Static and dynamic analyses of a Functionally Graded Magnetoelectroelastic Circular Plate

Abstract

A semi-analytical method, which makes use of the state space method and the one-dimensional differential quadrature method, is used to obtain the static and dynamic responses of a functionally graded magnetoelectroelastic circular plate with the material property varying only in the thickness direction. The analytical solution in the thickness direction can be obtained by using the state space method and the approximate solution in the radial direction can be derived through using the one-dimensional differential quadrature method. Based on the elastic theory of magnetoelectroelastic materials and the assumption that the mechanical, electric and magnetic properties of the materials vary continuously along the thickness direction and have the same exponential distribution, differential equations of equilibrium in terms of displacements, electric potential and magnetic potential can be presented. Numerical results are given to demonstrate the accuracy and superiority of the presented method. Some regular characteristics about the reactions of the circular plate in piezoelectric and piezomagnetic materials can be obtained by examples and the results can be used in the design of the corresponding structures.