A finite element model for a bi-layered piezoelectric plate-strip with initial stresses under a time-harmonic force

Abstract

The novelty of this study is presenting the analytical approach to investigate the dynamic response and the forced vibration by a time-harmonic force of a bi-layered piezoelectric plate-strip with initial stresses, resting on a rigid foundation. Material properties are varied perpendicular to the free surface of the plate-strip according to a simple power-law distribution. Firstly, the nonlinear mechanical equations of motion are linearized within the scope of the three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB). Furthermore, using the piezoelectricity material properties, linear electrical governing equations are derived. Next, the problem under consideration is solved by the finite element method (FEM) to determine, especially the frequency response of the body. The approach is verified by the previous results in the literature. In numerical results, the influences of the initial stress, the height ratio of the layers, thickness ratio, and dimensionless frequency parameters on the dynamic response and the forced vibration of the bi-layered piezoelectric plate-strip are presented and discussed in detail.