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Shock and Vibration
Volume 2, Issue 4, Pages 321-338

Differential Quadrature Analysis of Free Vibration of Symmetric Cross-Ply Laminates with Shear Deformation and Rotatory Inertia

Moinuddin Malik and Charles W. Bert

School of Aerospace and Mechanical Engineering, The University of Oklahoma, Norman, OK 73019-0601, USA

Received 10 January 1994; Accepted 30 January 1995

Copyright © 1995 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.


In the present work, laminates having two opposite edges simply supported are considered. The boundary conditions at the other two opposite edges may be general, and between these two edges, the thickness of the plate may be nonuniform. The theory used for the vibration analysis of such laminates includes shear deformation and rotatory inertia. The solution approach of the problem is semianalytical. By using the trigonometric functions describing the mode shapes between the simply supported edges, the governing plate equations are reduced to ordinary differential equations. The solution of the reduced equations is then sought by the differential quadrature method. The results reported in this article serve two objectives of the present investigations. One, it is demonstrated that the proposed semianalytical quadrature method offers a numerically accurate and computationally efficient technique for the title problem. Two, the relative effects of shear deformation and rotatory inertia are analyzed in a quantitative manner.