ACTIVE VIBRATION CONTROL OF PIEZOLAMINATED COMPOSITE BEAM AND PLATE

Abstract

Active sensing and control of dynamic systems has recently stimulated extensive research on smart structures and systems due to the development of proposed large space structures and flexible mechanical systems. To carry out active control effectively and economically, piezoelectric materials have been studied for use in smart systems as an alternative to discrete sensing and control system. Experimental investigations of both the smart materials and structures, though possible, are prohibitively expensive, and therefore they should be complemented with theoretical analyses. Theoretical formulations and finite element models based on third-order beam theory and classical plate theory are developed to model the dynamic as well as static response of laminated composite beams and plates with integrated piezoelectric sensors and actuators (S/As) and subjected to both mechanical and electrical loadings. By coupling a simple negative velocity feedback control algorithm in a closed control loop, it reflects the essence of active vibration control of structures in a very simple form, and therefore is easy to use in smart structure and system design. The developed finite element models are then applied to implement the simulation of active shape control and vibration suppression of laminated composite structures using piezoelectric sensors and actuators. First, a finite element model for the laminated composite beam with distributed piezoelectric actuators is developed by using Reddy's third-order beam theory. A static and dynamic analysis of a piezolaminated composite beam is made by the proposed model. The results are compared with those of the classical beam theory and the first-order shear deformation beam theory to show the efficiency, accuracy and appropriation of the developed model for both thin and moderately thick or thick laminated composite beam. Furthermore, by incorporating with the converse and direct piezoelectric equations, the previous developed model is extended for the active deformation and vibration control of composite beams with distributed piezoelectric S/As. A simple negative velocity feedback control algorithm is coupled in a closed control loop. The shape control and active vibration suppression of a cantilever composite beam are performed to demonstrate the presented model. The effects of the number and location of the piezoelectric S/As on the efficiency of the control systems are evaluated. Finally, based on the classical laminated plate theory and the principle of virtual displacements, a finite element model is developed for the shape control and active vibration suppression of laminated composite plates with integrated piezoelectric S/As. The model is validated by comparing with results available in the literature. It is then used to simulate the shape control and active free vibration suppression of laminated composite plates. The effect of stacking sequence, feedback control gain and position of sensor/actuators on the response of the plate is also investigated. Some important conclusions are obtained.