Characteristics of Wave Propagation in Functionally Gradient Piezoelectric Material Plates and its Response Analysis. Part 1: Theory.

Abstract

The numerical methods which have been proposed by the present authors for investigating the characteristics of waves in a functionally gradient material (FGM) plate and its transient responses are expanded for functionally gradient piezoelectric material (FGPM) plates. The material properties of the plate change gradually in the thickness direction, and are anisotropic in the plane of the plate. The plate is divided into N plate elements. The variational principle is used to derive approximate governing equations. The dispersion relation and the mode shape of the waves are obtained by using mechanical ane electrical boundary conditions. The energy velocities of the waves are formulated with the aid of the Rayleigh quotient. The method of Fourier transforms in conjunction with modal analysis is used to determine the displacement and electrostatic potential responses excited by mechanical loads and/or interdigital electrodes. The formulation of the theory is described in this paper.