Exact solutions for free vibrations of functionally graded thick plates on elastic foundations

Free vibration analysis of functionally graded thick plates on elastic foundation is carried out based on three-dimensional elasticity. An isotropic plate is assumed with Young's modulus and mass density varying exponentially through the thickness, and Poisson's ratio remaining constant. The state space method is used to derive an exact solution for a simply supported plate by expanding the state variables in trigonometric dual series. The effects of interaction between the plate surface and a Pasternak foundation are treated as the traction boundary conditions of the plate. The solution procedure is validated by comparing with established results for a homogeneous plate. Finally, the influences of foundation stiffness, foundation support, and gradient index on the natural frequencies are investigated.