Levy solution for free vibration analysis of functionally graded plates based on a refined plate theory

In this paper, analytical solution of a refined plate theory is developed for free vibration analysis of functionally graded plates under various boundary conditions. The theory accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The mechanical properties of functionally graded material are assumed to vary according to power law distribution of the volume fraction of the constituents. The Levy-type solution in conjunction with the state space concept is used to solve the equations of motion of rectangular plates with two opposite edges simply supported and the other two edges having arbitrary boundary conditions. The accuracy of the present solutions is verified by comparing the present results with those obtained using the classical theory, first-order theory, and higher-order theory.