Vibration control simulation of beams with piezoelectric actuators using impedance and FEM

Abstract

Vibration control simulations of beams with piezoelectric actuators using impedance method and FEM are presented in this paper. At first, one impedance matrix equation is used to describe the dynamic of one piezoelectric stretch actuator, and each impedance equation is equivalent to one mass-damping-spring (M-C-K) system. A FE harmonic analysis is carried out on piezoelectric stretch actuator and the equivalent system are determined by several frequency functions using FE results and numerical interpolations. Secondly, the equivalent system is used to build FE model of beams driven by piezoelectric bending actuators, which is consist of two piezoelectric stretch actuators located on the top and the bottom of the beam respectively. Once the frequency response data or transfer functions of the smart beam can be obtained by using impedance, the vibration control model with close-loop feedback can be established. At last, three numerical examples are used to verify the proposed methods. The results of one individual piezoelectric stretch vibrator show that, the predicted dynamic response is accord with the others. A simply-supported beam driven by piezoelectric bending actuators is considered as the second example. The center deflection of the beam is obtained and found to be quiet accurate comparing with the analytical result. The third example is to simulate vibration of one suspended piezoelectric bimorph beam under close-loop feedback control. The simulation result is also shown to be quite accurate by comparing with the other results, and the vibration absorption results are shown in the figures of this paper.