Dynamical Response of an Elastic Half-Space to Tangential Surface Loadings

[+] Author and Article Information
Chi-Chang Chao

Department of Aeronautical Engineering, Stanford University, Stanford, Calif.

J. Appl. Mech 27(3), 559-567 (Sep 01, 1960) (9 pages) doi:10.1115/1.3644041 History: Received June 17, 1958; Revised August 18, 1959; Online September 16, 2011


Exact and closed-form solutions are obtained for both tangential and vertical surface displacements of a homogeneous isotropic elastic half-space due to the application, at a point on the surface, of a concentrated force tangential to the plane boundary and varying with time as the Heaviside unit function. Similar expressions for the displacements in the interior of the body along a line directly below the applied force are derived. Solutions are obtained by a semi-inverse method with the aid of Laplace and Hankel transforms. The reciprocal relation in the static case, between tangential displacement due to a vertical force and vertical displacement due to a tangential force, is preserved in the dynamic case.

Copyright © 1960 by ASME
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