PMSM is turned off, the PMSM can be asymptotically stable to zero point. Numerical simulations further test the effectiveness of the theoretical analysis.
The rolling bearing fault signal under strong background noise is very weak because of environmental noise impaction and the attenuation of signal. The feature extraction of rolling bearings’ weak fault is very important in avoiding serious disaster, but it is also very difficult. Sparse decomposition has been used in the fault feature extraction of rolling bearings. But its performance is very poor when the background noise is very strong. This text combines the minimum entropy de-convolution (MED) and sparse decomposition to extract the feature of a rolling bearing’s weak fault. Firstly, the rolling bearing weak fault signal with strong background noise is de-noised using the MED method, and subsequently the de-noised signal is handled by sparse decomposition. Finally, the fault feature extraction method-envelope demodulation is carried on the last given signal and better results are obtained. In conclusion, through simulation and experiment the effectiveness and the feasibility of the proposed method are verified.
This paper aims at developing a model based on theoretical first principles involving nonlinear equations for the coupled heave and pitch dynamics of surface vehicles that is suitable for evaluating planar motion control strategies. The model developed uses a novel approach of representing the ship dynamics in the frequency domain that provides greater insight to the surface vehicle’s behavior over a wider operating range than the traditional time domain models. The theoretical model was validated by experimental data that was obtained from tow tank experiments. The theoretical model results compared well with the experimental data.
This paper is concerned with the construction of biorthogonal multiwavelet basis in the unit interval to form a biorthogonal flatlet multiwavelet system. Next a method to calculate integer and fractional derivatives of the dual flatlet multiwavelets by multiplying some matrices is suggested. The system is then used to solve a fractional convection–diffusion equation. The biorthogonality and high vanishing moments properties of this system result in efficient and accurate solutions. Finally, numerical results for some test problems with known solutions are presented and the absolute errors are compared with the errors resulting from the other bases.
In the present work, we study the propagation of time harmonic waves in an infinite thermo-viscoelastic material with voids. Four basic waves traveling with distinct speeds are found, out of which, one is a shear wave, and the remaining three are dilatational waves. All the dilatational waves are found to be coupled due to the presence of voids and thermal properties of the material, while the shear wave is found to be uncoupled and travels independently with the speed that exists in a linear viscoelastic medium. The speeds of propagation of all the waves are found to be complex valued and frequency dependent. Reflection phenomena of these waves from a mechanically stress-free and thermally insulated plane boundary of a thermo-viscoelastic half-space with voids have been investigated. Formulae for amplitudes and energy ratios corresponding to various reflected waves have been obtained and are presented in closed form. Numerical computations are performed for a specific model, and the results obtained are depicted graphically.
This paper presents a problem-solving procedure regarding brake-drum noise issues performed by engineers within a short time period and additional measures to be taken for avoiding similar issues in the future. Cimos TAM Ai company is a member of Cimos Group, which is a component producer in the automotive industry. We have taken the production of the rear brake-drums during the phase of the car manufacturing (transfer of production). Soon after the instigation of this production, the customer reported squealing issues with the brake-drums. No detailed information was received about the issue except that it occurred on new cars during everyday operation. It was our goal to find the root cause, fix the issue and take some preventive actions. Research was based on comparing the Cimos brake-drum (B) with the brake-drum of previous supplier (A). The research was focused on resonant frequency of the brake-drum as the most likely parameter connected to the squealing. First the natural frequency of drums A and B was determined by impact-hammer test. Then a numerical simulation was carried out with the goal of detecting the most problematic surface of the drum for causing the squealing. A weakness was found in the brake-drum design where no thickness or tolerance was specified at the critical area, and large deviations existed between the finished brake-drums. The problem was solved by changing the machining parameters. Besides solving the noise problem, an in-depth investigation was conducted into the gray cast-iron modulus of elasticity, in order to find a representative value for those small deformations occurring in cases dealing with noise-emission issues. This value proved to be higher than in the case of larger deformations as considered during mechanical and temperature behavior simulations.
Nowadays, LEGO Mindstorms robotics is widely used on campus to develop interactive teaching and learning. A well-developed learning material with the application of LEGO Mindstorms robotics can inaugurate efficient learning which can be used to motivate students of all ages in the learning process. The research investigates the willingness of subjects’ using LEGO Mindstorms robotics in learning by synthesizing the task-technology fit, the theory of planned behavior, the technology acceptance model, and the flow theory to explore their intention towards using Lego Mindstorms. Many factors were found that have a positive effect in learning LEGO Mindstorms robotics. The learning process and effectiveness can be influenced. A model formulation process is proposed in the present study.
One of the most widely adopted strategies for vibration control in both civil and mechanical engineering is based on the use of fuzzy control. Although fuzzy control methods have been successfully applied, there are still some drawbacks to using them in any control scheme. In this work, we address the stability problem of a fuzzy-based neural network (NN) model which is employed to approximate an ecosystem. The dynamics of the NN algorithm are converted into a linear differential inclusion representation for stability analysis. Finally, a stability criterion is derived using the fuzzy Lyapunov method to ensure the stability of the n-degree ecosystem.
In recent years, it has been remarkable to see the increasing number of studies related to the theory and application of fractional-order controllers, especially PIDμ controllers, in many areas of science and engineering. Research activities are focused on developing new analysis and design methods to ensure robustness in new or classical control problems. In this paper, we investigate switching systems. A frequency-domain design method is developed for switching systems for both integer- or fractional-order controllers, taking into account specifications regarding performance and robustness and ensuring the quadratic stability of the controlled system. Some examples are given to show the applicability and effectiveness of the proposed tuning method.
We consider the problem of suppressing oscillations of an elastically mounted rigid cylinder undergoing vortex-induced vibrations by linear and nonlinear active velocity feedback controllers. Each controller relies on an actuator, which imparts an opposing force to the cylinder motion, thereby reducing its high-amplitude oscillations. A strongly coupled fluid–structure numerical model is used to solve the fluid–structure interaction equations. The results show that the choice of the active feedback controller depends on the allowable controlled amplitude of the cylinder. It is found that a cubic velocity feedback controller is more efficient than its linear velocity counterpart when very small controlled amplitudes are desired.
This paper presents the experimental characterization and vibration control of a flexible robotic system. For this work, a test bench was built to characterize the harmonic drive (HD) and joint components, while control algorithms were designed and compared to minimize vibration. Encoder accuracy was critical since the difference in the measurements between two encoders was used to evaluate the vibrational behavior of the test set-up. Therefore, a laser tracker was used to characterize the error of the output encoder. Real-time compensation using this technique achieved an angular position accuracy of 50 µrad. Four rosette strain gauges were fixed to the HD’s flexible spline to determine its torsion. To reduce torque ripple, a real-time correcting function was applied. It was thus possible to reduce the error to 0.3% of the full-scale error. Two vibration control strategies were developed, namely, singular perturbation and feed-forward control. Simulation results showed that both control strategies greatly reduced vibration response compared to a common rigid control. However, test results showed that good vibration control could only be achieved with the feed-forward approach: the singular perturbation technique generated too much torque ripple to the motor. A feed-forward controller can quickly stabilize the link, achieving the same settling time as with the rigid control algorithm.
Using a combination of the cart-seesaw and the inverted pendulum system, this paper presents a novel laboratory apparatus called the cart-pendulum-seesaw (CPS) system. The proposed pneumatic CPS is a classic example of a super articulated mechanical system. The resulting system has two inputs: a force applied to the cart and another force applied to the loading cart which tries to balance the seesaw test-bed. With two inputs and four available for the measurement outputs, the unstable multi-input-multi-output system offers an interesting control challenge. This study breaks down the system into several tasks, one for pendulum swinging up and the other for seesaw balancing. The pendulum is first swung up; then, balancing the pendulum at the upright position with a fuzzy controller, the seesaw is balanced by another fuzzy controller. This study incorporates a fuzzy coordinator into the seesaw system to take control action in extreme situations. The experimental device is used to evaluate the efficiency of the proposed methodology. Unlike other model-based methods, the proposed fuzzy control methodology does not need an accurate measurement of all state parameters; moreover, it is robust for parameter changes and other disturbances in the system.
Over many years the math model has developed rapidly, especially on internal solitary wave, intelligent robot interaction, artificial intelligence, fuzzy Lyapunov, tension leg platform (TLP), consumer and service quality. However, the math learning attitude is an important element to promote measurement studies. After testing math, it will present whether students who learn math by teaching integrating with math games or traditional teaching were influenced or not. This paper concludes that after accepting varied teaching methods, the result of analysis of covariance in a math learning attitude scale for students in a low score group did not present significance variance (F value: 3.461; p value = 0.078 > 0.05) excluding the scores in a pre-test. It was close to critical value. Hence, students who can accept "teaching integrating with math games" are superior to students who can accept "traditional teaching" in a forward change of math learning attitude.
The optimum design of a base isolation (BI) system in the framework of total probability theory cannot be applied in many real situations when the required detailed information about the uncertain parameters are limited and the maximum possible ranges of variations are only known and can be modeled as an uncertain but bounded type. The interval analysis based bounded design optimization usually applied in such cases are the worst case measures and unsuitable for practical design. Moreover, such a design method does not consider the variation of the performance of an isolated system due to uncertainty and may not correspond to an optimum design yielding maximum performance with its minimum dispersion. The robust optimization requiring only the bounds on the magnitude of the uncertain parameters will be a viable alternative in such situations. The present study deals with the robust optimization of BI system for seismic vibration mitigation of structures characterized by bounded uncertain parameters. The robust optimization is performed by using a two-criteria equivalent optimization problem, where the weighted sum of the nominal value of the maximum root mean square acceleration of the superstructure and its dispersion is optimized. The bounded design optimization is also performed to demonstrate the effectiveness of the proposed robust optimization approach. A five-storied building frame with attached isolator elucidates the effectiveness and importance of the proposed design approach by comparing the present robust optimization results with the results obtained by the bounded design optimization procedure.
The main purpose of this thesis is to develop a small wheeled SUMO robot for use in contests. The main controller of the robot is a microcontroller PIC16F877A which uses Pulse Width Modulation (PWM) signals to drive H-Bridge circuits and control two DC motors. In this study, "actuation", "perception", and "cognition" are at the core of this robot’s functions. The perception function requires the analysis of useful messages detected by the robot’s sensors. The cognition function necessitates finding the solution for these messages and making the decision as to how to respond fittingly. The actuation functions to order the drivers to actuate some essential behaviors for the competitive scenario. These processes must be carried out by the robot autonomously.
Radiofrequency identification (RFID) is currently used in different applications, including robots. Meanwhile, the e-book reader has played as important a role for reading. Therefore, any research combining these may create an innovative service.
The purpose of this study is to develop a mobile robot e-book reader with the application of RFID technology for proving electronic content automatically. Furthermore, users’ attitude and intention toward the system is evaluated by a proposed hybrid mode including Technology Readiness Index (TRI), Technology Acceptance Model (TAM), Expectation Confirmation Model (ECM) and Flow theory to measure users’ adoption to use the platform. The results reveal users’ intention to use the platform.
