Lamb waves in a functionally gradient material plate and its transient response. (Part 1. Theory).

Abstract

The numerical methods which have been proposed by the present authors for Lamb waves in an anisotropic laminated plate and its transient responses are expanded for the wave propagation analysis of functionally gradient material (FGM) 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. In the element, we assume that the material properties change linearly in the thickness direction, and that the displacement field is expressed by second-order polynomials. The principle of virtual work is used to develop approximate dynamic equilibrium equations. The dispersion relation and the mode shape of the Lamb waves are obtained by using the free boundary conditions. The energy velocities of the Lamb waves are formulated with the aid of the Rayleigh quotient. The method of Fourier transforms in conjunction with the modal analysis is used to determine the response of displacements. The formulation of the theory is described in this paper.