Three-dimensional free vibration analysis of functionally graded material plates resting on an elastic foundation

This paper describes a method for three-dimensional free vibration analysis of rectangular FGM plates resting on an elastic foundation using Chebyshev polynomials and Ritz's method. The thickness can vary from thin to very thick. The elastic foundation is considered as a Winkler model. The analysis is based on a linear, small-strain, three-dimensional elasticity theory. The proposed technique yields very accurate natural frequencies and mode shapes of rectangular plates with arbitrary boundary conditions. A simple and general programme has been used for this purpose. For a plate with geometric symmetry, the vibration modes can be classified into symmetric and antisymmetric ones in that direction. In such a case, the computational cost can be greatly reduced while maintaining the same level of accuracy. Convergence studies and a comparison have been carried out using isotropic and FGM square plates with four simply-supported and clamped edges as examples. The results show that the present method enables rapid convergence, stable numerical operation and very high computational accuracy. Parametric investigations are presented for two-constituent metal–ceramic functionally graded clamped square plates on an elastic foundation with respect to different thickness–side ratios, gradient indexes and foundation stiffnesses.