Scattering relations for point-generated dyadic fields in two-dimensional linear elasticity

Athanasiadis, C.; Sevroglou, V.; Stratis, I.

doi:10.1090/S0033-569X-06-01041-0

Authors: C. Athanasiadis, V. Sevroglou and I. G. Stratis
Journal: Quart. Appl. Math. 64 (2006), 695-710
MSC (2000): Primary 74J20; Secondary 74B05
DOI: https://doi.org/10.1090/S0033-569X-06-01041-0
Published electronically: October 31, 2006
MathSciNet review: 2284466
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Abstract: The problem of scattering of elastic waves by a bounded obstacle in two-dimensional linear elasticity is considered. The scattering problems are presented in a dyadic form. An incident dyadic field generated by a point source is disturbed by a rigid body, a cavity, or a penetrable obstacle. General scattering theorems are proved, relating the far-field patterns due to scattering of waves from a point source set up in either of two different locations. The most general reciprocity theorem is established, and mixed scattering relations are also proved. Finally, a relation between the incident and the scattered wave which refers to the mechanism of energy transfer of the scatterer, the so-called optical theorem, is established.

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