On the scattering of two-dimensional elastic point sources and related near-field inverse problems for small discs
The problem of scattering of a point-generated elastic dyadic field by a bounded obstacle or a penetrable body in two dimensions is considered. The direct scattering problem for each case is formulated in a dyadic form. For two point sources, dyadic far-field pattern generators are defined and gener...
Gespeichert in:
| Veröffentlicht in: | Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2009-08, Vol.139 (4), p.719-741 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 741 |
|---|---|
| container_issue | 4 |
| container_start_page | 719 |
| container_title | Proceedings of the Royal Society of Edinburgh. Section A. Mathematics |
| container_volume | 139 |
| creator | Athanasiadis, C. E. Pelekanos, G. Sevroglou, V. Stratis, I. G. |
| description | The problem of scattering of a point-generated elastic dyadic field by a bounded obstacle or a penetrable body in two dimensions is considered. The direct scattering problem for each case is formulated in a dyadic form. For two point sources, dyadic far-field pattern generators are defined and general scattering theorems and mixed scattering relations are presented. The direct scattering problem for a rigid circular disc is considered, and the exact Green function and the elastic far-field patterns of the radiating solution in the form of infinite series are obtained. Under the low-frequency assumption, approximations for the longitudinal and transverse far-field patterns of the scattered field are obtained, in addition to an asymptotic expansion for the corresponding scattering cross-section. A simple inversion scheme that locates the radius and the position of a rigid circular disc, which is based on a closed-form approximation of the scattered field at the location of the incident point source, is proposed. |
| doi_str_mv | 10.1017/S0308210507001059 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_603217249</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cupid>10_1017_S0308210507001059</cupid><sourcerecordid>2075715051</sourcerecordid><originalsourceid>FETCH-LOGICAL-c354t-4da1e062e901b1ce8ad573cc373b448aa940322c95ed4975319f14c13d4dd8573</originalsourceid><addsrcrecordid>eNp1UE1LAzEUDKJgrf4Ab8H7arLJbpqj-FFFQcQK3kKavNXoftS81I9_b0pFD-JpDjPz3swQss_ZIWdcHd0xwSYlZxVTjGXQG2TEpRKF4qXcJKMVXaz4bbKD-MwYqyeVGpF409P0BBSdTQli6B_p0ND0PhQ-dNBjGHrbUmgtpuDoYgh9ojgsowOktvc0ZiqBpz3YWDQBWk9D_wYRgS7iMG-hQ9oMkWJn25b6gA53yVZjW4S9bxyT-_Oz2clFcX0zvTw5vi6cqGQqpLccWF2CZnzOHUysr5RwTigxl3JirZZMlKXTFXipVSW4brh0XHjpfe4mxuRgfTcHeV0CJvOcg-c6aOrs5KqUOov4WuTigBihMYsYOhs_DWdmtaz5s2z2FGtPwAQfPwYbX0ythKpMPb01s4fTc60vpuYq68X3D9vNY_CP8Jvk_y9fMzGKbA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>603217249</pqid></control><display><type>article</type><title>On the scattering of two-dimensional elastic point sources and related near-field inverse problems for small discs</title><source>Cambridge University Press Journals Complete</source><creator>Athanasiadis, C. E. ; Pelekanos, G. ; Sevroglou, V. ; Stratis, I. G.</creator><creatorcontrib>Athanasiadis, C. E. ; Pelekanos, G. ; Sevroglou, V. ; Stratis, I. G.</creatorcontrib><description>The problem of scattering of a point-generated elastic dyadic field by a bounded obstacle or a penetrable body in two dimensions is considered. The direct scattering problem for each case is formulated in a dyadic form. For two point sources, dyadic far-field pattern generators are defined and general scattering theorems and mixed scattering relations are presented. The direct scattering problem for a rigid circular disc is considered, and the exact Green function and the elastic far-field patterns of the radiating solution in the form of infinite series are obtained. Under the low-frequency assumption, approximations for the longitudinal and transverse far-field patterns of the scattered field are obtained, in addition to an asymptotic expansion for the corresponding scattering cross-section. A simple inversion scheme that locates the radius and the position of a rigid circular disc, which is based on a closed-form approximation of the scattered field at the location of the incident point source, is proposed.