Three-Dimensional Vibration Analysis of Thick Shells of Revolution
Publication: Journal of Engineering Mechanics
Volume 125, Issue 12
Abstract
A 3D method of analysis is presented for determining the free vibration frequencies and mode shapes of hollow bodies of revolution (i.e., thick shells), not limited to straight-line generators or constant thickness. The middle surface of the shell may have arbitrary curvatures, and the wall thickness may vary arbitrarily. Displacement components u;gf, uz, and u;gu in the meridional, normal, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the ϕ and z directions. Potential (strain) and kinetic energies of the entire body are formulated, and upper-bound values of the frequencies are obtained by minimizing the frequencies. As the degree of the polynomials are increased, frequencies converge to the exact values. Novel numerical results are presented for two types of thick conical shells and thick spherical shell segments having linear thickness variations and completely free boundaries. Convergence to four-digit exactitude is demonstrated for the first five frequencies of both types of shells. The method is applicable to thin shells, as well as thick and very thick ones.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 125 • Issue 12 • December 1999
Pages: 1365 - 1371
History
Received: Jan 23, 1998
Published online: Dec 1, 1999
Published in print: Dec 1999
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