Showing papers by "Yiu-Yin Lee published in 2002"

Dynamic stability of a curved beam under sinusoidal loading

Abstract: This paper is a study of snap-through properties of a non-linear dynamic buckling response to sinusoidal excitation of a clamped—clamped buckled beam. Using a simple formula, the highly non-linear motion of snap-through and its effects on the overall vibration response have been studied. The non-linear governing equation obtained here is solved using the Runge—Kutta (RK-4) numerical integration method. Critical parameters at the onset of the snap-through motion, which vary with different damping coefficients and linear circular frequencies of a flat beam, are studied and given in terms of the excitation level and response displacement. The relationships between static and dynamic responses at the start of the snap-through motion are also predicted. The analysis brings out various characteristic features of the phenomenon, i.e. (a) small oscillations about the buckled position, (b) chaotic motion of intermittent snap-through and (c) large oscillations of continuous snap-through motion crossing the ...

Numerical simulation model of vibration responses of rectangular plates embedded with piezoelectric actuators

Abstract: A numerical simulation model for random large amplitude vibration control of composite plate using piezoelectric material is presented. The H∞ control design is employed to suppress the large amplitude vibrations of composites plates under random loading. The numerical simulation model is developed and based on the finite element method. The finite element governing equation includes fully coupled structural and electrical nodal degrees of freedom, and consider the von Karman large amplitude vibration. The modal reduction method using the structural modes is adopted to reduce the finite element equations into a set of modal equations with fewer degrees of freedom. The modal equations are then employed for controller design and time domain simulation. In the simulations without control, the value of the linear mode to the nonlinear deflection is quantified; and the minimum number of linear modes needed for accurate model is obtained. In the simulations with control, it is shown that the truncated modes, which are neglected in the control design, deteriorate the controller performance. Generally, the vibration reduction level is not monotonically increasing with the size of the piezoelectric actuator. The optimal piezoelectric actuator size depends on the excitation level. For higher excitation level, optimal actuator size is larger. The H∞ controller based on the linear finite element formulation gives better vibration reduction for small amplitude vibration, but it still gives reasonable performance for large amplitude vibration provided that the piezoelectric actuator is big and powerful enough.

Analytical model for predicting nonlinear random and snap-through response of buckled plates

Abstract: This paper presents a simplified model for predicting the nonlinear random response of flat and buckled plates. Based on a single mode representation of vibration response, r.m.s. values of the strain response to broadband excitation are evaluated for different static buckled configurations using the equivalent linearization technique. The dynamic effects on the overall strain response due to instability motion of snap-through are included. Parametric studies are performed in which the influences of the clamped and simply-supported boundaries, aspect ratio of the plate, thickness and length of the plate are considered. Using a simple single-model formula, the results of dynamic buckling motion were compared with finite-element models as well as experimental results. The comparisons between analytical results and experimental results help to assess the accuracy of the theory and the conditions under which deviations from the theory due to effects of imperfection and higher modes are significant. It is found that the theoretical model is useful for design and checking of computer results for curved plates in a slightly deflected form (initial deflection less than twice the thickness of plate) and the prediction accuracy on nonlinear analysis is higher than existing design formula based on linear response.