Vibration of Plates Subject to Arbitrary In-Plane Loads—A Perturbation Approach

[+] Author and Article Information
S. F. Bassily, S. M. Dickinson

The University of Western Ontario, London, Ontario, Canada

J. Appl. Mech 40(4), 1023-1028 (Dec 01, 1973) (6 pages) doi:10.1115/1.3423119 History: Received June 01, 1972; Revised November 01, 1972; Online July 12, 2010


Perturbation theory is used to obtain the natural frequencies and mode shapes of lateral vibration of rectangular plates under arbitrary in-plane loading in terms of a power series in a loading parameter, commencing from known approximate or “exact” solutions of the same plate under no in-plane loading. The range of loading over which the solution is applicable is shown to be extendible to practically any limit by the introduction of a stepwise perturbation technique. Numerical results demonstrating the applicability and accuracy of the analysis are presented for plates subject to uniform, linear, and parabolic in-plane stress distributions. Simple approximate frequency expressions are also given.

Copyright © 1973 by ASME
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