Plane Dyadic Wave Scattering by a Small Rigid Body and Cavity in 3D Linear Elasticity

Vassilios Sevroglou, Panayiotis Vafeas and Konstantinos G. Lallas ()
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Vassilios Sevroglou: Department of Statistics & Insurance Science, University of Piraeus, GR 185 34 Piraeus, Greece
Panayiotis Vafeas: Department of Chemical Engineering, University of Patras, GR 265 04 Patras, Greece
Konstantinos G. Lallas: Department of Statistics & Insurance Science, University of Piraeus, GR 185 34 Piraeus, Greece

Mathematics, 2025, vol. 13, issue 12, 1-14

Abstract: In this paper, we study the 3D elastic scattering problem of plane dyadic waves for a rigid body and a cavity in linear elasticity. Initially, for each case, we formulate the direct scattering problem in a dyadic form, and we give the corresponding longitudinal and transverse far-field scattering amplitudes. Due to dyadic formulation of the problems, the main outcome of this paper is to establish the necessary energy considerations as well as to present functionals and formulas for the differential and the scattering cross-section in order to measure the disturbance created by the scatterer to the propagation of the plane dyadic incident field. Further, we assume that our incident field is scattered by a “small” rigid body or cavity and relative results for low-frequency scattering are obtained. Finally, we prove similar corresponding expressions for energy functionals in the far-field region, along with expressions for the differential and the total scattering cross-section, which are recovered as special cases.

Keywords: elastic dyadic wave scattering; scattering cross-section; low-frequency approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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