Nonsymmetric Modes of Complete Spherical Shells

by John F. Gormley,
William C. L. Hu,

Serial Information: Journal of the Engineering Mechanics Division, 1969, Vol. 95, Issue 3, Pg. 545-558

Document Type: Journal Paper


A matrix method is applied to calculate the mode shapes and frequencies of nonsymmetric vibrations of complete spherical shells. Based upon a thin shell theory incorporating transverse shear and rotatory inertia, the solution is obtained through Fourier expansions of the meridional mode functions, which are also expressible in terms of associated Legendre functions. As has previously been shown within the framework of membrane theory, the frequency spectra of nonsymmetric modes (n > 1) are found to degenerate to that of axisymmetric vibration for the refined shell theory. Numerical results of nonsymmetric mode shapes are presented.

Subject Headings: Vibration | Numerical methods | Matrix (mathematics) | Spherical shells | Transverse shear | Rotation | Inertia | Fourier analysis

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