Buckling and vibration analysis of non-homogeneous rectangular Kirchhoff plates resting on two-parameter foundation

Effect of two parameter foundation has been analyzed on the transverse vibrations of non-homogeneous rectangular plates of uniform thickness when the two opposite edges are simply supported and these are subjected to linearly varying in-plane forces on the basis of Kirchhoff plate theory. The non-homogeneity of the plate material is assumed to arise due to the exponential variation in young's modulus and density of the plate material along one direction. Using Levy approach, the partial differential equation governing the motion of such plates has been reduced to an ordinary differential equation. Differential quadrature method has been used to obtain the frequency equations for two different combinations of clamped and simply supported boundary conditions at the other two edges. These frequency equations have been solved numerically using MATLAB. The lowest three roots of these equations have been reported as first three natural frequencies corresponding to the first three modes of vibration. The effect of various parameters such as foundation parameters, non-homogeneity parameter, density parameter, aspect ratio, in-plane force parameter and loading parameter has been investigated on the frequencies. By allowing the frequency to approach zero, the critical buckling loads for various value of different parameters have been computed. Three dimensional mode shapes for a specified plate for both the boundary conditions have been plotted. A comparison of results with those available in literature has been presented.