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RESEARCH PAPERS

Wave Function Expansions and Perturbation Method for the Diffraction of Elastic Waves by a Parabolic Cylinder

[+] Author and Article Information
S. A. Thau

Department of Mechanics, Illinois Institute of Technology, Chicago, Ill.

Yih-Hsing Pao

Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, N. Y.

J. Appl. Mech 34(4), 915-920 (Dec 01, 1967) (6 pages) doi:10.1115/1.3607856 History: Received November 04, 1966; Revised June 12, 1967; Online September 14, 2011

Abstract

The dynamic response, including the stresses at the surface, of a rigid parabolic cylinder in an infinite elastic solid is studied for an incident plane compressional wave. The method of separation of variables in parabolic coordinates is used. With the wave function for one of the scattered waves expanded into a series of those for the other wave, the total scattered fields are then determined numerically by inverting a truncated infinite matrix. The same problem is solved also by a recently developed method of perturbation which describes the two waves in elastic solids in terms of wave functions with a common wave speed. With the latter method, the total scattered waves are determined analytically for the various orders of perturbation, and these results supplement the numerical wave function expansion results in the low-frequency range.

Copyright © 1967 by ASME
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