Plane Dyadic Wave Scattering by a Small Rigid Body and Cavity in 3D Linear Elasticity
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 am...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-06-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/12/1975 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850168390204784640 |
|---|---|
| author | Vassilios Sevroglou Panayiotis Vafeas Konstantinos G. Lallas |
| author_facet | Vassilios Sevroglou Panayiotis Vafeas Konstantinos G. Lallas |
| author_sort | Vassilios Sevroglou |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8df47f17e0e04ffa893dc19950bf1c0e |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-8df47f17e0e04ffa893dc19950bf1c0e2025-08-20T02:20:58ZengMDPI AGMathematics2227-73902025-06-011312197510.3390/math13121975Plane Dyadic Wave Scattering by a Small Rigid Body and Cavity in 3D Linear ElasticityVassilios Sevroglou0Panayiotis Vafeas1Konstantinos G. Lallas2Department of Statistics & Insurance Science, University of Piraeus, GR 185 34 Piraeus, GreeceDepartment of Chemical Engineering, University of Patras, GR 265 04 Patras, GreeceDepartment of Statistics & Insurance Science, University of Piraeus, GR 185 34 Piraeus, GreeceIn 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.https://www.mdpi.com/2227-7390/13/12/1975elastic dyadic wave scatteringscattering cross-sectionlow-frequency approximation |
| spellingShingle | Vassilios Sevroglou Panayiotis Vafeas Konstantinos G. Lallas Plane Dyadic Wave Scattering by a Small Rigid Body and Cavity in 3D Linear Elasticity Mathematics elastic dyadic wave scattering scattering cross-section low-frequency approximation |
| title | Plane Dyadic Wave Scattering by a Small Rigid Body and Cavity in 3D Linear Elasticity |
| title_full | Plane Dyadic Wave Scattering by a Small Rigid Body and Cavity in 3D Linear Elasticity |
| title_fullStr | Plane Dyadic Wave Scattering by a Small Rigid Body and Cavity in 3D Linear Elasticity |
| title_full_unstemmed | Plane Dyadic Wave Scattering by a Small Rigid Body and Cavity in 3D Linear Elasticity |
| title_short | Plane Dyadic Wave Scattering by a Small Rigid Body and Cavity in 3D Linear Elasticity |
| title_sort | plane dyadic wave scattering by a small rigid body and cavity in 3d linear elasticity |
| topic | elastic dyadic wave scattering scattering cross-section low-frequency approximation |
| url | https://www.mdpi.com/2227-7390/13/12/1975 |
| work_keys_str_mv | AT vassiliossevroglou planedyadicwavescatteringbyasmallrigidbodyandcavityin3dlinearelasticity AT panayiotisvafeas planedyadicwavescatteringbyasmallrigidbodyandcavityin3dlinearelasticity AT konstantinosglallas planedyadicwavescatteringbyasmallrigidbodyandcavityin3dlinearelasticity |