Vibration and Buckling of Orthotropic Rectangular Plates

摘要

The present investigation analyses the buckling and vibration behavior of thin orthotropic rectangular plates resting on Winkler type elastic foundation and subjected to linearly varying in-plane normal stresses along two opposite simply supported edges (y=0 and b). The other two edges (x=0 and a) may be clamped, simply supported or free. A semi-analytical approach has been used for the solution of partial differential equation governing the motion of such configurations. Accordingly the transverse displacement w is assumed to vary as sin pπy/b, which reduces the governing equation of motion to an ordinary differential equation in x with variable coefficients. Resulting equation is then solved by differential quadrature method for three different combinations of boundary conditions namely, C-C, C-S and C-F where C, S, F stand for clamped, simply supported and free respectively, and first symbol denotes the condition at x=0 and second symbol at x=a. The effect of foundation parameter with in-plane force parameter, loading parameter and aspect ratio has been studied for the first three modes of vibration. The critical buckling loads by allowing frequencies to approach zero have been obtained. Modes shapes are shown for a specified plate. Comparison of results with those available in the published literature demonstrates the computationally efficiency of the method.