Abstract
The paper deals with 3D dynamic response of a coated elastic half space subject to in-plane surface loading. The problem is formulated by a pair of elliptic equations over the interior and a two dimensional singularly perturbed hyperbolic equation expressed in terms of shear wave potentials along the interface. As an example, a point force acting one of the in-plane axis is considered and the integral solution of the normal displacement along the interface is derived through the use of the relation between the wave potentials.
Highlights
Propagation of surface waves has been the focus of intensive research since its introduction by the monumental work of Rayleigh [1]
The problem is formulated by a pair of elliptic equations over the interior and a two dimensional singularly perturbed hyperbolic equation expressed in terms of shear wave potentials along the interface
A long wave model for the coated half space derived in [9] and an asymptotic model for the in-plane surface wave of elastic half-space derived in [13] have been extended to the case of an in-plane loading for a three-dimensional elastic half-space coated by a thin layer
Summary
Propagation of surface waves has been the focus of intensive research since its introduction by the monumental work of Rayleigh [1]. Chadwick extended Friedlander’s analysis and expressed the Rayleigh wave ...eld in terms of a single harmonic function via a relation between the wave potentials at the surface of the elastic half-plane [3]. This relationship was, extended to three dimensions in [4]. In the last section numerical computations based on the derived approximate formulae are presented
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