This paper established a thorough optimization procedure of the multiple tuned-mass-damper system to suppress the vibration levels of the curved beam-type structures with multiple vibration dominant modes. A hybrid optimization methodology, which combines the global optimization method based on the Genetic Algorithm and the local optimization method based on Sequential Quadratic Programming, has been developed. The established hybrid optimization procedure is then utilized to find the optimum values of the design parameters, namely, the spring stiffness, damping factor and the position of the attached tuned-mass-damper systems, in order to suppress the vibration amplitude either at a particular mode or at several modes simultaneously.
The system of generalized Sylvester matrix equations
A1XD1+E1XB1=C1
A2XD2+E2XB2=C2
...
:::
AmXDm+EmXBm=Cm
(including Sylvester and Lyapunov matrix equations as special cases) has nice applications in various branches of control and system theory. In the present paper, we consider this system over the generalized centro-symmetric matrix X. By extending the Jacobi and the Gauss–Seidel iterations and by applying the hierarchical identification principle, we propose a gradient-based iterative algorithm for finding the generalized centro-symmetric solution of the system. It is shown that the iterative algorithm consistently converges to the generalized centro-symmetric solution for any initial generalized centro-symmetric matrix. A numerical experiment is also given to show the effectiveness of the proposed algorithm.
An analysis is presented of the forced vibrations of non-homogeneous rectangular plate of variable thickness on the basis of classical plate theory. The non-homogeneity of the plate material is assumed to arise due to the variation in density which is assumed to vary linearly. The thickness of the plate also varies linearly. Approximate formulae are proposed for estimating the maximum deflection of a rectangular plate subject to a uniformly distributed harmonic lateral load. Maximum deflection for the different values of the fundamental frequency of vibration is computed for a simply supported-free-simply supported-free plate for various values of taper constant, non-homogeneity constant and aspect ratios. Results are presented in graphical form.
The web in the internet nowadays is well-developed, especially while it is coming to the internet of cloud computing. Information is the Web of natural resources. An appointment calendar, a photo album, a health record, a telephone bill an internal solitary wave, an artificial intelligence robot, an intelligent tension leg platform, even consumer and service quality etc. are all natural resource examples. In the study, the site configuration objects are conducted by adopting the site models of scholars’ studies in relation to users’ expectations and mental models. The results revealed that the website function rapidly achieved convenience. A complete organization technique update and social level promotion are performed simultaneously.
Mobile devices are getting increasingly popular and have been widely used in recent years. Many mobile device applications are used in iPads, iPhones, and Android-based phones and devices. Currently, Google Play has more than 300,000 applications, and had more than 10 billion application downloads in December 2010. Meanwhile, game development is expanding fast, whether it is single player games or online games. Therefore, how to combine the learning content with games will be a great help for learning anytime and anywhere.
The purpose of the research is the development of an application program interactive game-based learning system for mobile systems. The system was evaluated by the product performance program evaluation. The results reveal the advantages of the system having a simple appearance for users to understand its contents, and for it to have appropriate instructions as well as explanations with pictures.
This paper presents simulation and experimental studies of controls for time-delayed dynamical systems. An inverted pendulum made by Quanser is used as a model system. We investigate two control design methods: optimal feedback gain with the semi-discretization method and a high-order control design. Both simulations and experiments are carried out to demonstrate the utility of the control. The semi-discretization method offers optimal controls without increasing the dimensions of the gain vector, while high-order control involves an increased number of gains. The disadvantages and advantages of both methods are discussed with the support of simulation and experimental results. This paper highlights the fact that high-order control is determined by an Nth order filter where N is the discretization level. We have also found that the performance of high-order control appears to be insensitive to N.
This paper treats the adaptive synchronization problem of a class of uncertain chaotic systems with uncertainties, delay and unknown inputs in a drive-response framework. A robust adaptive observer-based response system is designed to synchronize a given delayed chaotic system without the knowledge of upper bounds of uncertainties and unknown inputs. Furthermore, the unknown inputs can be approximately recovered directly by the concept of equivalent control signal. To highlight our method, we improve the robustness of ciphering in a secure communication system. Computer simulation is also given for the purpose of illustration and verification.
Carbon nanotube oscillators which can generate frequencies in the gigahertz range have attracted much attention in recent years. A number of studies on double-walled carbon nanotube (DWCNT) oscillators can be found in the literature, while other mechanisms of these oscillators with a higher number of oscillating nanotubes have not been well studied. This paper aims to investigate the motion properties of triple-walled carbon nanotube (TWCNT) oscillators in which the inner and middle tubes have telescopic motions with respect to the outer tube. To this end, the continuum approximation together with the Lennard-Jones potential function is utilized. In comparison with DWCNT oscillators, the triple-walled ones have shown a variety of motion patterns. In this respect, different types of motion patterns are classified and demonstrated. Moreover, it is observed that these nano-oscillators are so sensitive to their initial conditions. For this reason, a phase division of initial separation distances that generate different motion patterns is also presented.
A novel control for a nonlinear two-dimensional (2-D) overhead crane is proposed. Instead of the complex design procedures used in classic methods, the proposed scheme combines the principles of neural networks (NNs) and variable structure systems (VSS) to derive control signals needed to drive the cart smoothly, rapidly and with limited payload swing. The merits include the robustness and model-free properties of the sliding mode and neural based controllers, respectively. Simulations performed using a scaled 2-D mathematical model of the crane confirm the effectiveness of the proposed method.
In general, the tensile forces on hanger cables of a suspension bridge play an important role in evaluating the bridge condition. Two tensile force estimation methods, which are based on a string or cable equation, have been widely applied to estimate the tensile forces by using the measured frequencies on hanger cables. However, both methods are not applicable to short hanger cables because the frequencies of short cables are severely sensitive to flexural rigidity. Thus, in this study the tensile forces of hanger cables, shorter than 10 meters, were estimated by back analysis of the cable frequencies measured from the Gwangan suspension bridge in Korea. To verify the feasibility of back analysis, the results from back analysis and existing methods are compared with the average measured tensile forces after completion. From the comparison, it can be inferred that back analysis results reasonably agree with the average measured tension of the short hanger cable after completion. Therefore, it is concluded that back analysis applied in this study can be an appropriate tool for estimating tensile forces of short hanger cables.
As a first endeavor, the dynamic response of functionally graded (FG) beams under a moving heat source is investigated. The material properties are assumed to be temperature-dependent and graded in the thickness direction. A two-dimensional finite element method (FEM) is employed to obtain the temperature distribution throughout the beam. Then, the effect of a two-dimensional variation of temperature on the dynamic response of an FG beam with arbitrary boundary conditions is formulated based on the first-order shear deformation beam theory (FSDBT). The resulting equations of motion are transformed into a system of algebraic equation by employing the FEM in conjunction with Newmark’s time integration scheme. In order to validate the formulation and method of solution, the exact solution is achieved in the case of isotropic beams with simply supported boundary conditions. It is shown that good agreement exists between the presented approach and the exact solution. Finally, the effect of different parameters on the dynamic response of FG beams under moving heat source is studied.
In this paper we first introduce fractional orthogonal Jacobi functions then we obtain a new fractional derivative operational matrix for these orthogonal functions. It is based on the relationship between the coefficients of the fractional Taylor series and fractional Jacobi function expansions. We also apply this new operational matrix to the collocation method for solving general multi-order fractional differential equations (FDEs) and nonlinear fractional integro–differential equations (FIDEs). We also present several test problems. The numerical results show that our new scheme is very effective and convenient for solving FDEs and FIDEs.
The purpose of this study is to explore the low-frequency advantages and characteristics of the hydraulic mounts used for vibration isolation of an earth-moving machinery cab. For the feature of the cab’s center of mass being relatively high above the cab’s supporting surface, the pitch and roll vibrations of the cab are prone to generate in the low frequency range. A six-degree-of-freedom (d.f.) model of the cab supported by hydraulic mounts with quadratic damping is set up in this paper. And the simulation which compares performance of the hydraulic mounts and the rubber mounts used in the cab is carried out. It shows that the cab system with quadratic damping hydraulic mounts has remarkable efficiency to mitigate the vibrations and in turn to enhance the cab comfort, but its nonlinear damping characteristic has almost no effect on the natural frequencies of the cab system. A new approach is also proposed, which considers the absolute displacement of the pitch motion of the cab besides the traditional absolute accelerations, to improve the indications of the ride comfort for the suspended cab with a high-positioned mass center in the isolation design of the earth-moving machinery cab.
This paper presents two soft computing techniques, fuzzy logic and neural network, to design a new control scheme for switching a shunt active power filter (APF). This control scheme consists of three control loops, namely a voltage loop, current loop and reference generator. The reference current signal generated by this controller is used to generate gating pulses for APF switches. The reference generator is based on neural network or fuzzy logic. The performance of the proposed neural controller is evaluated and compared with a linear control scheme, incorporating a resonant selective linear reference generator. Simulations are carried out using Matlab Simulink and the results show that the proposed system is capable of compensating the harmonic current to a minimum level.
Nowadays, wireless and mobile devices not only change people’s lives but also the demarcation line of web service applications. The mobile is a device for jobs, entertainment and personal computation. The purpose of the current research is to apply interactive theory for exploring and designing an interactive cross platform for mobile devices, PCs, and tablet PCs in robots. It is further tested with two contents, an E-book and a flash game to evaluate its performance. A user-friendly interface is designed with open source software. In the future, the cross platform system will be further developed for education, engineering, and other appliances.
Permanent magnet synchronous motors (PMSM) are widely used in high performance applications demanding smooth torque, accurate speed and position control. However the existing PMSM drive produces high torque ripples. The major challenge is to develop new torque control schemes to minimize the torque ripples so as to suit the application requirements. This paper describes two instantaneous field oriented torque control techniques - 1) Iterative learning controller (ILC) in combination with hysteresis pulse width modulation and 2) Iterative learning controller in combination with space vector pulse width modulation (SVPWM) to reduce torque ripples in PMSM drive. These techniques are simulated for drive performance under different load conditions using the Simulink library in MATLAB Version 10.0 and the results obtained are presented and compared. The simulation results show that the ILC with SVPWM technique has less torque ripples.
Solving the linear system Ax = b is an active area of research in engineering. Many researchers have applied preconditioners to the linear system Ax = b. In this work, we introduce two new preconditioners for solving linear systems. The best property of the introduced preconditioners is that they can be used under weaker conditions than the previous preconditioners in the literature. We propose preconditioned associated accelerated overrelaxation (AOR) iterative methods with these two new preconditioners, and give the corresponding convergence results. Numerical examples show an improvement in the convergence rate of the AOR preconditioned iterative matrices.
Thin-walled structures under thermo-acoustic loadings exhibit a complex nonlinear response which results in high cycle fatigue failure. The aim of the present paper is to analyze the influences of thermal-acoustic excitations on nonlinear dynamics response, and then give the corresponding multi-axial fatigue life estimation. The nonlinear responses of a clamped aluminum plate (2024-T3) under different thermal-acoustic loadings are firstly obtained, which include the response of the plate in pre/post buckled conditions and in snap-through conditions. Then the statistical properties with different temperatures and sound pressure levels are analyzed for further research on nonlinear response dynamics. Based on the thermo-acoustic response obtained, the rain flow matrix scheme is used to determine the distribution of fatigue cycles. Then the Miner accumulative damage model is employed to predict high cycle fatigue life, combined with a non-zero mean stress model. Results show that the fatigue life of a pre-buckled plate decreases with the increase of temperature. For a post-buckled plate, as the temperature increases, the fatigue life of the plate undergoing persistent snap-through keeps decreasing to the lowest point, and then increases after entering an intermittent snap-through regime.
