Eigenvalue Problems of Rectangular Plates With Mixed Edge Conditions

[+] Author and Article Information
L. M. Keer

Department of Civil Engineering, Northwestern University, Evanston, Ill.

B. Stahl

Amoco Production Company, Tulsa, Okla.

J. Appl. Mech 39(2), 513-520 (Jun 01, 1972) (8 pages) doi:10.1115/1.3422709 History: Received January 06, 1971; Revised June 03, 1971; Online July 12, 2010


The vibration and stability of plates with mixed edge conditions are considered in this paper. A simply supported rectangular plate which is clamped along the central portion on two opposite edges and a plate with partial clamping along one edge are analyzed. The problems are formulated as dual series equations and reduced to homogeneous Fredholm integral equations of the second kind. Comparisons with numerical results obtained by other investigators are made. Vibration and buckling mode shapes are illustrated. A vibration analysis of a plate simply supported adjacent to the corners is also made. This case is formulated as a coupled system of dual series equations which is reduced to a system of homogeneous integral equations. In all of the solutions given, the singularity is isolated and treated analytically.

Copyright © 1972 by ASME
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