Linear modal analysis of ring shaped - elliptical plate using finite element method

Abstract

Abstract In this paper, the wave propagation of a transversely isotropic thin ring - shaped elliptical plate made up of piezo electric material is considered. The surfaces are assumed to be traction free and coated with electrodes. The trail functions are introduced to uncouple the equations of motion and electric property. A computer program solving the finite element method (FEM) is developed and the numerical calculations are given for an array of six-noded shell elements. The non-dimensionalized natural frequencies of the elliptical plate in different wave numbers under different boundary condition for symmetric and antisymmetric modes are calculated and are plotted as dispersion curves. The proposed model is effective and simple and can be applied to problems with exact solution or a finite element approximation to the governing equations.