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.
Dynamical Response of an Elastic Half-Space to Tangential Surface Loadings
Department of Aeronautical Engineering, Stanford University, Stanford, Calif.
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Chao, C. (September 1, 1960). "Dynamical Response of an Elastic Half-Space to Tangential Surface Loadings." ASME. J. Appl. Mech. September 1960; 27(3): 559–567. https://doi.org/10.1115/1.3644041
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