Uncoupled Wave Systems and Dispersion in an Infinite Solid Cylinder

[+] Author and Article Information
Yoon Young Kim

Division of Applied Mechanics, Stanford University, Stanford, Calif. 94305

J. Appl. Mech 56(2), 347-355 (Jun 01, 1989) (9 pages) doi:10.1115/1.3176089 History: Received May 26, 1988; Revised October 28, 1988; Online July 21, 2009


In this study, it is shown that there exist uncoupled wave systems for general non-axisymmetric wave propagation in an infinite isotropic cylinder. Two cylindrical surface conditions corresponding to the uncoupled wave systems are discussed. The solutions of the uncoupled wave systems are shown to provide proper bounds of Pochhammer’s equation for a free cylindrical surface. The bounds, which are easy to construct for any Fourier number in the circumferential direction, can be used to trace the branches of Pochhammer’s equation. They also give insight into the modal composition of the branches of Pochhammer’s equation at and between the intersections of the bounds. More refined dispersion relations of Pochhammer’s equation are possible through an asymptotic analysis of the itersections of the branches of Pochhammer’s equation with one family of the bounds. The asymptotic nature of wave motion corresponding to large wave numbers, imaginary or complex, for Pochhammer’s equation is studied. The wave motion is asymptotically equivoluminal for large imaginary wave numbers, and is characterized by coupled dilatation and shear for large complex wave numbers.

Copyright © 1989 by ASME
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