Free Vibration of a Point-Supported Spherical Shell

[+] Author and Article Information
T. Irie, G. Yamada, Y. Muramoto

Department of Mechanical Engineering, Hokkaido University, Sapporo, Japan 060

J. Appl. Mech 52(4), 890-896 (Dec 01, 1985) (7 pages) doi:10.1115/1.3169164 History: Received December 01, 1983; Revised January 01, 1985; Online July 21, 2009


An analysis is presented for the free vibration of an elastically or a rigidly point-supported spherical shell. For this purpose, the deflection displacements of the shell are written in a series of the products of the associated Legendre functions and the trigonometric functions. The dynamical energies of the shell are evaluated, and the frequency equation is derived by the Ritz method. For a rigidly point-supported shell, the Lagrangian multiplier method is conveniently employed. The method is applied to a closed spherical shell supported at equispaced four points located along a parallel of latitude; the natural frequencies and the mode shapes are calculated numerically, and the effects of the point supports on the vibration are studied.

Copyright © 1985 by ASME
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