Prediction of frequencies of free axisymmetric vibration of two-directional functionally graded annular plates on Winkler foundation

In the present paper, first three natural frequencies of free axisymmetric vibration of two-directional functionally graded annular plates resting on Winkler foundation are predicted using differential quadrature method (DQM) and Chebyshev collocation technique. Frequency equations for a plate clamped at both the edges and another plate simply supported at both the edges are obtained using both the methods. The effect of volume fraction index, coefficient of radial variations, exponent of the power law, foundation parameter, radius ratio and boundary condition is discussed on first three natural frequencies. Nonhomogeneous/homogeneous isotropic materials are deduced as particular cases of functionally graded material. The accuracy and efficiency of the present approaches are confirmed through comparison of frequencies for homogeneous isotropic annular plates. Two-dimensional mode shapes for both the boundary configurations are also plotted.