Three-dimensional free vibration analysis of thick functionally graded plates on elastic foundations

The research works on the three-dimensional (3D) free vibration analyses of functionally graded (FG) plates are limited to plates with simply supported boundary conditions and without elastic foundations. Hence, the free vibration analysis of thick FG plates supported on two-parameter elastic foundation is presented. The formulations are based on the three-dimensional elasticity theory. Plates with two opposite edges simply supported and arbitrary boundary conditions at other edges are considered. A semi-analytical approach composed of differential quadrature method (DQM) and series solution is adopted to solve the equations of motions. The material properties change continuously through the thickness of the plate, which can vary according to power law, exponentially or any other formulations in this direction. The fast rate of convergence of the method is demonstrated and comparison studies are carried out to establish its very high accuracy and versatility. Some new results for the natural frequencies of the plate are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. The new results can be used as benchmark solutions for future researches.