Natural Frequencies and Mode Shapes for Axisymmetric Vibration of Deep Spherical Shells

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

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

J. Appl. Mech 32(3), 553-561 (Sep 01, 1965) (9 pages) doi:10.1115/1.3627258 History: Received October 15, 1964; Revised February 01, 1965; Online September 15, 2011


This paper contains the results of an approximate analysis of the axially symmetric vibrations of deep spherical elastic shells. The approximation is based on the asymptotic formulas for Legendre functions of large degree. The results are relatively simple approximate formulas for the natural frequencies and mode shapes under a variety of boundary conditions at the shell edge. The results agree very well with values obtained by Kalnins, using numerical methods.

Copyright © 1965 by ASME
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