Exact Transient Response of an Elastic Half Space Loaded Over a Rectangular Region of Its Surface

[+] Author and Article Information
F. R. Norwood

Sandia Laboratories, Albuquerque, N. Mex.

J. Appl. Mech 36(3), 516-522 (Sep 01, 1969) (7 pages) doi:10.1115/1.3564710 History: Received January 27, 1969; Online September 14, 2011


The response of an elastic half space to a normal impulsive loading over one half and also over one quarter of its bounding surface is considered. By a simple superposition the solution is obtained for a half space loaded on a finite rectangular region. In each case the solution was found to be a superposition of plane waves directly under the load, plus waves emanating from bounding straight lines and the corners of the loaded region. The solution was found by Cagniard’s technique and by extending the real transformation of de Hoop to double Fourier integrals with singularities on the real axis of the transform variables. Velocities in the interior of the half space are given for arbitrary values of Poisson’s ratio in terms of single integrals and algebraic expressions.

Copyright © 1969 by ASME
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