Buckling and Vibration of Non-Homogeneous Orthotropic Rectangular Plates with Variable Thickness Using DQM

The present work analyzes the buckling and vibration behavior of non-homogeneous orthotropic rectangular plates of variable thickness and subjected to constant in-plane force along two opposite simply supported edges on the basis of classical plate theory. The other two edges may be clamped, simply supported, and free. For non-homogeneity of the plate material, it is assumed that Young's moduli and density vary exponentially along one direction. The governing partial differential equation of motion of such plates has been reduced to an ordinary differential equation using the sine function for mode shapes between the simply supported edges. This has been solved numerically employing DQM. The effect of various parameters has been studied on the natural frequencies for the first three modes of vibration. Critical buckling loads by allowing frequencies to approach zero have been computed. Comparison has been made with the known results.