Dispersion of Flexural Waves in an Elastic, Circular Cylinder

[+] Author and Article Information
Yih-Hsing Pao

Cornell University, Ithaca, N. Y.

R. D. Mindlin

Columbia University, New York, N. Y.

J. Appl. Mech 27(3), 513-520 (Sep 01, 1960) (8 pages) doi:10.1115/1.3644033 History: Received May 13, 1959; Online September 16, 2011


In this paper it is shown how the branches of Pochhammer’s frequency equation for flexural waves in a circular cylinder may be constructed approximately with the aid of a grid of simpler curves and asymptotic equations for long and short wave lengths. With very little computation, in comparison with that required in the direct determination of the roots of Pochhammer’s equation, a qualitative view is obtained of the relations between frequency, phase velocity, group velocity, and propagation constant, for any branch, as well as some information as to the shapes of the modes.

Copyright © 1960 by ASME
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