Vibration Suppression of a Cantilevered Piezoelectric Laminated Composite Plate Subjected to Hygrothermal Loads

Abstract

In this paper, the vibration suppression strategy for a cantilevered rectangular piezoelectric laminated composite plate is proposed by using the piezoelectric patches, which are attached to the upper and lower surfaces of the plate as the actuators and sensors, respectively. The main contributions of this study is as follows: Firstly, Based on classical laminated plate theory and considering the action of piezoelectric loadings, the dynamics equation of a piezoelectric laminated composite plate subjected to hygrothermal loads is derived by using Hamilton's principle. The partial differential equations of the piezoelectric laminated composite plate are discretized to a two-degree-of-freedom control equation by using Galerkin method. Secondly, According to the discrete nominal model, a robust controller for the uncertain systems is proposed. Based on the state space equation, the output feedback controller for the system is designed. In the constructed full-dimensional state observer, the estimated state feedback is introduced to construct a closed-loop feedback system. Using the Lyapunov Matrix Inequality (LMI) method and Lyapunov Stability Theory, the feedback gain matrix and observation gain matrix for the system are designed to make the closed-loop system asymptotically stable. Finally, the accuracy and effectiveness of the controller are verified by numerical simulation.