In the present study, the free vibration characteristics of single- and double-walled carbon nanotubes (SWCNTs and DWCNTs) are investigated on the basis of a nonlocal elastic shell model. Eringen’s nonlocal elasticity equations are applied to the classical Donnell shell theory to incorporate the size-effects into the vibration analysis of carbon nanotubes (CNTs). An exact solution is developed for the governing equations of the nonlocal elastic shell model with the inclusion of size effects. Molecular dynamics (MD) simulations are performed to obtain fundamental frequencies of SWCNTs and DWCNTs with different values of aspect ratio and types of chirality. To derive the appropriate values of a nonlocal parameter for vibrations of SWCNTs and DWCNTs, the results of the continuum model are matched with those of MD simulations. This study shows that the small scale effects in the nonlocal model make nanotubes more flexible.
In condition monitoring of mechanical equipment, the collected signals are mostly mixtures of several different sources. It is very important to recover the individual effects of each source for exact feature extraction and further fault diagnosis. A blind separation method based on second-order cyclic statistics is presented for convolved cyclostationary processes such as those observed in rotating machinery. The convolutive mixtures in time domain are transformed into instantaneous mixtures in frequency domain by discrete Fourier transform (DFT). Then the aim is to find a separating matrix that simultaneously and jointly diagonalizes the set of cyclic spectral density (CSD) matrices of the observed signals. Examples of successful separation are provided on both synthetic convolutive mixed bearing signals and real data tested from a gearbox.
Micro-milling is inherently unstable and chattering with aberrational tool vibrations. While the time response is bounded, however, micro-milling can become unstably broadband and chaotic in the frequency domain, inadvertently rendering poor tolerance and frequent tool damage. A novel simultaneous time-frequency control theory is applied to negate the various nonlinear dynamic instabilities including tool chatter and tool resonance displayed by a multi-dimensional, time-delayed micro-milling model. The time and frequency responses of the force and vibration of the model agree well with the experimental results published by Jun et al. A multi-variable control scheme is realized by implementing two independent controllers in parallel to follow a target signal representing the desired micro-milling state of stability. The control of unstable cutting at high spindle speeds ranging from 63,000 to 180,000 rpm and different axial depth-of-cuts are investigated using phase portrait, Poincaré section, and instantaneous frequency (IF). The time-frequency control scheme effectively restores dynamic instabilities, including repelling manifold and chaotic response, back to an attracting limit cycle or periodic motion of reduced vibration amplitude and frequency response. The force magnitude of the dynamically unstable cutting process is also reduced to the range of stable cutting.
This paper considers identification problems for Wiener systems with saturation and dead-zone nonlinearities. The basic idea is to obtain the identification model of such a nonlinear system using a switching function, and to propose a gradient-based iterative identification algorithm using the iterative technique. An example is provided to show the effectiveness of the proposed algorithm.
The longitudinal free vibration problem of a micro-scaled bar is formulated using the strain gradient elasticity theory. The equation of motion together with initial conditions, classical and non-classical corresponding boundary conditions for a micro-scaled elastic bar is derived via Hamilton’s principle. The resulting higher-order equation is solved for clamped-clamped and clamped-free boundary conditions. Effects of the additional length scale parameters on the frequencies are investigated. It is observed that size effect is more significant when the ratio of the microbar diameter to the additional length scale parameter is small. It is also observed that the difference between natural frequencies predicted by current and classical models becomes more prominent for both lower values of slenderness ratio of the microbar and for higher modes.
We use the residue harmonic balance scheme to study the periodic motions of a class of second-order delay-differential equations with cubic nonlinearities near and after Hopf bifurcation. The multiple solutions are found by homotopy continuation. Then, the approximation to any desired accuracy for a specific solution is captured by solving linear equations iteratively. The second-order solutions give good predictions for the frequency and amplitude, which are verified by the Runge–Kutta numerical solutions. Two typical examples, the temporal dynamics of the delay Liénard oscillator and the delay feedback Duffing system, are studied and compared. The results show how to trace analytically the relevant effect of the stiffness coefficient and the time delay on the dynamics and on the number of periodic solutions, even for large values of the bifurcation parameters.
The propagation of waves in micropolar thermoelastic homogeneous plate with two temperatures subjected to stress free thermally insulated and isothermal conditions is investigated. The secular equations for both symmetric and skew-symmetric wave mode of propagation have been derived. Helmholtz decomposition technique has been used to simplify mathematical model and frequency equations for different mechanical conditions. The regions of secular equations are obtained and some special cases such as thin plate and short wavelength waves of the secular equations are also discussed. The phase velocity and attenuation coefficient are computed numerically and depicted graphically. The amplitudes of stress components and thermodynamic temperature distribution for the symmetric and skew-symmetric wave modes are computed analytically and presented graphically. Results of some earlier workers have been deduced as particular cases.
In this article we review some intelligent and robotic algorithm approaches and propose a novel neural-network (NN) based approach for nonlinear systems. The nonlinear systems can be represented by the nonlinear Tagaki-Sugeno (T-S) and NN models. The linear differential inclusion state-space representation is utilized to deal with the controlled systems. The stability conditions and controller design for this representation are derived based on the fuzzy parallel distributed compensation scheme which is employed to construct a global fuzzy logic controller by blending all local state feedback controllers. The time-delay states that exist in the nonlinear simulated example, including the chaotic disturbances, are given to show the feasibility of the proposed fuzzy controller design approach.
In recent years, due to the rapid development of the internet, cloud computing has become a hot topic. Accomplishing tasks through the computer and the internet is generally getting much easier and more efficient; meanwhile, the number of social network users has recently grown at a rapid pace, which is even more remarkable. The purpose of this study is to exploit the use of a cloud services platform for information exchange in combination with the popular contemporary community sites, while developing the site architecture based on the socio-technical system’s theory (socio-technical system) as an indicator.
In this study, nonlinear vibrations of an axially moving string are investigated. The main difference of this study from other studies is that there is a nonideal support between the opposite sides, which allows small displacements. Nonlinear equations of motion and boundary conditions are derived using Hamilton’s principle. Equations of motion and boundary conditions are converted to nondimensional form. Thus, the equations become independent from geometry and material properties. The method of multiple scales, a perturbation technique, is used. A harmonically varying velocity function is chosen for modeling the axial movement. String as a continuous medium is investigated in two regions. Vibrations are investigated for three different cases of the excitation frequency . Stability analysis is carried out for these three cases, and stability boundaries are determined for the principle parametric resonance case. Thus, differences between ideal and nonideal boundary conditions are investigated.
Feature extraction plays an important role in fault diagnosis. It is critical to extract the representative features for improving the classification performance. An intelligent fault diagnosis method based on Marginal Fisher analysis (MFA) is put forward and applied to rolling bearings. The high-dimensional features in time-domain, frequency-domain and wavelet-domain are extracted from the raw vibration signals to obtain rich faulty information. Subsequently, MFA excavates the underlying low-dimensional fault characteristics embedded in the high-dimensional feature space by preserving local manifold structure. Thus, the optimal low-dimensional features are obtained to characterize the various fault conditions of rolling bearings and finally fed into the simplest k-nearest neighbor classifier to recognize different fault categories. The diagnosis results validate the feasibility and effectiveness of the proposed fault diagnosis method, compared with the other three similar approaches.
Based on interval analysis and the interval extension method, the upper and lower bounds of feedback performance for optimal control in physical space and in modal space, and static and dynamic characteristics for the smart truss with interval parameters, are analyzed. The first-order and second-order topology optimization models are built, where the cross-section areas, topology variables, control design parameters and the number and placements of actuators are taken as design variables. The objective function to minimize is the total mass, and the constraints are also imposed on the allowable voltages of actuators, static displacements, static stresses, first natural frequency of open-loop system and damping ratio of closed-loop system. Genetic algorithm is used as the optimization method. The solutions of numerical examples show that the optimization model and the proposed method are effective.
In this article we review several intelligent and robotic algorithm approaches and then propose a novel neural-network (NN)-based approach for nonlinear systems. The nonlinear systems can be represented by the nonlinear Takagi-Sugeno and NN models. Linear differential inclusion (LDI) state-space representation is utilized to deal with stability analysis and control problems on oceanic structures. The stability conditions for the neural-fuzzy logic criteria are derived utilizing the LDI representation. The stability analysis via Lyapunov theory can guarantee the stability of a time-delay tension leg platform (TLP) system.
This paper proposes a novel distributed nonlinear controller for a hyper redundant articulated nimble adaptable trunk robot to track a desired trajectory in the robot’s workspace. The distributed control strategy consists of controlling the last joint by assuming that the remaining joints are stable and follow their desired trajectories. Then, going backward to the (n - 1)th joint, the same strategy is applied, and so on, until the first joint. The proposed control law guarantees the global asymptotical stability of the tracking errors. This global stability is proved using Lyapunov theory. The proposed approach is implemented in real time on a seven degree-of-freedom articulated nimble adaptable trunk robot. Experimental results and a comparison with the computed torque approach show the effectiveness of the approach and good tracking performance in the workspace.
Recently, existence of dynamical bifurcations and chaos has been shown by some researchers in simple power system networks. In this paper, a novel approach is first proposed to design stabilizing controllers for synchronization of chaotic systems with a tridiagonal structure and its initial investigation in complex power systems. During the design procedure, an original nonlinear affine system is firstly transformed into a stable system with special tridiagonal structure. Secondly, controllers are developed to synchronize the transformed chaotic system. It is the first time that chaotic synchronization and its initial application have been studied in complex power systems with tridiagonal structure. Finally, the Lü system, the Chua circuit system and the Van der Pol system are used to demonstrate the effectiveness of the proposed approach by applying them to a standard power system.
The centrifugal flywheel governor is a mechanical device that automatically controls the speed of an engine and avoids the damage caused by an abrupt change of load torque. Recent research has discovered that this system exhibits very rich and complex dynamics such as chaos. In this paper, the problem of finite-time stabilization of non-autonomous chaotic centrifugal flywheel governor systems in the presence of model uncertainties, external disturbances, fully unknown parameters and input nonlinearities is studied. Appropriate adaptation laws are designed to undertake the system’s unknown parameters. Using the adaptation laws and finite-time control theory, a robust adaptive controller is derived to stabilize the non-autonomous uncertain centrifugal flywheel governor system with nonlinear control inputs in a given finite time. The finite-time stability and convergence of the closed-loop system are analytically proved. A numerical simulation is given to show the robustness and effectiveness of the proposed finite-time controller and to verify the theoretical results of the paper.
Accurate modeling of flexible mechanisms is an open research topic, and different models have been presented since the 1970s. In this work, a novel approach for modeling of three-dimensional flexible mechanisms is presented, based on an equivalent rigid-link system, with respect to which elastic deformations are defined and computed. Concepts of three-dimensional kinematics are used in order to define an effective relationship between the rigid body and the elastic motion. The model is based on a compact kinematic formulation and, for a specific mechanism, there is no need for customizing the formulation. By using the principle of virtual work, a coupled dynamic formulation is found. A crucial advantage of this method is that it is not necessary to explicitly formulate the compatibility equations expressing the link connections, since they are included in the matrices of the system dynamics. The model was applied to a specific three-dimensional flexible mechanism. The results, compared with the Adams-Flex™ software, show a good agreement, thus proving the effectiveness of the methodology.
