An energy analysis of the free vibrations of isotropic spherical shells

The free vibrations of isotropic spherical shells, having one boundary open and the other either open or closed, are investigated by using a variational development of the equations of motion based upon classical shell theory. Expressions are derived for each of the individual contributions to both...

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Bibliographic Details
Published in:Journal of sound and vibration 1980-12, Vol.73 (3), p.379-404
Main Authors: de Souza, V.C.M., Croll, J.G.A.
Format: Article
Language:English
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Summary:The free vibrations of isotropic spherical shells, having one boundary open and the other either open or closed, are investigated by using a variational development of the equations of motion based upon classical shell theory. Expressions are derived for each of the individual contributions to both the membrane and bending strain energies, and used to obtain the energy profiles for mode-shapes associated with each of the natural vibration frequencies. Results for shell geometries ranging from a shallow cap to a hemispherical dome, for a wide variety of thickness to radius ratios, provide a clearer picture of the nature of the shell's resistance to linear vibrations. Suggestions are made as to how these isotropic energy profiles may be used as an aid for the design of both isotropic and orthotropic shells which embody some prescribed dynamic characteristics.
ISSN:0022-460X
1095-8568
DOI:10.1016/0022-460X(80)90522-2