Optimal Forms of Shallow Shells With Circular Boundary, Part 1: Maximum Fundamental Frequency

[+] 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

R. Parbery

Department of Mechanical Engineering, The University of Newcastle, New South Wales 2308, Australia

J. Appl. Mech 51(3), 526-530 (Sep 01, 1984) (5 pages) doi:10.1115/1.3167668 History: Received June 01, 1983; Revised October 01, 1983; Online July 21, 2009


Thin, shallow, elastic shells with given circular boundary are considered. We seek the axisymmetric shell form which maximizes the fundamental frequency of vibration. The boundary conditions, material, surface area, and uniform thickness of the shell are specified. We employ a bimodal formulation and use an iterative procedure based on the optimality condition to obtain optimal forms. Results are presented for clamped and simply supported boundary conditions. For the clamped case, the optimal forms have zero slope at the boundary. The maximum fundamental frequency is significantly higher than that for the corresponding spherical shell if the boundary is clamped, but only slightly higher if it is simply supported.

Copyright © 1984 by ASME
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