Diffractions of Horizontal Shear Waves by a Parabolic Cylinder and Dynamic Stress Concentrations

[+] 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 33(4), 785-792 (Dec 01, 1966) (8 pages) doi:10.1115/1.3625183 History: Received October 26, 1965; Revised April 28, 1966; Online September 15, 2011


Diffractions of horizontally polarized shear waves by a parabolic cylinder are studied by using the expansion of solutions to the wave equation in terms of Weber’s functions. The parabolic cylinder is either empty or filled with rigid material. Also, the problems of a semi-infinite line crack and a semi-infinite rigid ribbon as two limiting cases are treated. Displacements and stresses are calculated near the base of the parabola. In the case of a line crack or a rigid ribbon, the singular behavior of stresses is shown to be of the order of (kr)−1/2 , where k is the wave number and r the distance from the tip.

Copyright © 1966 by ASME
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