In the present paper the continuous model method is applied to the prototype of a wind turbine tower in order to perform its modal structural analysis. This mathematical analysis is used as an alternative approach to the modal analysis method that uses discrete models. It is well known that in discrete models with high-level discretization and a large number of finite elements, several open questions on the accuracy, the convergence and the stability of the solution arise during the modal or response history analysis. In this sense, the results of the analysis by means of discrete modeling are in several cases doubtful and, therefore, a modal analysis by applying a continuous model as an effective alternative is recommended. To this end, the present paper proposes a continuous model approach to calculate the eigen-frequencies, periods and mode shapes to a wind turbine tower prototype. Starting from the equilibrium of forces on a differential element of the structure, the equation of motion of the tower is formulated and using in turn the known boundary conditions at the two ends of the wind tower, the tower eigen-problem is numerically treated and solved. The action of the higher mode-shapes is very important and may become critical in the case that the tower is subjected to strong dynamic loading (cf. e.g. wind) and simultaneously is excited by a strong seismic motion.
Fast Fourier transform-based near-field acoustic holography requires that the acoustic field should be sampled with a uniform spacing which is less than a half wave length of the highest frequency of interest to avoid spatial aliasing. Therefore, a large number of microphones are demanded for high frequencies. To overcome this difficulty and enhance the reconstruction accuracy, a data interpolation method based on the wave superposition algorithm (WSA) is proposed. At first, WSA is employed to regenerate the acoustic pressures between the measurement points. Then, the accuracy of the regenerated data is improved through an iterative process. In the end, taking the interpolated pressures as input data, the acoustic field can be reconstructed precisely with relatively few measurements. To solve the inherent ill-posed problem, Tikhonov regularization method together with generalized cross validation parameter choice method is utilized in the data interpolation method. Numerical simulation and experimental results demonstrate that this method can enhance the reconstruction accuracy and efficiency.
A robust nonlinear controller has been designed to control the surge speed and the heading angle of a marine surface vessel. The control actions are carried out through the propeller and the rudder. Moreover, a nonlinear observer has been devised to accurately estimate the surge speed and the yaw angle and their time derivatives. Both the controller and the observer are designed based on a reduced-order model of the ship. However, their performances have been assessed on a six degree-of-freedom ship model, which accounts for the wave excitation, retardation forces, nonlinear restoring forces, wind and sea-current resistive loads. Furthermore, the model accounts for the physical limitations of both the rudder and the ship propulsion system. The simulation results demonstrate the capability of the integrated controller-observer system in providing a good tracking characteristic of the ship in spite of significant modeling imprecision and environmental disturbances.
This paper investigates the propagation of crack due to horizontally polarized shear waves in a magnetoelastic self-reinforced medium. The methodology includes the Weiner-Hopf technique. The effects of reinforcement and magnetic field on the propagation of the crack have been studied. The stress intensity factor at the crack tip for a concentrated force of a constant intensity has been calculated and depicted by means of graphs for various cases. It is observed that self-reinforcement increases the stress intensity factor whereas magnetoelastic coupling parameter has the reverse impact. It is remarkable to state that the stress intensity factor decreases with the increase in the length of crack. Also, the comparative study has been made through graphs to find the effect of reinforcement over the reinforced-free case on the stress intensity factor. Moreover, some important peculiarities have been observed in graphs.
A simplified analytical model for predicting the acoustic performance of an underwater sound absorption coating is presented in this paper. The sound absorption coating contains hexagonally arrayed cylindrical cavities, so the unit cell of sound absorption coating could be approximated as a cylindrical tube. When the plane wave normally impinges on the sound absorption coating, the axisymmetric wave which propagates in the viscoelastic cylindrical tube will be excited. According to the two-dimensional analytic model, only the first mode (the lowest) should be taken into account in the acoustic performance estimation at low frequencies, because the attenuation of the first propagating mode is much lower than the others. Based on this conclusion, the simplified analytical approach has been given as follows: to solve the characteristic equation, the wavenumber of axisymmetric wave will be obtained firstly; then, the effective impedance of viscoelastic cylindrical tube can be calculated after the axial stress and the axial displacement are averaged, and the reflection coefficient and the transmission coefficient of sound absorption coating can be easily calculated by using the transfer matrix. Comparisons of the simplified analytical model to the finite element method and to the experiment data validate that the present model is a workable and satisfactory approach to predict the acoustic performance of sound absorption coating. In the final section, the effects of several parameters such as the cavity geometry and the acoustical termination on the performance of sound absorption coating have been discussed using the present model.
In this paper, we study the propagation of a torsional surface wave in a homogeneous crustal layer over an initially stressed mantle with linearly varying directional rigidities, density and initial stress under the effect of an imperfect interface. Twelve different types of imperfect interface have been considered using triangular, rectangular and parabolic shapes. A variable separable technique is adopted for the theoretical derivations and analytical solutions are obtained for the dispersion relation by means of Whittaker function and its derivative. Dispersion equations are in perfect agreement with the standard results when derived for a particular case. The graph is self-explanatory and reveals that the phase velocity of a torsional surface wave depends not only on the wave number, initial stress, inhomogeneity and depth of the irregularity but also on the layer structure.
The vibration and stability analyses are presented for axially compressed three-layered truncated conical shells with a functionally graded (FG) middle layer surrounded by elastic media. The material properties of functionally graded materials (FGMs) are assumed to be graded in the thickness direction according to simple power law and exponential distributions in terms of the volume fractions of the constituents. Five sets of the material mixture are considered. The Pasternak model is used to describe the reaction of the elastic medium on the truncated conical shell. The fundamental relations, the modified Donnell-type dynamic stability and compatibility equations for the three-layered truncated conical shell with an FGM middle layer are derived. The governing equations are solved by using the Galerkin method and obtained expressions for dimensionless frequency parameters and dimensionless critical axial loads for three-layered truncated conical shells with the FG middle layer with and without an elastic foundation. The numerical results reveal that variations of the shell thickness-to-FGM thickness ratio, lengths-to-radius ratio, Winkler foundation stiffness, shear subgrade modulus of the foundation, material mixture and compositional profiles of the FG middle layer have significant effects on the values of dimensionless critical axial load and dimensionless frequency parameter. The results are verified by comparing the obtained values with those in the existing literature.
In this paper, an adaptive controller is investigated for a class of uncertain single-input-single-output nonlinear systems preceded by an unknown backlash-type hysteresis nonlinearity, which is modeled by a differential equation. Backstepping design procedure is employed to construct the control input and adaptation laws. A new algorithm is designed to reduce the computational burden compared with previous work for unknown backlash-type hysteresis. Based on Lyapunov stability theory, all the signals in the closed-loop system are bounded, and the system output can track the reference signal to a bounded compact set. An example for hard disk drives with hysteresis friction nonlinearity is given to verify the feasibility of the proposed approach.
This paper presents a formulation and numerical solutions of an optimal control problem of a linear time-invariant space–time fractional diffusion equation. The main aim of this formulation is minimization of a performance index, which is a functional of both state and control functions of the diffusion system. The dynamics of the system are defined by the space–time fractional diffusion equation in the sense of Caputo and fractional Laplacian operators. The separation of variables technique and a spectral representation of a fractional Laplacian operator are applied to determine the eigenfunctions that represent the space parameters. Therefore, the state and control functions are defined by linear infinite combinations of eigenfunctions. Optimality conditions described by Euler–Lagrange equations are found by using a Lagrange multiplier technique. The Grünwald–Letnikov definition is used to approximate to the time fractional derivative. The applicapability and effectiveness of the numerical scheme are shown by comparison of analytical and numerical solutions for a numerical example. Finally, the variations of problem parameters are analyzed, with some figures obtained using MATLAB.
To simulate the contact and separation of wheels and rails accurately, the stiffness between them should be correct. This paper developed a nonlinear moving wheel element based on a simple point contact scheme to simulate moving train problems, where the element stiffness is set to a power function directly fitted from the finite-element result of the wheel and rail contact analysis. The finite-element result of the wheel/rail contact analysis indicates that the changes in vertical stiffness with changing contact forces can be accurately fitted by using the proposed power function, and the horizontal stiffness can be simply regressed using a constant. The validated example in this paper shows that the nonlinear moving wheel element can simulate the complicated contact and separation problem correctly, both in the displacement and contact force fields, and the major advantage is that a fine mesh is not necessary in the moving train contact analysis.
An innovative design procedure for controlling a nonlinear system subject to Poisson white noise excitation to target a specified stationary probability density function is proposed based on the approximate generalized Fokker–Planck–Kolmogorov equation of a Poisson-white-noise-excited nonlinear system. First, the technique for deriving the generalized Fokker–Planck–Kolmogorov equation of the Poisson-white-noise-excited nonlinear system is briefly reviewed. Then, the approach for designing the feedback control of nonlinear stochastic systems under Poisson white noise excitations to target a pre-specified stationary probability density function is presented. Finally, an example is given to illustrate the procedure and effectiveness of the proposed control strategy.
An optimal design is presented to maximize the fundamental damping loss factor of sandwich rectangle plates and beams with general boundary conditions. With an extensive development of the classical laminate theory and energy method, the loss factor of sandwich laminate with a thin viscoelastic core is deduced. For sandwich-laminated plates and beams, the effect of fiber orientation of the orthotropic layer on the loss factor has been studied. The aspect ratio is very important in structural design for plates and beams. In this work, the effects of aspect ratios of sandwich laminates on optimal fundamental loss factors are investigated. The maximum fundamental loss factor and optimal fiber orientation have been obtained and analyzed for different sandwich laminates with the aspect ratio as a variable.
This paper proposes a numerical model for analyzing torsional vibration of a ground vehicle propeller shaft system. By considering the elasticity and energy of the propeller system, a Lagrangian approach has been used to derive the equation of motion, yielding a highly nonlinear three degree-of-freedom system with five coupled inertias. The model takes into account the dynamics of a Hooke’s joint, a crack-induced parametric excitation, tractive torque at the driving wheels and transient vibration of a rear drive ground vehicle transmission. The forces exciting the vibrations of the propeller shaft system are evaluated by quantifying the tractive forces at the road wheels, Hooke’s joint force, the crack force and the forces emanating from the engine through the clutch and gear box. Subsequently, the forces are projected onto the propeller shaft by either direct coupling or by gearing. Consequently, the nonstationary response of the system in various scenarios has been determined and evaluated by a wavelet transform. By analysis, it is demonstrated that the model is useful for investigating nonlinear vibration of a typical propeller shaft system used in light ground vehicles.
The damage of unallowable blast induced vibrations on the concrete structures results in a decrease in the safety of its structures. This paper develops a three dimensional anisotropic dynamic damage model for Dagangshan arch dam subjected to blast loading. The multiple damage failure criteria are adopted as the failure criteria of the dynamic damage evolution of concrete. From the simulation of the dynamic damage process in the arch dam due to the blast loading, some process fields of the dynamic displacement, the dynamic stress, dynamic damage distribution and other necessary information for the safety evaluation are obtained. The results obtained using the proposed model show that the nonlinear behavior of concrete dams can be satisfactorily predicted. This will provide a reasonable theoretical support on the safety evaluation of the capability of concrete arch dams against blast loading and useful information for further research in these areas.
