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Shock and Vibration
Volume 20, Issue 5, Pages 879-894

Buckling and Vibration of Non-Homogeneous Rectangular Plates Subjected to Linearly Varying In-Plane Force

Roshan Lal and Renu Saini

Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India

Received 28 October 2012; Revised 11 January 2013; Accepted 18 March 2013

Copyright © 2013 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The present work analyses the buckling and vibration behaviour of non-homogeneous rectangular plates of uniform thickness on the basis of classical plate theory when the two opposite edges are simply supported and are subjected to linearly varying in-plane force. For non-homogeneity of the plate material it is assumed that young's modulus and density of the plate material vary exponentially along axial 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 resulting equation has been solved numerically employing differential quadrature method for three different combinations of clamped, simply supported and free boundary conditions at the other two edges. The effect of various parameters has been studied on the natural frequencies for the first three modes of vibration. Critical buckling loads have been computed. Three dimensional mode shapes have been presented. Comparison has been made with the known results.