Accurate Dynamic Electromechanical Solution for Rectangular Piezoelectric Plate Based on Modified FSDT

Abstract

In this study, the modified first-order shear deformable theory (FSDT) is applied to analyze the resonant characteristics of piezoelectric (PZT) moderately thick plate vibrators with different thicknesses. A simple and straightforward simplification method between mechanical and electrical functions is also proposed based on the modified FSDT. The natural frequencies and associated mode shapes of piezoelectric plates with completely free boundary are analyzed. The displacement fields of the flexural modes are presented based on the superposition method. This analytical method provides a strong-form novel solution for the flexural-dominated motion’s out-of-plane and in-plane coupling displacement fields. The solutions of displacement functions, which are obtained from the superposition method, show excellent convergence for numerical calculation. To verify the validity of the theoretical solution, the resonant frequencies and the corresponding mode shapes are compared with that obtained by the finite element method (FEM) and experimental measurements using the amplitude-fluctuation electronic speckle pattern interferometer (AF-ESPI) technique. According to the electromechanical formula and the derived theoretical solution, four types of electrode are designed to excite the moderately thick PZT specimen for examining the application feasibility of the proposed method. It is shown in this study that the theoretical analysis, numerical calculation, and experimental measurement are fully compared, and excellent agreements of the piezoelectric moderately thick plate are also obtained.