</description><identifier>ISSN: 0308-2105</identifier><identifier>EISSN: 1473-7124</identifier><identifier>DOI: 10.1017/S0308210507001059</identifier><language>eng</language><publisher>Edinburgh, UK: Royal Society of Edinburgh Scotland Foundation</publisher><subject>Elasticity ; Geometry ; Mathematics ; Theorems</subject><ispartof>Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 2009-08, Vol.139 (4), p.719-741</ispartof><rights>Copyright © Royal Society of Edinburgh 2009</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c354t-4da1e062e901b1ce8ad573cc373b448aa940322c95ed4975319f14c13d4dd8573</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.cambridge.org/core/product/identifier/S0308210507001059/type/journal_article$$EHTML$$P50$$Gcambridge$$H</linktohtml><link.rule.ids>164,314,776,780,27901,27902,55603</link.rule.ids></links><search><creatorcontrib>Athanasiadis, C. E.</creatorcontrib><creatorcontrib>Pelekanos, G.</creatorcontrib><creatorcontrib>Sevroglou, V.</creatorcontrib><creatorcontrib>Stratis, I. G.</creatorcontrib><title>On the scattering of two-dimensional elastic point sources and related near-field inverse problems for small discs</title><title>Proceedings of the Royal Society of Edinburgh. Section A. Mathematics</title><addtitle>Proceedings of the Royal Society of Edinburgh: Section A Mathematics</addtitle><description>The problem of scattering of a point-generated elastic dyadic field by a bounded obstacle or a penetrable body in two dimensions is considered. The direct scattering problem for each case is formulated in a dyadic form. For two point sources, dyadic far-field pattern generators are defined and general scattering theorems and mixed scattering relations are presented. The direct scattering problem for a rigid circular disc is considered, and the exact Green function and the elastic far-field patterns of the radiating solution in the form of infinite series are obtained. Under the low-frequency assumption, approximations for the longitudinal and transverse far-field patterns of the scattered field are obtained, in addition to an asymptotic expansion for the corresponding scattering cross-section. A simple inversion scheme that locates the radius and the position of a rigid circular disc, which is based on a closed-form approximation of the scattered field at the location of the incident point source, is proposed.</description><subject>Elasticity</subject><subject>Geometry</subject><subject>Mathematics</subject><subject>Theorems</subject><issn>0308-2105</issn><issn>1473-7124</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNp1UE1LAzEUDKJgrf4Ab8H7arLJbpqj-FFFQcQK3kKavNXoftS81I9_b0pFD-JpDjPz3swQss_ZIWdcHd0xwSYlZxVTjGXQG2TEpRKF4qXcJKMVXaz4bbKD-MwYqyeVGpF409P0BBSdTQli6B_p0ND0PhQ-dNBjGHrbUmgtpuDoYgh9ojgsowOktvc0ZiqBpz3YWDQBWk9D_wYRgS7iMG-hQ9oMkWJn25b6gA53yVZjW4S9bxyT-_Oz2clFcX0zvTw5vi6cqGQqpLccWF2CZnzOHUysr5RwTigxl3JirZZMlKXTFXipVSW4brh0XHjpfe4mxuRgfTcHeV0CJvOcg-c6aOrs5KqUOov4WuTigBihMYsYOhs_DWdmtaz5s2z2FGtPwAQfPwYbX0ythKpMPb01s4fTc60vpuYq68X3D9vNY_CP8Jvk_y9fMzGKbA</recordid><startdate>200908</startdate><enddate>200908</enddate><creator>Athanasiadis, C. E.</creator><creator>Pelekanos, G.</creator><creator>Sevroglou, V.</creator><creator>Stratis, I. G.</creator><general>Royal Society of Edinburgh Scotland Foundation</general><general>Cambridge University Press</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7QF</scope><scope>7QQ</scope><scope>7SC</scope><scope>7SE</scope><scope>7SP</scope><scope>7SR</scope><scope>7TA</scope><scope>7TB</scope><scope>7U5</scope><scope>7XB</scope><scope>88I</scope><scope>8AL</scope><scope>8BQ</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>F28</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>H8D</scope><scope>H8G</scope><scope>HCIFZ</scope><scope>JG9</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</scope><scope>M2P</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PHGZM</scope><scope>PHGZT</scope><scope>PKEHL</scope><scope>PQEST</scope><scope>PQGLB</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>200908</creationdate><title>On the scattering of two-dimensional elastic point sources and related near-field inverse problems for small discs</title><author>Athanasiadis, C. E. ; Pelekanos, G. ; Sevroglou, V. ; Stratis, I. G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c354t-4da1e062e901b1ce8ad573cc373b448aa940322c95ed4975319f14c13d4dd8573</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Elasticity</topic><topic>Geometry</topic><topic>Mathematics</topic><topic>Theorems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Athanasiadis, C. E.