This investigation addresses the stability problem for ecosystem modeling. Fuzzy system modeling and stability conditions are reviewed. A stability criterion in terms of a fuzzy Lyapunov direct method is combined to guarantee the asymptotic stability of the nth order Volterra equation. Some simulation results are discussed demonstrating the effectiveness of this method.
This paper investigates the nonlinear modeling of a smart tensegrity structure of Geiger’s type with active damping using pairs of displacement actuator and force sensor, collocated at the lower end of strings and/or struts. A control strategy based on decentralized collocated integral force feedback is employed. A linear model is first used to optimize the number and the location of the active tendons. A geometric nonlinear dynamic procedure is then used for the analysis of the response of the structure with and without active control. An incremental-iterative solution based on a Newmark direct integration method and a modified Newton–Raphson scheme is adopted for solving the nonlinear equation of motion. For high excitations, the nonlinear dynamic behavior of the smart cable dome is observed and damping is successfully added to the system. The responses with and without control of particular modes are studied in frequency and time domains. The results obtained indicate that the active control strategy presented in this paper is adequate for vibration attenuation of Geiger domes.
Synchronous lateral vibration is a frequent cause of machine failure and is probably the most common source of machine noise and vibration. Among the broad ranges of faults that cause synchronous vibration, mass unbalance and bow are the most common faults present in the rotor and hence their detailed understanding is required. In the present study, a rotor model having both mass unbalance and bow is analyzed to find the influence of these faults on the synchronous response. The synchronous response of a rotor is a function of influence coefficients due to mass unbalance and bow. The influence coefficients are analytically derived using transfer matrix method for rotor bearing system having both mass unbalance and bow. The correction unbalance vector required to balance the rotor at its first bending critical speed is computed using these analytically derived influence coefficients and the rotor responses measured at a speed much lower than the first bending critical speed. The balancing method needs a good mathematical model for the rotor system in finding the influence coefficients for mass unbalance and bow. This procedure helps in estimating the correction mass in a single trial run and using a single balancing plane, thus reducing the cycle time for balancing flexible rotors. Experiments are carried out on a test rig to verify the procedure.
The very-large-scale integration (VLSI) implementation of a probabilistic neural network image interpolator based on a neural network model is provided in this paper. The interpolator takes into consideration both smoothness (flat region) and sharpness (edge region) characteristics at the same model. A single neuron, combined with particle swarm optimization training, is used for sharpness/smoothness adaptation. A highly efficient VLSI architecture of a probabilistic neural network image interpolator is designed in field-programmable gate array for supporting real-time digital zooming/scaling applications. The functional architecture of the proposed image interpolator is decomposed in three main functional modules: edge adaptation module, Gaussian module and interpolator module, as well as a top-level pipelining controller. The data throughputs achieved are 20 fps in XGA format at 20 Mhz system clock.
A multi-input multi-output (MIMO) random vibration control method is proposed for a multi-axis hydraulic shaking table system to replicate the reference power spectral density (PSD). Kinematics analysis is presented to reduce cross-coupling between the axes of the hydraulic shaking table. The time histories generated by time domain randomization in conventional MIMO random vibration control have spectral leakage between the frequency resolutions. The drive signal PSD is used in the proposed control method to design a linear time-invariant system. Circular convolution is then proposed to implement the designed system and convert the PSD to time histories with white noise. Experimental results obtained in step response and two-axis PSD replication show the effectiveness of the proposed control method.
The correlation criterion proposed in this article and called nc2o (normalized cross complex orthogonality) is based on the bi-orthogonality properties between rotor mode shapes calculated at different speeds of rotation. This criterion is proved using an industrial laminated rotor composed of disks and two fluid film bearings, whose characteristics depend on the speed of rotation. The industrial finite element model shows that the nc2o criterion provides a more efficient mode pairing of rotor shapes than those obtained by using classical correlation criteria. Moreover this criterion makes it easier to plot Campbell diagrams for strongly speed-of-rotation-dependent structures.
Internal waves are gravity waves that occur within a stratified fluid rather than on the surface. The governing equations are derived to cover density differences in a stratified two-layer fluid within a two-dimensional internal wave domain in this study. The proposed perturbation model considers the relationship between nonlinearity and frequency dispersion at O() = O(μ2), but ignores the viscous effects. The governing equations are formed based on the continuity equation and Euler equations to simulate the realistic movement of an experimental internal solitary wave (ISW) over a variable seabed. The focus is on using the equations governing interfacial wave motion to describe the motion in detail, especially the interaction between an ISW and the seabed topography.
For multi-degree-of-freedom dynamical systems, a novel control method was proposed to realize synchronization and anti-synchronization of chaos between the original and derived systems. The presented method was proved theoretically and realized by linear coupling of velocity. Furthermore, for any coupling coefficient larger than the critical value, the two systems can continue synchronization and anti-synchronization by the coupling method. This means that the synchronization and anti-synchronization can be kept within a wide range of coupling parameters. The simulation results for Duffing and Mathieu systems proved that the proposed method was correct and effective.
The authors proposed a pipelined multiprocessor system-on-a-chip (PMPSoC) design flow for the rapid prototyping of a streaming multimedia processing system. The PMPSoC design flow consists of a modular design of algorithm, data arrangement, pipelined controller design, hardware/software (HW/SW) co-simulation and HW/SW co-synthesis. The streaming data processing system can be divided into several individual and independent modules. Each independent module function is completed by an embedded processor by software. Applying the pipelining technology synthesizes the hardware of the main controller to integrate all modules and increase the total system performance. A simulator of a pipelined multiprocessor system was completed. The advantages of the proposed design methodology are: the simulation level is increasing from register transfer level (RTL) to transaction level model (TLM). It can reduce the time of system verification immensely. Additionally, after the system architecture is decided, the simulator can produce a simulation platform of a pipelined multiprocessor system automatically. The accuracy of the multiprocessor system function can be verified before the accomplishment of a system hardware circuit to reach the purpose of a rapid prototype. The authors also completed the corresponding of TLM’s pipelined controller and processor’s RTL circuit. When the system TLM verification is finished, the hardware circuit is also synthesized. The PMPSoC design flow was applied to design the system-on-a-chip for fingerprint person authentication application. In the same frequency of a system clock, the computational performance of fingerprint recognition on the PMPSoC is increasing 430.7% more than on a processor. The memory can be reduced 32.53%. It has the characteristic of low power consumption. The experimental result shows that the PMPSoC design methodology has high application value.
This paper presents a method for controlling the position, velocity, and acceleration of a rigid and flexible four bar coupler. The dynamic model is formulated using a new form of Kane's equations of motion for constrained systems. The formulation results in equations of motion that are separated in the accelerations. Lyapunov theory is then applied to the dynamic model to develop nonlinear tracking control laws for the rigid and flexible couplers. Numerical simulation is used to demonstrate the system performance showing a significant reduction in the flexible coupler vibration when using active control based on the flexible dynamic system model.
Numerous workers are exposed to vibrations which can turn out to be fatal for the health. Athletes can be included in this population, in particular cyclists who are exposed to vibration due to the irregularity of the road. This nuisance depends of the duration of exposure and the range of vibrations. While the worker is mostly directly excited by a vibrating system, the cyclist is indirectly subjected to it. He undergoes the vibrations of an excited sub-structure which is the bicycle. So the bicycle plays the role of a vibration filter or amplifier. In this paper we propose to (i) study the transmission of vibrations to the cyclist after excitation on a paving road, (ii) calculate the limit time of exposure to this type of excitation rate by the use of the standard ISO 5349 and the European directive 2002/44/EC, and (iii) compare the weighting curve of the standard with a vibrations transmissibility curve obtained between the collarbone and the stem. For this particular case of an excited sub-structure, a weighting curve is proposed by considering the first modal frequency of the bicycle.
This paper researches the chaotic phenomenon of the permanent magnet synchronous motor (PMSM) in electric vehicles when the PMSM is in power on or power off and analyzes the chaos of the PMSM when parameters are within a certain range. Bifurcation diagram, phase portraits and Poincareé maps present traits of chaos in the PMSM. Finally, an effective way of controlling chaos is put forward by an external sinusoidal dither signal which is input to the PMSM when in power off. Some simulations are presented to demonstrate effectiveness of the method and to test what effect a sinusoidal dither signal of different frequencies has on chaos control of a PMSM.
In this paper, a survey comparing some of the present linear control algorithms for the active control of sinusoidal tonal disturbances is made. The design procedure for each of the methods is presented in detail and the similarities in the design are pointed out. The methods are studied in a common framework in order to allow analytical comparison. The focus of the analysis is in the best obtainable control performance in terms of the vibration mitigation, the controller robustness and the sensitivity to process noise and model errors. In addition, some issues related to the transient behavior of the algorithms, such as the convergence rate, are evaluated in time-domain simulations . The purpose of this study is to establish a clear view on the differences and similarities between the present algorithms and to provide some insight for a system specialist, on how to choose an appropriate control algorithm for a particular problem. It will be shown that the choice for an appropriate algorithm is problem dependent.
Current damping identification methodologies typically require measurements of complex eigenvalues, complex eigenvectors, and the applied force. Also, these methods can be sensitive to measurement noise. Most importantly, only a few current methods can be used for regions of high modal density. Thus, the work herein utilizes the frequency response of a system to identify modal damping in regions of (low and) high modal density. This method does not require knowledge of the absolute forcing, rather only the relative forcing is needed. Results are presented for a mistuned blisk, and the proposed method is compared with an alternative damping identification technique.
Although neural networks (NNs) have been successfully applied many times, there are still some drawbacks in any control scheme. In this study an NN-based model is applied for an n-degree ecosystem. The Takagi-Sugeno fuzzy model representation and fuzzy Lyapunov method are extended to analyze the ecosystem stability. During the stability analysis, the linear matrix inequality conditions are derived using the fuzzy Lyapunov theory to guarantee the stability and stabilization of the n-degree ecosystems. The suitability of the proposed stability conditions are demonstrated with a numerical simulation.
Static and dynamic multiobjective topology optimization of trusses with interval parameters is investigated. The uncertain parameters of the trusses are described by an interval model. The multiobjective topology optimization model of trusses with interval parameters is constructed. On the basis of Taylor expansion and natural interval extension, the stress and displacement response intervals under static loads and inherent natural frequency interval of truss are deduced. The non-deterministic optimization problem is transformed into a deterministic programming problem by minimizing maximum standards and the concept of interval possibility degree. The Pareto CMOPGA (genetic algorithm for constrained multiobjective optimization problem) embedding structural stability examination on the basis of ranking is adopted to solve the constrained multiobjective optimization problem. Two numerical examples show that the proposed method is effective and reasonable.
A crane is generally modeled as a simple pendulum with a point mass attached to the end of a massless rigid link. Numerous control systems have been developed to reduce payload oscillations in order to improve safety and positioning accuracy of crane operations. However, large-size payloads may transform the crane model from a simple-pendulum system to a double-pendulum system. Control systems that consider only one mode of oscillations of a double pendulum may excite large oscillations in the other mode. In multi-degree-of-freedom systems, command-shaping controllers designed for the first mode may eliminate oscillations of higher modes provided that their frequencies are odd integer multiples of the first mode frequency. In this work, a hybrid command-shaper is designed to generate acceleration commands to suppress travel and residual oscillations of a double-pendulum overhead crane. The shaper consists of a primary double-step command-shaper complemented by a virtual feedback system. The primary command-shaper is designed to eliminate oscillations in a slightly modified version of the crane model with frequencies satisfying the odd integer multiple criterion. The virtual feedback loop is then used to modify the commands of the primary shaper to accommodate the difference between the modified and the original models of the crane. It is shown that the suggested hybrid command-shaper is capable of minimizing oscillations of both modes of a scaled experimental double-pendulum model of an overhead crane. Results show that the hybrid command-shaper produces a reduction of 95% in residual oscillations in both modes of the double pendulum over the time-optimal rigid-body commands.
