Free vibration of a bi-layered composite plate of a piezoelectric semiconductor and a piezoelectric dielectric

We study the free vibration of a piezoelectric bi-layered plate composed of a piezoelectric semiconductor (PS) layer and a piezoelectric dielectric (PD) layer. The macroscopic theory of a PS consisting of the conventional theory of piezoelectricity and the drift-diffusion theory of semiconductors is used. The nonlinear equations for drift currents of electrons and holes are linearized for small perturbation of carrier density. The first-order zigzag approximation for in-plane displacements and electric potential through the thickness of each layer is used. Interfacial continuity of the displacement, the transverse shear stress, and the electric potential between the PS layer and the PD layer is ensured, which is very important and also experienced by layered structures. The number of independent unknown variables is reduced from 11 to 5 by using the interfacial continuity and the zero shear stress conditions at the top and bottom surfaces. The governing equation and corresponding boundary condition are derived using Hamilton's principle. An analytical solution of a simply supported composite plate is obtained. The effects of steady-state electron density, axial force, and the geometric parameters on the vibration frequency and modes are discussed. The obtained results may be useful for further theoretical analysis of PS composites and practical application of piezotronic devices made from PS and PD materials.