In-plane-dominated vibration characteristics of piezoelectric thick circular plates based on higher-order plate theories

Numerous engineering applications exist for the piezoelectric effect, which results from the electromechanical coupling between electrical and mechanical fields. In-plane vibrations of piezoelectric plates’ resonance frequencies and associated mode shapes have been thoroughly investigated. However, analytical solutions for in-plane-dominated vibrations of thick piezoelectric circular plates are limited. In this paper, higher-order plate theories for the in-plane-dominated vibration characteristics of piezoelectric circular thick plates under fully clamped and completely free boundary conditions are presented. The resonant frequencies and associated mode shapes were investigated based on two higher-order plate theories: second-order shear deformation plate theory and third-order shear deformation plate theory, as well as simplified third-order linear piezoelectric theory. Hamilton's principle was applied to derive equations of motion and boundary conditions. In the theoretical analysis, the resonant frequencies, associated mode shapes and distribution of electric displacements for various radius-to-thickness ratios were calculated. The numerical results obtained by the finite element method were compared with those obtained from theoretical analysis. Excellent agreement was found between the theoretical and numerical results for the thick piezoelectric circular plates.