In this paper we propose the design and control of a novel two-layer optical table. An optical table normally needs to isolate two main vibration sources: the ground disturbances and the load disturbances. Because the suspension settings for suppressing these two disturbances conflict with each other, we applied disturbance response decoupling (DRD) techniques to treat them independently. First, we used passive elements to insulate the ground disturbances. Second, we employed DRD methods to design active robust controllers that would drive piezoelectric transducers to improve the load responses without influencing the ground responses. Finally, the designed controllers were implemented for experimental verification. The DRD theorem and robust controllers were confirmed to be effective at suppressing system vibrations.
Mobile robots with suspension systems can absorb vibration induced by rough roads, but due to center-of-gravity (CG) shift, the suspended platform is subject to vibration when the platform moves with acceleration. This paper presents approaches based on the particle swarm optimization (PSO) algorithm to overcome the following vibration problems: (1) when the suspended platform moves with a static manipulator, vibration of the suspended platform occurs due to CG shift, (2) when the suspended platform and the manipulator move simultaneously, the vibration is caused by the dynamic manipulator. For the first problem, a method for the optimization of multi-input shapers using PSO is adopted with chaos to reduce the residual vibration. For the second problem, an approach based on PSO with chaos is developed to suppress the vibration by searching for the time-jerk synthetic optimal trajectories of the manipulator. Finally, the authors perform the resulting shapers and optimal trajectories on the presented models and demonstrate the vibration can be controlled to a desired level effectively in both problems.
The objective of this paper is to investigate the effects of laminate scheme, crack ratio (a/h) and crack position (L1/L) on the free vibration and lateral buckling of a cantilever slender rectangular beam such as an airplane wing or a wind turbine blade with a single edge crack. The local flexibility approach is adopted to model the crack, based on linear fracture mechanics and the Castigliano theorem. The governing matrix equations for free vibration and buckling load are derived from the standard beam element and cracked beam element combined with the local flexibility concept. The results are obtained numerically using the finite element method, based on the energy approach and are given for crack ratios up to 0.5 at crack positions up to 0.9 ratio. Polynomial approximation for displacements gives results with reasonable accuracy.
In this paper, we present a method for solving multi-dimensional fractional optimal control problems. Firstly, we derive the Bernstein polynomials operational matrix for the fractional derivative in the Caputo sense, which has not been done before. The main characteristic behind the approach using this technique is that it reduces the problems to those of solving a system of algebraic equations, thus greatly simplifying the problem. The results obtained are in good agreement with the existing ones in the open literature and it is shown that the solutions converge as the number of approximating terms increases, and the solutions approach to classical solutions as the order of the fractional derivatives approach 1.
The purpose of this paper is to propose a useful method to implement active magnetic bearings (AMBs) on an existing rotating shaft which rotates on conventional bearings. This is feasible if AMBs can produce the same reaction loads of conventional ones and if the size of vane is large enough to host an AMB. As this substitution could offer some difficulties due to the different size between magnetic bearings and conventional ones, a set of equations are performed to show that a variation of some parameters can solve this problem. The journal ratio is the geometrical parameter introduced to develop the present analysis. The variation of journal ratio does not produce a variation of the pole’s surface so that the reaction load does not change. The results are analyzed by numerical analysis by mathematical relationships involving the design parameters, magneto-static simulations and dynamic simulation on shaft when it is tested by disturbance rejection and reference tracking input in order to analyze the differences on dynamic behavior of the shaft on its suspended sections. Results show that the displacement pattern of the suspended sections remains unchanged, confirming that the reaction load, produced by pole expansion, remains the same varying the journal ratio.
In recent years, the collective behavior of ants has inspired wide-ranging research in the field of sociobiology. This is due to the fact that a swarm (ant colony) formed by a group of simple agents (ants) exhibits autonomous behavior that both solves problems with a high degree of reliability and displays a high degree of adaptability. This paper aims to advance two ant-inspired collective problem-solving systems which are based upon the principles and algorithms of ant foraging and object gathering behavior. The ant-inspired algorithm was compared against a genetic algorithm and a simulated annealing algorithm. These experiments revealed that the ant algorithm provided high quality and stable problem-solving mechanisms. Additionally, the results show that these emergent collective problem-solving mechanisms do not require prior planning, central supervision or control. Therefore, these ant-inspired collective problem-solving systems provide problem-solving capabilities which are both autonomous and robust.
The present paper describes a methodology devised to study the engine block displacement of an internal combustion engine in the radial direction due to combustion force and inertia forces. The combustion force produced in in-cylinder is a substantial function of angular displacement and then correlated with pressure and temperature. Other than the substantial function, combustion force depends on chamber design, injection parameters, flow patterns and fuels. But inertia is a function of angular displacement and a mass of reciprocating parts. Speed is directly related to combustion by means of indicated pressure and the indicated torque respectively. The engine was taken for an analysis along with speed and load as the design variables. The engine block displacement, time-domain frequency, wave form, side thrust and in-cylinder force were examined for the analysis. The results obtained provide the combined effect of combustion force and inertia force induced displacement, uncertainty in combustion processes, nonlinear vibration of the engine block, and vibration spectra. This new approach in engine parameter design bestows insight with the combustion force and inertia induced vibration and source of noise in the diesel engine.
It is known that the commonly used performance indicator for vibration isolation - force transmissibility - over-simplifies the vibration problem. Therefore, Mak and Su propose a power transmissibility approach that includes the effect of floor dynamics and the interactions of the mounting points between machine and floor. However, their model does not consider transient vibration excitation. The question motivating this study is the occasional problem which arises due to the sudden or frequent starting and stopping of vibratory machines. In this paper, a transient power transmissibility approach is proposed to assess the performance of isolators in a transient vibration excitation. A spring-mass-movable floor system is considered in the simulation, and the spring isolator is first selected using the steady-state power transmissibility approach of Mak and Su. A system disturbed by two transient excitations as typically experienced by building services equipment is then analyzed. The results indicate the necessity of using transient power transmissibility in the selection of isolators for a transient vibration.
In this paper the non-planar nonlinear dynamic responses of an axially loaded rotating Timoshenko beam subjected to a three-directional force traveling with a constant velocity is studied. On deriving the nonlinear coupled partial differential equations (PDEs) of motion the stretching effect of the beam’s neutral axis due to the pinned-pinned ends’ condition in conjunction with the von Karman strain-displacement relation are considered. The beam’s nonlinear governing coupled PDEs of motion for the bending rotations of warped cross-section, longitudinal and lateral displacements are derived using Hamilton’s principle. To obtain the dynamic responses of the beam, derived PDEs of motion are solved by applying Galerkin’s method. Furthermore, subsequent to the verification of obtained results, a parametric study on the dynamic responses of the beam is conducted by changing the value of the concentrated traveling force-bending moment, load velocity, frequency fluctuation of the load velocity and rotational speed of the beam, respectively. It is observed that the existence of nonlinearity in the governing coupled PDEs of motion due to the beam mid-plane stretching introduces a noticeable effect on the size of the beam’s stiffness.
An active vibration control scheme is proposed for suppressing the vibration of the high-speed induction electric spindle with a built-in force actuator to improve the performance of high-speed milling system. The built-in force actuator is a set of windings, which are added to the stator of electric spindle motor. An improved fast block least mean square (FBLMS) adaptive filter is adopted to produce the reference control force, which is used to obtain the control current of force actuator, and then a controlled, non-contact electromagnetic control force on the electric spindle is produced by the force actuator to control actively chatter, unbalanced vibration and disturbance signals of milling system. The built-in motorized spindles dynamic is modeled by means of the finite element method, the dynamic milling, the air gap excitation current of torque and radial electromagnetic control force are modeled, the control force coefficient and the unbalanced magnetic pull force coefficient are identified by finite element analysis, and then the active vibration control scheme for the flexible induction electric spindle is designed. The vibration, with a different frequency component, is investigated. The results show that the improved FBLMS adaptive filter and the proposed active control scheme have an obvious effect on suppressing the spindle chatter, unbalanced vibration and other frequency vibration components in the built-in motorized milling spindle.
This paper proposes an evolutionary design methodology of multilayer feedforward neural networks based on the constructive approach. The authors elaborate an adjustable processing element as a primitive neuron model. The neural layer can be constructed by assembling several neurons. The multilayer neural network can be finally constructed through cascading several neural layers. The constructive approach facilitates substantially the extraction of design specifications from a multilayer neural network. Based on the constructive representation of multilayer feedforward neural networks, a genetic encoding method is used, after which the evolution process is elaborated for designing the optimal neural network. The results of these experiments reveal that this methodology is superior to the error back-propagation algorithm both for its executing efficiency and performance.
In this study a seismic performance assessment of school buildings, which have been built in accordance with template unreinforced masonry school projects in Turkey, has been conducted. For this purpose, the most widely used three template projects have been selected. The seismic performances of these buildings have been evaluated for various earthquake levels. This evaluation has been carried out in compliance with the Turkish earthquake code entered into force in 2007. The effects of material strength and plan features on the performance of masonry school structures have been investigated within the scope of this study. It has been concluded that school buildings with template design are far from satisfying the required performance criteria. For spectral acceleration of 0.80 g, which is expected in a 475 year period in the seismic Zone 1, the average exceedance ratio for life safety performance limit is more than 80% considering different material strengths. Upon evaluation of the results a building capacity index is proposed for rapid seismic assessment of masonry school buildings.
The purpose of the present paper is to apply the differential transformation method (DTM) to deal with the vibration problem of stepped beams with general end supports and elastically constrained ends. The method demonstrates several advantages, such as rapid convergence, high accuracy, and computational stability. Unlike some approximate approaches which require correct assumed admissible function, the differential transformation method gives all natural frequencies and their mode shapes without any frequency missing. By using the DTM algorithms fully provided in this paper with general mathematical software packets, natural frequencies and mode shapes of these beams can be obtained easily for every boundary condition. Aspects such as boundary conditions, spring constant values, stepped beam types, step ratio and step location, which have a significant impact on frequencies and mode shapes, are taken into investigation in this paper.
This paper discusses research conducted by the Army Research Laboratory (ARL) - Vehicle Technology Directorate (VTD) on advanced suspension control. ARL-VTD has conducted research on advanced suspension systems that will reduce the chassis vibration of ground vehicles while maintaining tire contact with the road surface. The purpose of this research is to reduce vibration-induced fatigue to the Warfighter as well as to improve the target aiming precision in-theater. The objective of this paper was to explore the performance effectiveness of various formulations of the generalized predictive control algorithm in a simulation environment. Each version of the control algorithm was applied to an identical model subjected to the same ground disturbance input and compared to a baseline passive suspension system. The control algorithms considered include a generalized predictive controller (GPC) with implicit disturbances, GPC with explicit disturbances, and GPC with preview control. The suspension model used was a two-degree-of-freedom dof quarter-car model with a given set of vehicle parameters. The performance of the control algorithms were compared based on their effectiveness in controlling peak acceleration and overall average acceleration over a range of vehicle speeds. The algorithms demonstrated significant reductions in the chassis acceleration of the quarter-car model.
