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Point-Source Elastic Scattering by a Nested Piecewise Homogeneous Obstacle in an Elastic Environment

¹ Department of Mathematics, National University of Athens, Panepistemiopolis, GR 15784 Athens, Greece
² Department of Statistics and Insurance Science, University of Piraeus, GR 18534 Piraeus, Greece
³ School of Applied Mathematical and Physical Sciences, National Technical University of Athens, GR 15773 Athens, Greece

^* To whom correspondence should be addressed.

	Abstract

A nested piecewise homogeneous elastic scatterer is embedded in a homogeneous elastic environment. The scatterer's core may be rigid, cavity, Robin, or lossy penetrable. A 2D or 3D incident elastic field, generated by a point-source located in the homogeneous environment, impinges on the scatterer. The scattering problem is formulated in a dyadic form. The main purpose of this paper is to establish scattering relations for the elastic point-source excitation of a nested piecewise homogeneous scatterer. To this direction, we establish reciprocity principles and general scattering theorems relating the scattered fields with the corresponding far-field patterns. Furthermore, for a scatterer excited by a point-source and a plane wave, mixed scattering relations are derived. The optical theorem, relating the scattering cross-section with the field at the point-source's location a is recovered as a corollary of the general scattering theorem. We present a detailed investigation for the 2D case and summarize the results for the 3D case, pointing out the main differences in the analysis.

Key Words: linear elasticity, point source fields, nested piecewise homogenous obstacle, reciprocity principle, general scattering theorem, mixed scattering relations, optical theorem

First published on March 11, 2009
Mathematics and Mechanics of Solids 2009, doi:10.1177/1081286508102048


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