Asymptotic Analysis of the Axisymmetric Vibrations of Shells

[+] Author and Article Information
E. W. Ross

U. S. Army Materials Research Agency, Watertown, Mass.

J. Appl. Mech 33(1), 85-92 (Mar 01, 1966) (8 pages) doi:10.1115/1.3625031 History: Received February 09, 1965; Revised June 29, 1965; Online September 15, 2011


An asymptotic analysis is carried out for the equations of axisymmetric vibrations of thin shells, somewhat analogous to the procedure by which geometrical optics is obtained from electromagnetic theory. It is found that two types of asymptotic solutions are obtained, roughly classifiable as high-frequency membrane solutions and bending solutions. Two explicit representations of these solutions are obtained, one for the shallow region of a shell and the other for the nonshallow region. A number of interesting conclusions emerge from the analysis.

Copyright © 1966 by ASME
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