Three dimensional vibration analysis of multi-layered graphene sheets embedded in polymer matrix is carried out employing nonlocal continuum mechanics. By using the Fourier series expansion in the in-plane axis, the governing equations in term of displacements can be obtained. By exerting the traction free surface boundary conditions to the eigenfrequency equation, natural frequencies are obtained. Accuracy of the present work is validated by comparing the numerical results with those obtained in the open literature. The effect of nonlocal parameter, length of square plate, aspect ratio, plate thickness and half wave numbers in the frequency behavior are examined.
Free vibrations and the transverse response of sandwich plates with viscoelastic cores under wide-band random excitation is studied with special attention to the so-called pumping, thickness-shear and stretching modes. The quadratic displacement field is adopted for all displacement components of the core to accurately capture the higher modes excited by the wide-band excitation. The Love-Kirchhoff plate theory is used for the face layers. The viscoelastic behavior of the core is modeled by the Golla–Hughes–McTavish method. An analytical solution using the normal mode method is provided for the simply supported boundary conditions by including a different family of modes. The effects of some geometric and material properties on the frequencies, damping ratios and also root mean square responses are explored. The participation of the through-the-thickness deformation in the bending mode vibration of the top layer is also investigated, which is found to be mostly resulting from the second order term of the transverse displacement expansion in symmetric configurations. Moreover, the alteration of the response with the exclusion of a different family of modes from the solution is investigated.
This paper is devoted to the investigation of the role of a single degree-of-freedom (d.o.f) nonlinear energy sink (NES) with nonlinear damping characteristics in annihilating undesired periodic response regimes and simultaneously preserving strongly modulated responses (SMR) in a harmonically excited three d.o.f system consisting of two linear coupled oscillators and an NES attached to it. The NES parameters are tuned such that they are able to eliminate all undesired periodic branches and to have the SMR region in the vicinity of both modes of the system concurrently. The tuning procedure leads to a maximum SMR interval which is achievable using this type of the NES in the vicinity of each excited mode. According to the results, design requirements are achieved using this type of the NES for a two d.o.f primary system for the first time. But, further increase in the d.o.f of the system will lead to a restriction of the range of harmonic excitation amplitude of the first oscillator for which the design requirements would be satisfied.
Nowadays, the system identification methods applied to civil structures are rising in order to get a better understanding of structural behavior and improve traditional analytical analysis. Accurate identification of the modal parameters of a structure is essential because it allows building a proper analytical model, and it discloses the difficulties that may not have been considered in analytical studies, as well as finding out the existence of structural damages or deterioration, and sometimes estimating the remaining life of the structure. A clear disadvantage of most experimental methodologies is to require of a long sampling time window that stresses the structure under test. This paper shows the effectiveness of a novel methodology based on the multiple signal classification (MUSIC) algorithm and its high-resolution properties, applied for identifying most of the natural modes and analyzing vibration signals in a truss-type structure by using a reduced sample data set and short sampling time window. It has the advantage of submitting the structure to a reduced fatigue and stress during testing as a difference from other works, where the analysis involves putting the structures under severe fatigue and stress. Identifying most of the natural modes in the truss-type structure is realized at first by locating the fundamental mode in a frequency region, and the other natural modes are identified in higher frequencies, where each of these natural modes is located in different frequency regions. Thus, the MUSIC algorithm can identify most of the natural modes in different frequency regions of a vibration signal successfully.
A variational method is proposed to study the free vibration of joined cylindrical-conical shells (JCCSs) subjected to classical and non-classical boundary conditions. A JCCS is divided into its components (i.e., conical and cylindrical shells) at the cone-cylinder junction. The interface continuity and geometric boundary conditions are approximately enforced by means of a modified variational principle and least-squares weighted residual method. No constraints need to be imposed a priori in the admissible displacement functions for each shell component. Reissner-Naghdi's thin shell theory is used to formulate the theoretical model. Double mixed series, i.e. the Fourier series and Chebyshev orthogonal polynomials, are adopted as admissible displacement functions for each shell component. To test the convergence, efficiency and accuracy of the present method, free vibrations of JCCSs are examined under various combinations of edge support conditions. The results obtained in this study are found to be in a good agreement with previously published results where possible, and those from the finite element program ANSYS. The effects of elastic foundation stiffness and semi-vertex angle on frequency characteristics of the JCCSs are also discussed.
In this work, vibration reduction in randomly forced systems is considered using a new vibration absorber setup. In the new setup, the absorber consists of a mass spring and damper, and is attached such that it separates the primary system from the fixed support. White noise excitation is assumed and the objective function is the mean square value of the primary system response function. For given damping and mass ratios of the system, the optimal stiffness and damping ratios of the absorber are determined. The optimal parameters are obtained in an analytical closed form when the primary system is undamped, and calculated numerically for damped primary systems. It is shown that an optimal mass ratio exists, unlike the case of classical absorbers where performance increases with increasing absorber mass. The optimal parameters associated with the optimal mass ratio are calculated and tabulated for a range of primary system damping ratios. The efficiency of the proposed absorber is discussed and compared to that of the classical absorber.
This paper concerns free vibration analysis of single-story multi-bay planar frame structures. An exact analytical solution is obtained using a wave vibration approach, in which vibrations are described as waves propagating along uniform structural elements and are reflected and transmitted at structural discontinuities. The coupling effects between bending and longitudinal vibrations in the multi-bay frames are taken into account. Both natural frequencies and modeshapes are obtained. Numerical examples are presented along with comparisons to results available in the literature.
The aim of this paper is to generalize the Euler–Lagrange equation obtained by Almeida et al., where fractional variational problems for Lagrangians, depending on fractional operators and depending on indefinite integrals, were studied. The new problem that we address here is for cost functionals, where the interval of integration is not the whole domain of the admissible functions, but a proper subset of it. Furthermore, we present a numerical method, based on Jacobi polynomials for solving this problem.
In this study, a finite element method is developed for analyzing the supersonic flutter of A low aspect ratio stiffened trapezoid wing. The finite element approach uses 20 degrees-of-freedom (d.f.) flat shell element, 12 d.f. three-dimensional beam element and quasi steady linear piston aerodynamic theory to evaluate the skins of wing, the stiffeners and aerodynamic pressure, respectively. The solution of the constructed equation system will lead to an eigenvalue problem, in which its eigenvalues can be obtained using the generalized method. In this paper, three numerical examples are investigated and the calculation results of the first and second ones are used for validation. These comparisons entirely endorse the accuracy of this modeling approach. Besides, in the third applicable example, the influences of the stiffener size and airflow yawing are scrutinized on supersonic flutter characteristics of the stiffened low aspect ratio trapezoid wing. The results evince that the size of stiffener strongly affects on the critical dynamic pressure, which its minimum occurs when the airflow is parallel to the base edge of the wing.
This work is devoted to investigating the coexistence of anti-synchronization (AS) and complete synchronization (CS) of two identical delay hyperchaotic Lü systems via partial variables. Based on the Lyapunov stability theory, a simple synchronization scheme only with linear inputs is considered. The sufficient conditions of synchronization are also obtained for both linear feedback and adaptive control approaches. The coexistence of AS and CS between two nearly identical delay chaotic systems with unknown parameters is explored. A single input controller is proposed and the adaptive parameter update laws are developed. Numerical simulation results are presented to demonstrate the effectiveness of the proposed chaos synchronization scheme.
The method of reverberation-ray matrix proposed by Pao et al. is applied to analyze the transient response of a multi-span pipe conveying fluid. The pipe under transverse vibration is considered as Timoshenko beam conveying axial flow. In the process of analysis, fast Fourier transform is used to convert the partial differential equation into ordinary differential equation. The support points of the pipe are chosen as the elements’ nodes. The transient wave motions at each node are divided into incident and reflected wave. By virtue of continuity and balance condition, the scattering relation is established between the above wave motions. The transient response is obtained by inverse fast Fourier transform. In the examples, the natural frequencies are calculated for single- and multi-span pipe conveying fluid with different fluid velocity, and great agreement is shown with the published literature. And then the transient responses, such as deformation, velocity, shear force and bending moment are obtained for a two-span pipe conveying fluid under different fluid velocity.
Water leakage is an important component of water loss. Many methods have emerged from urban water supply systems (WSSs) for leakage control, but it still remains a challenge in many countries. Pressure management is an effective way to reduce the leakage in a system. It can also reduce the power consumption. To have a better understanding of leakage in WSSs, to control pressure and leakage effectively, and for optimal design of WSSs, suitable modeling is an important prerequisite. In this paper a model with the main objective of pressure control and consequently leakage reduction is presented. Following an analogy to electric circuits, first the mathematical expression for pressure drop over each component of the pipe network (WSS) such as pipes, pumps, valves and water towers is presented. Then the network model is derived based on the circuit theory and subsequently used for pressure management in the system. A suitable projection is used to reduce the state vector and to express the model in standard state-space form.
Fluid-film bearings can suffer from flow-induced instabilities known as ‘whirl’ and ‘whip,’ especially when supporting lightly-loaded shafts. This phenomenon can lead to large rotor (self-excited) vibrations, which eventually result in rotor-bearing failure. In this paper, we introduce a new active hydrodynamic bearing to mitigate such vibrations in lightly loaded rotating machines. The system contains a rotating bushing, actuated by a motor, that serves as the control input. This input is used to control the mean flow velocity in the bearing and thereby the journal vibration. A simple feedback control law is proposed for the bushing velocity, and numerical simulations are presented to evaluate the active bearing.
The first-passage failure of single-degree-of-freedom nonlinear oscillators with fractional derivative under Gaussian white noise excitations is studied. First, the term associated with fractional derivative is approximately equivalent to amplitude-dependent quasi-linear damping and stiffness forces by using the generalized harmonic balance technique and the given system is replaced by an equivalent nonlinear stochastic system without fractional derivative. Then, the equivalent nonlinear stochastic system state is approximately represented by a one-dimensional diffusive process through stochastic averaging. The backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the conditional mean of first-passage time are established from the averaged Itô equation of the total energy and solved numerically, respectively. Finally, two examples are worked out in detail and the analytical results are validated by those from the Monte Carlo simulation of original systems.
This paper studies the sloshing suppression problem in point-to-point liquid container transfer via a Prismatic–Prismatic–Revolute robot. A multi-mass–spring model is introduced for the characterization of the most prominent liquid-sloshing modes. The control inputs are two forces and a torque applied to the prismatic joints and the revolute joint, respectively. The control objective is to control the robot end-effector movement while suppressing the sloshing modes. A nonlinear mathematical model that reflects all of these specifications is first derived. Then, a Lyapunov-based nonlinear feedback controller is designed to achieve the control objective. Finally, a simulation example is included to demonstrate the effectiveness of the controller.
