Free Vibration of Two-Directional Functionally Graded Annular Plates Using Chebyshev Collocation Technique and Differential Quadrature Method

This article deals with the free axisymmetric vibration of two-directional functionally graded annular plates. Ceramic and metal are considered two constituents of the functionally graded material (FGM), which are graded through thickness and radial directions of the plate. The Chebyshev collocation technique and differential quadrature method are employed to derive the frequency equations for an annular plate with both edges clamped and another one with both edges simply supported. The results for nonhomogeneous isotropic annular plates are also presented. The accuracy and efficiency of the present approach are confirmed through comparison of the frequencies obtained for homogeneous isotropic annular plates. Identical results are obtained for the two methods used. The effects of volume fraction index, coefficient of radial variation, exponent of power law, inner to outer radii ratio, and boundary conditions are discussed on the first three natural frequencies. It is found that the frequency of a functionally graded annular plate is greater than that of a homogeneous annular plate.