International Journal of Structural Stability and Dynamics

This paper presents an electromechanical coupled dynamic equation for the lateral-flexural and torsional vibrations of a flexible ring for an electromechanical integrated electrostatic harmonic actuator as well as the equation of the forced response of the electromechanical integrated electrostatic harmonic actuator to voltage excitation. By solving these equations, the natural frequency and vibration modes of the flexible ring for the actuator are investigated. Changes in the natural frequency with respect to the main system parameters are also examined and the dynamic responses of the actuator to voltage excitation obtained.

This paper presents the elastic strain energy, the potential energy with the second order terms of finite rotations, and the kinetic energy with rotary inertia effect for thin-walled composite beams of mono-symmetric cross-section. The equations of motion and force-displacement relationships are derived from the energy principle and explicit expressions for displacement parameters are given based on power series expansions of displacement components. The exact dynamic stiffness matrix is determined using the force-displacement relationships. In addition, the finite element model based on Hermitian interpolation polynomial is developed. In order to verify the accuracy and validity of the formulation, numerical examples are solved and the solutions are compared with results from ABAQUS's shell elements, analytical solutions from previous researchers and the finite element solutions using the Hermitian beam elements. The influence of constant and linearly variable axial forces, fiber orientation, and boundary conditions on the vibration behavior of composite beam are also investigated.

With the view to achieving a more perfect microvibration-free working environment for high technology equipment such as semiconductors and optical microscopes, the authors investigate the use of a 6-DOF microvibration hybrid control system to mitigate two types of vibration (ground motion and direct disturbance). This hybrid control system comprises a table, five air springs as passive mounts and eight magnetostrictive actuators as active control actuators. To facilitate the feedback control and performance evaluation of the hybrid control system based on the one-third octave band spectra with the absolute velocity being the target, the analytical model of a hybrid control system that incorporates magnetostrictive actuators is established in the absolute coordinates. The control performance of the platform with a hybrid control system is assessed by comparing with the case of the platform with a passive control system. Simulation results indicate that the proposed platform with hybrid control system for microvibration is superior to that with passive control system because of its higher control performance against ground motion and direct disturbance for a wide range of frequencies.

Two or more dynamical systems can achieve external synchronization motions with an especially designed controller, in which one dynamical system is considered as the master, and the other as the slave. In this paper, a general strategy of feedback control to carry out the external synchronization is firstly introduced. The master system consists of a hysteretic device to account for the friction phenomenon, and the slave system comprises a hardening stiffness component that can generate the third order displacement as a Duffing system. The slave system can keep in synchronization with the movements of the master via a feedback control strategy. A stability analysis of the synchronization errors is conducted. Different synchronization motions under different system parameters are simulated, based on which discussions are made for the effects of the controller parameters.

The identification of damping in a structural system is extremely important for reliable prediction of response of dynamic systems. The present study focuses on the damping parameters identification of linear multi-degree of freedom (MDOF) systems defined by Rayleigh damping model. A system identification (SI) algorithm based on the free vibration response of structures is proposed to identify the damping parameters. In doing so, the equation error based SI approach is readily developed for identification of damping properties at element level. The formulation is elucidated using numerically simulated modal data obtained through finite element analysis. The robustness of the algorithm is also studied by Monte Carlo simulation based error sensitivity analysis. The identified damping values are found to be in consistent with those of pre-assigned values used to simulate modal data.

Glass wall supporting systems, comprising of pre-tensioned high strength trusses made from alloy steel bars, behave nonlinearly under wind and other loads. For a proper analysis and design, second-order and large deflection analyses are mandatory as the structural response like stress and deflections are highly dependent on the small movements and temperature effects. Also, careful consideration must be given to various effects such as support settlement due to live loads and material creep, temperature change, pre-tension force and wind pressure. It is not uncommon to see many glass wall systems fail in a simulated wind load test under the simulated design wind speed. This paper presents a rigorous analysis and design of this type of structural systems used in two projects in Hong Kong. The key message is the need to use "section strength check" in place of the member design adopted in the conventional effective length method for design of practical structures behaving nonlinearly since the prescriptive buckling check formulae become inaccurate or even invalid. The use of stability function allowing for initial imperfections in place of cubic Hermite element is proposed here because of the high degree of nonlinearity.

This paper presents the discrete singular convolution (DSC) method for solving buckling and vibration problems of rectangular plates with all edges transversely supported and restrained by uniform elastic rotational springs. The opposite plate edges are subjected to a linearly varying uni-axial in-plane loading. The rationale for using DSC method stems from its numerical stability and flexible implementation for structural analysis. To verify the present approach, convergence and comparison studies for rectangular plates with different combinations of elastically restrained and classical edges are carried out. Accurate buckling and vibration solutions of plates having two opposite edges elastically restrained and the other two sides clamped, or all edges elastically restrained are presented.

Vibration analysis is carried out for compressively loaded and thermally loaded postbuckled functionally graded material (FGM) plates with piezoelectric fiber reinforced composite (PFRC) actuators. The temperature field is assumed to be uniformly distributed over the plate surface but it varies through the thickness. The electric field has a non-zero-valued component E_Z. Material properties of the substrate FGM layer are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The material properties of both FGM and PFRC layers are assumed to be temperature-dependent. The formulations are based on a third order shear deformation plate theory and the general von Kármán-type equation that include thermo-piezoelectric effects. The numerical illustrations cover small- and large- amplitude vibration characteristics of postbuckled, mid-plane symmetric FGM plates with surface-bonded or embedded PFRC actuators under uniform and non-uniform temperature fields. The results for monolithic piezoelectric actuators, which is a special case in the present study, are compared with those of PFRC actuators. The results reveal that control voltage has a small effect on the vibration characteristics of the compressed postbuckled FGM plate with PFRC actuators but has a relatively large effect on the natural frequency of thermally postbuckled plates.

A symplectic numerical approach to the stability analysis of nonlinear parametric excited systems with multi-degree-of-freedom is developed and the stability of a nonlinear vibration system depends on the dynamic behavior of its perturbation. The nonlinear parameter-varying differential equations for the perturbation motion are expressed in the form of Hamiltonian equations with time-varying Hamiltonian, and are converted further into the classical Hamiltonian equations with extended time-invariant Hamiltonian by augmenting the state variables. The solution to the augmented Hamiltonian equations has the symplectic structure in terms of the symplectic transformation. Then the difference equations of the symplectic Runge-Kutta algorithm with a sufficient condition are constructed, which is proved to preserve the intrinsic symplectic structure of the original solution. In particular, the symplectic Gauss-Runge-Kutta algorithm with stage 2 and order 4 is proposed and applied to the stability analysis of a nonlinear system. Unstable regions based on the nonlinear periodic-parameter perturbation equation are obtained by using the symplectic Gauss-Runge-Kutta algorithm, analytical solution method and non-symplectic conventional Runge-Kutta algorithm to verify the higher accuracy of the proposed algorithm. Unstable regions based on the nonlinear perturbation are given to illustrate the improvement over those based on the linear perturbation. The developed symplectic approach to the stability analysis can preserve the symplectic structure of the original system and is applicable to nonlinear parametric excited systems with multi-degree-of-freedom.