This paper deals with the problem of controlling flexible link manipulators on the dynamic phase of the trajectory. A flexible beam/arm is an appealing option for civil and military applications, such as space-based robot manipulators. However, flexibility brings with it unwanted oscillations and severe chattering which may even lead to an unstable system. To tackle these challenges, a novel control architecture scheme is presented. First, a nonlinear controller based on the equation of motion of the robot is elaborated. Its aim is to produce a stable tracking control and dump the vibration of the links. Then, an adaptive cerebellar model articulation controller is implemented to compensate for structured and unstructured uncertainties. Efficiency of the new controller obtained is tested facing an important variation of the dynamic parameters of the manipulator. Simulation results on a dynamic trajectory with a high acceleration/deceleration ratio show the effectiveness of the proposed control strategy.
In this paper, the authors proposed an approach for solving nonsmooth continuous and discontinuous ordinary differential equations which is based on a generalization of the Taylor expansion. First is considered a generalized derivative for nonsmooth functions with a single variable which is proposed by Kamyad et al. Then, the generalized Taylor expansion of nonsmooth functions is introduced and used to state an approach. Finally, some numerical examples of nonsmooth ordinary differential equations are solved.
In hammer mills, the grinding process consists of hitting the material by hammers, articulated on a rotor. It is important, however, that the percussions applied to the hammer are not transmitted to the articulation. The position of the hammer articulation should be determined so that the percussion given by the collision with the particles of material is applied in the centre of percussion. Because the conditions of the percussion center are not always accomplished, unbalances depending on the connection percussions appear and produce supplementary perturbations. These effects are estimated by the transmission ratio of the percussion to the articulation. This is checked by measuring the appearance of some amplified vibration levels in conditions of increased transmission ratio of percussion.
By setting a partition on the domain and approximating each part with a sector of a suitable circle, the system solution was identified as a trigonometric series with unknown coefficients. After bringing into account the harmony and smoothness of the solution, the problem was transferred into a new linear one in which it was involved with radon measures. Existence of the optimal solution for the new problem was proved automatically. Then, by some discretization schemes, it was also shown that how the optimal classical trajectory and control were identified simultaneously via the results of a finite linear programming. To see the advantages of this general, simple and linear new method, a numerical simulation was also presented.
Time delays exist in active control systems. Although a time delay in most cases is small, it results in the actuator applying energy to the control system with a time delay. This might cause instability of the dynamic systems and degrade the performance of the control systems. The objective of the present work is to propose a feasible methodology that can achieve good control performance for a dynamic beam structure system by time-delayed boundary torque actuators. The control problem is to determine optimal time-delayed boundary control by minimizing a given performance criterion. The performance criterion is specified as a weighted quadratic functional of the dynamic responses of the beam which is to be minimized at a specified terminal time using continuous time-delayed torque actuators. The modal expansion approach is used to convert the optimal control problem of a distributed parameter system into the optimal control problem of a linear lumped parameter system (LPS). A direct state-control parameterization approach is proposed where wavelets are employed to solve time-delayed LPS. The operational matrices of integration and delay are utilized to reduce the solution of linear time-varying delayed systems to the solution of algebraic equations. A numerical simulation is presented to illustrate the efficiency of the proposed control algorithm.
An investigation into the development of a closed-loop vibration control strategy for flexible manipulator systems is presented in this paper. Development of the controller is carried out in two phases. A collocated position controller on the basis of a proportional-derivative feedback control technique is developed first and then a command-filter vibration controller is developed based on the dominant vibration modes of the system and placed inside the position control loop. While the purpose of the position controller is to place the end-point of the manipulator at a position of demand, the objective of the vibration controller is to reduce motion-induced vibration of the manipulator arising from structural flexibility of the system during fast maneuvers. Low-pass and band-stop elliptic filters are used in designing the vibration controller to filter out input energy at dominant vibration modes of the manipulator so that it is not excited at its natural frequencies. The performances of the controllers are assessed within a simulation environment of a single-link flexible manipulator. It is demonstrated that while the performance of the position controller in controlling the rigid body motion of the manipulator is as expected, significant reduction in the level of structural vibration of the system is achieved with the help of the vibration controller.
This investigation addresses the stability problem of multiple time-delay Takagi-Sugeno (T-S) fuzzy systems subjected to disturbances. A novel criterion, designed in terms of the fuzzy Lyapunov method, is merged with the linear matrix inequality theory to ensure the asymptotic stability of the multiple time-delay T-S fuzzy systems. Furthermore, the neural network modeling approach and H infinity control performance are employed to improve the controller design for parallel distributed compensation. Finally, the application of the criterion demonstrates the feasibility of the controller design.
This paper presents a novel adaptive-based vibration control algorithm for smart structures, despite the model parameter variations, unstructured uncertainties, and environmental disturbances. The rate of vibration suppression can be managed in the proposed method, by taking a desired exponential decaying trajectory. Since the proposed method is established by taking various perturbations into account, it can be applied to a wide class of structures without any conservative hypotheses. The stability analysis is presented based on the Lyapunov’s direct method. In order to verify the effectiveness of the method, numerical analyses are presented and discussed by applying the developed vibration control methodology to a smart beam.
This study introduces the use of fuzzy neural networks with intent to clearly visualize the advantages of the approach. Particle swarm optimization as the underlying optimization tool is discussed. Different models of fuzzy neural networks can be envisioned. It is worth stressing that the underlying concept is general enough and any other formalism of information granules could be considered as well. Over the past decades, the Chinese market has developed rapidly, especially on intelligent robot interaction and even tension leg platform. Consequently, Chinese learning has increased. E-learning has also become another learning mechanism and is already quite popular. In the study, optical character recognition software is developed in the android phone system. A questionnaire is designed as a base technology acceptance model, and, according to the dimensions, to make assumptions. Using a structural equation model analysis framework to analyze the recovery over the questionnaire, the conclusion of this study and the possible direction of future research are finally arrived at.
The rapid and sway-less conveyance of crane loads has been an essential task and a field of research; considering the broad application of transportation of goods and materials by these systems. In this paper, a neural network self tuner (NNST) controller, which aims to move the load precisely as well as to eliminate its sway, is presented. This controller is capable of being trained flexibly for either increasing the speed of load transportation or decreasing its sway. The developed training algorithm, in this paper, is inspired by a sway elimination method of input shapers. The proposed training method provides the controller with the capability to remove the majority of load sway, at the outset of transportation, and transport it with a slight sway. The results show that the neural network controller with the proposed training method, in the same time, is capable of removing the sway of the load in a better way and be more appropriate for longer distances compared to a proportional-integral-derivative controller with constant gain. Besides, compared to standard input shapers, the NNST controller is more robust to cable length variations as well as length uncertainty by utilizing the feedback. Using a lab scale gantry crane model, the feasibility of empirical implementation is proved and results are verified.
The use of composite materials for weight reduction of shaft drivelines has positive impacts in different applications. The driveshafts design is mostly dictated by its natural frequencies. In order to maximize the natural frequencies, shafts are built in one, two or more segments. Analysis of such components has complexities in dealing with two-segments, shear deformation, and material coupling effects. This paper presents a theory that includes shear deformation and rotary inertia along with coupling effects to analyze transverse vibration behavior of generally laminated shafts with intermediate joints. Equivalent modulus of elasticity is used instead of traditional stiffness terms to account for material coupling. The equations of motion are solved using generalized differential quadrature. Results were compared with those published in the literature and finite element simulations, and it has been shown that the present method can accurately predict transverse vibration behaviors of generally laminated two-segment shafts with a lumped mass.
How to protect shipboard personnel from the shock events induced by underwater explosion is a very interesting subject for ship designers. In this study, the potential attenuation performance of an elastic polymer foam cushion inserted between standing-man and ship deck is investigated theoretically. An 8-degree-of-freedom nonlinear lumped-parameter model is applied to predict the standing-man’s biodynamic responses and injury potential. The cushion is modeled by a chain of masses separated by nonlinear springs and dampers in parallel to simulate the micro inertia, stiffness and rate-dependent effects exhibited by common polymer cellular materials. Two variables, kickoff speed ratio and deck reaction force ratio corresponding to two types of typical injury potential of standing-men, are defined as evaluation parameters. The influence of critical buckling force level, material rate dependent effect as well as some other design factors on the attenuation performance of the foam cushion is discussed in detail. Some general design rules are also presented.
The application range of a mobile robot is very wide, and includes cleaning, carrying, guiding, manufacturing, remote exploration, artificial intelligence, entertainment and even cooking, tension leg platform, consumer and service quality. As the different conditions required, a biped robot may have to decide the correct direction, cross ditches, stand up when it has fallen down, move along sloping surfaces, avoid some obstacles, and do other things during a walking test. It is difficult designing such a robot because its dynamics are very complex, and it is hard to control the stability of biped walking. Hence, for operating and ensuring the stability of biped walking, it is necessary to generate an effective control method and good trajectory. The contribution focuses on mechanical components.
In this paper, a fuzzy-rule-based semi-active control of building frames using semi-active variable orifice dampers (VODs) is presented. Additionally, the consequences of well-known characteristics of near-fault ground motions, forward directivity and fling step, on the seismic response control is investigated. The membership functions and fuzzy rules of the fuzzy controller were optimized by genetic algorithm. To illustrate the efficiency of the proposed fuzzy controller strategy in application and effects of near-fault ground motions, numerical simulation for a 10-story building frame equipped with VODs is presented. The VODs are installed in all storeys to prevent damage to the structure from severe earthquakes. The controlled response of the frame was compared with results obtained by controlling the frame by the classical clipped-optimal control method based on linear quadratic regulator theory. Results revealed that the fuzzy logic controller is capable of improving the structural responses and VODs are promising for reducing seismic responses during near-fault earthquakes.
For a magnetically suspended flywheel (MSFW), the residual unbalance of rotor can cause synchronous vibration and reduce the attitude control precision of spacecrafts. To eliminate the vibration caused by the residual unbalance of rotor suspended by magnetic bearing, the theorem of unbalance vibration is researched, and it is pointed out that the vibration can be successfully suppressed through the elimination of synchronous component in magnetic suspension forces by a magnetic suspension force compensation method. Based on the general notch filter, this method is proposed to be closed-loop style when the rotor rotates beyond its critical stable speed and to be open-loop style when the speed of the rotor is less than the critical stable speed by additional displacement stiffness compensation segment, open and closed-loop control method. The stability of this method is analyzed and the ability to eliminate n octave synchronous is verified in the whole speed range of the rotor. Experimental results demonstrate that this method can suppress the unbalance vibration significantly in the operation speeds of MSFW and is suitable for MSFW in that the rotor traverses its critical stable speed frequently.
The unified matrix polynomial approach (UMPA) was developed in order to understand and derive various experimental modal analysis algorithms (which have been developed in isolation) using a common mathematical formulation. Various commercially available algorithms – such as the polyreference time domain, least squares complex exponential, and eigensystem realization algorithm etc. – can be explained using UMPA methodology, which makes it easier to understand both the advantages and limitations of such algorithms. In view of this fundamental characteristic of the UMPA, this paper aims at using the approach to understand, explain and develop the stochastic subspace identification (SSI) algorithm - a popular time domain operational modal analysis (OMA) algorithm. The roots of SSI algorithm lie in the identification of linear dynamic systems, traditionally a communications and controls engineering area. By means of the UMPA, the SSI algorithm’s similarity to a high order time domain OMA algorithm can be shown. It can also be shown that state transition matrices identified using the SSI algorithm and UMPA formulation are related to each other through a similarity transformation, thus characterizing the same system.