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RESEARCH PAPERS

Elastic Waves in Inhomogeneous Elastic Media

[+] Author and Article Information
Adnan H. Nayfeh

Department of Aerospace and Mechanical Engineering Sciences, University of California, San Diego, La Jolla, Calif.

Siavouche Nemat-Nasser

Department of Civil Engineering, The Technological Institute, Northwestern University, Evanston, Ill.

J. Appl. Mech 39(3), 696-702 (Sep 01, 1972) (7 pages) doi:10.1115/1.3422775 History: Received December 31, 1970; Revised July 22, 1971; Online July 12, 2010

Abstract

The WKB solution is derived together with the condition for its validity for elastic waves propagating into an inhomogeneous elastic medium. Large frequency expansion solution is also derived. It is found that the WKB solution agrees with that derived for large frequencies when the frequency approaches infinity. Some exact solutions are deduced from the WKB solution. Finally, we consider motions in medium which consists of a material with harmonic periodicity. The solution is obtained by means of a perturbation method. It is shown that, only when the wavelength of the incident wave is small compared with the periodicity-length of the material, the WKB solution constitutes a good approximation. When the wavelength is comparable with this periodicity-length, then, in certain special cases, the material cannot maintain time-harmonic waves; such harmonic waves are not “stable.” These and other solutions are discussed in detail.

Copyright © 1972 by ASME
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