On the far field amplitude for elastic waves. (English) Zbl 0893.73019

Alves, Carlos J. S.; Ha-Duong, Tuong

Meister, Erhard (ed.), Modern mathematical methods in diffraction theory and its applications in engineering. Proceedings of the Sommerfeld ’96 workshop. Freudenstadt, Germany. September 30–October 4, 1996. Frankfurt am Main: Peter Lang, Europ. Verlag der Wissenschaften. Methoden Verfahren Math. Phys. 42, 49-67 (1997).

Summary: It is known that the solution of an elastic scattering problem behaves asymptotically like a sum of a spherical \(P\) wave and a spherical \(S\) wave. This result, as its acoustic counterpart, can be generally proved by way of some integral representation formula, which contains rather complicated terms in the elastic case. We adopt here a different viewpoint, considering the scattered wave as a solution of the inhomogeneous Navier’s equation with a distribution data, and obtain both simpler proofs for these results and more precise properties of the far field amplitudes, in particular a characterization theorem for elastic far fields and a density result.
For the entire collection see [Zbl 0869.00053].

MSC:

74J20	Wave scattering in solid mechanics
74J10	Bulk waves in solid mechanics

Keywords:

elastic scattering; spherical \(P\) wave; spherical \(S\) wave; integral representation formula; inhomogeneous Navier’s equation; characterization theorem