</creatorcontrib><creatorcontrib>Pelekanos, G.</creatorcontrib><creatorcontrib>Sevroglou, V.</creatorcontrib><creatorcontrib>Stratis, I. G.</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Aluminium Industry Abstracts</collection><collection>Ceramic Abstracts</collection><collection>Computer and Information Systems Abstracts</collection><collection>Corrosion Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Engineered Materials Abstracts</collection><collection>Materials Business File</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection (ProQuest)</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>Aerospace Database</collection><collection>Copper Technical Reference Library</collection><collection>SciTech Premium Collection</collection><collection>Materials Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Computing Database</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central (New)</collection><collection>ProQuest One Academic (New)</collection><collection>ProQuest One Academic Middle East (New)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Applied & Life Sciences</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Proceedings of the Royal Society of Edinburgh. Section A. Mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Athanasiadis, C. E.</au><au>Pelekanos, G.</au><au>Sevroglou, V.</au><au>Stratis, I. G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the scattering of two-dimensional elastic point sources and related near-field inverse problems for small discs</atitle><jtitle>Proceedings of the Royal Society of Edinburgh. Section A. Mathematics</jtitle><addtitle>Proceedings of the Royal Society of Edinburgh: Section A Mathematics</addtitle><date>2009-08</date><risdate>2009</risdate><volume>139</volume><issue>4</issue><spage>719</spage><epage>741</epage><pages>719-741</pages><issn>0308-2105</issn><eissn>1473-7124</eissn><abstract>The problem of scattering of a point-generated elastic dyadic field by a bounded obstacle or a penetrable body in two dimensions is considered. The direct scattering problem for each case is formulated in a dyadic form. For two point sources, dyadic far-field pattern generators are defined and general scattering theorems and mixed scattering relations are presented. The direct scattering problem for a rigid circular disc is considered, and the exact Green function and the elastic far-field patterns of the radiating solution in the form of infinite series are obtained. Under the low-frequency assumption, approximations for the longitudinal and transverse far-field patterns of the scattered field are obtained, in addition to an asymptotic expansion for the corresponding scattering cross-section. A simple inversion scheme that locates the radius and the position of a rigid circular disc, which is based on a closed-form approximation of the scattered field at the location of the incident point source, is proposed.</abstract><cop>Edinburgh, UK</cop><pub>Royal Society of Edinburgh Scotland Foundation</pub><doi>10.1017/S0308210507001059</doi><tpages>23</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0308-2105 |
| ispartof | Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 2009-08, Vol.139 (4), p.719-741 |
| issn | 0308-2105 1473-7124 |
| language | eng |
| recordid | cdi_proquest_journals_603217249 |
| source | Cambridge University Press Journals Complete |
| subjects | Elasticity Geometry Mathematics Theorems |
| title | On the scattering of two-dimensional elastic point sources and related near-field inverse problems for small discs |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-18T22%3A06%3A16IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20the%20scattering%20of%20two-dimensional%20elastic%20point%20sources%20and%20related%20near-field%20inverse%20problems%20for%20small%20discs&rft.jtitle=Proceedings%20of%20the%20Royal%20Society%20of%20Edinburgh.%20Section%20A.%20Mathematics&rft.au=Athanasiadis,%20C.%20E.&rft.date=2009-08&rft.volume=139&rft.issue=4&rft.spage=719&rft.epage=741&rft.pages=719-741&rft.issn=0308-2105&rft.eissn=1473-7124&rft_id=info:doi/10.1017/S0308210507001059&rft_dat=%3Cproquest_cross%3E2075715051%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=603217249&rft_id=info:pmid/&rft_cupid=10_1017_S0308210507001059&rfr_iscdi=true |