Finite element analysis and vibration control of piezoelectric laminated plates based on precise integration

A piezoelectric laminated finite element based on the three-order shear deformation theory is proposed for the bending and vibration analysis of piezoelectric laminated structures. The dynamic equations of piezoelectric laminated structure are formulated by invoking the proposed finite element and using Hamilton's principle. The equations are solved via the precise integration method. The algorithm for solving the Riccati equation for the linear quadratic optimal control is presented with the precise integration method, and the linear quadratic optimal control law is designed to eliminate the vibration. Finally, two numerical examples are given, and the results indicate that the proposed finite element is capable of analyzing the piezoelectric laminated structure with high accuracy, and the presented linear quadratic optimal control is feasible.