An efficient coupled zigzag third-order theory for dynamic analysis of multilayered piezoelectric semiconductor plates

Abstract

Different from piezoelectric (PE) dielectrics, piezoelectric semiconductors (PSs) show the interaction between electromechanical field and mobile charges. This not only makes PSs have great potential for developing electronic devices, but also presents a lot of multi-field coupled problems that need to be investigated. In this paper, an efficient coupled zigzag third-order theory (CZTT) is developed for the dynamic analysis of a multilayered PS plate. The continuity of the mechanical displacements, the transverse shear stresses and the electrical fields at each layer interface are ensured. The shear traction-free condition and electrical short circuit condition are enforced at the top and bottom surfaces of the multilayered PS plates. The number of primary field variables is reduced to seven and is independent of the number of layers. The governing equations and the corresponding boundary conditions are derived using Hamilton principle. An analytical solution for a simply supported multilayered PS plate is obtained. The vibration frequency and damping for three-layer PS plates are calculated using the analytical solution and verified through the finite element (FE) simulation. The effects of steady-state electron density, different stacking sequences and thickness ratios on dynamic characteristics are discussed. The size-dependent dynamic behaviors resulting from the semiconductor (SC) property are revealed. It is shown that the dynamic behaviors can be divided into three coupling statuses according to the density value of steady-state electron. The vibration frequency is significantly weakened within a certain range of steady-state electron density due to the screen effect of free electrons. The findings could be useful to the analysis and design of layered composites made of smart PS materials.