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RESEARCH PAPERS

The Bending, Buckling, and Flexural Vibration of Simply Supported Polygonal Plates by Point-Matching

[+] Author and Article Information
H. D. Conway

Cornell University, Ithaca, N. Y.

J. Appl. Mech 28(2), 288-291 (Jun 01, 1961) (4 pages) doi:10.1115/1.3641670 History: Received March 16, 1960; Online September 16, 2011

Abstract

The bending by uniform lateral loading, buckling by two-dimensional hydrostatic pressure, and the flexural vibrations of simply supported polygonal plates are investigated. The method of meeting the boundary conditions at discrete points, together with the Marcus membrane analog [1], is found to be very advantageous. Numerical examples include the calculation of the deflections and moments, and buckling loads of triangular square, and hexagonal plates. A special technique is then given, whereby the boundary conditions are exactly satisfied along one edge, and an example of the buckling of an isosceles, right-angled triangle plate is analyzed. Finally, the frequency equation for the flexural vibrations of simply supported polygonal plates is shown to be the same as that for buckling under hydrostatic pressure, and numerical results can be written by analogy. All numerical results agree well with the exact solutions, where the latter are known.

Copyright © 1961 by ASME
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