On Vibrations of Elastic Spherical Shells

[+] Author and Article Information
P. M. Naghdi

University of California, Berkeley, Calif.

A. Kalnins

Yale University, New Haven, Conn.

J. Appl. Mech 29(1), 65-72 (Mar 01, 1962) (8 pages) doi:10.1115/1.3636499 History: Received December 19, 1960; Online September 16, 2011


This investigation is concerned with axisymmetric as well as asymmetric vibrations of thin elastic spherical shells. First, with the limitation to torsionless axisymmetric motion, the basic equations for spherical shells of the classical bending theory of Love’s first approximation are reduced to a system of two coupled differential equations in normal displacement of the middle surface and a stress function; this system of equations is applied to free vibrations of a hemispherical shell with a free edge and numerical results are obtained for the lowest natural frequency as a function of the thickness of the shell. The remainder of the paper is, in the main, devoted to a study of asymmetric vibrations of a hemispherical shell with a free edge according to the extensional theory. Numerical results for natural frequencies (of the four lowest circumferential wave numbers) and mode shapes are given and the results are compared with the prediction of Rayleigh’s inextensional theory.

Copyright © 1962 by ASME
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