Free vibration analysis of multi-directional functionally graded circular and annular plates

This paper addresses the free vibration of multi-directional functionally graded circular and annular plates using a semianalytical/ numerical method, called state space-based differential quadrature method. Three-dimensional elasticity equations are derived for multi-directional functionally graded plates and a solution is given by the semi-analytical/numerical method. This method gives an analytical solution along the thickness direction, using a state space method and a numerical solution using differential quadrature method. Some numerical examples are presented to show the accuracy and convergence of the method. The most of simulations of the present study have been validated by the existing literature. The non-dimensional frequencies and corresponding displacements mode shapes are obtained. Then the influences of thickness ratio and graded indexes are demonstrated on the non-dimensional natural frequencies.