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.
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December 1985
Research Papers
Free Vibration of a Point-Supported Spherical Shell
T. Irie,
T. Irie
Department of Mechanical Engineering, Hokkaido University, Sapporo, Japan 060
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G. Yamada,
G. Yamada
Department of Mechanical Engineering, Hokkaido University, Sapporo, Japan 060
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Y. Muramoto
Y. Muramoto
Department of Mechanical Engineering, Hokkaido University, Sapporo, Japan 060
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T. Irie
Department of Mechanical Engineering, Hokkaido University, Sapporo, Japan 060
G. Yamada
Department of Mechanical Engineering, Hokkaido University, Sapporo, Japan 060
Y. Muramoto
Department of Mechanical Engineering, Hokkaido University, Sapporo, Japan 060
J. Appl. Mech. Dec 1985, 52(4): 890-896 (7 pages)
Published Online: December 1, 1985
Article history
Received:
December 1, 1983
Revised:
January 1, 1985
Online:
July 21, 2009
Citation
Irie, T., Yamada, G., and Muramoto, Y. (December 1, 1985). "Free Vibration of a Point-Supported Spherical Shell." ASME. J. Appl. Mech. December 1985; 52(4): 890–896. https://doi.org/10.1115/1.3169164
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