Optimal Forms of Shallow Cylindrical Panels With Respect to Vibration and Stability

[+] Author and Article Information
R. H. Plaut

Department of Civil Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Va. 24061

L. W. Johnson

Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Va. 24061

J. Appl. Mech 53(1), 135-140 (Mar 01, 1986) (6 pages) doi:10.1115/1.3171700 History: Received June 15, 1984; Revised April 15, 1985; Online July 21, 2009


Thin, shallow, elastic, cylindrical panels with rectangular planform are considered. We seek the midsurface form which maximizes the fundamental frequency of vibration, and the form which maximizes the buckling value of a uniform axial load. The material, surface area, and uniform thickness of the panel are specified. The curved edges are simply supported, while the straight edges are either simply supported or clamped. For the clamped case, the optimal panels have zero slope at the edges. In the examples, the maximum fundamental frequency is up to 12 percent higher than that of the corresponding circular cylindrical panel, while the buckling load is increased by as much as 95 percent. Most of the solutions are bimodal, while the rest are either unimodal or trimodal.

Copyright © 1986 by ASME
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