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Verification of surface wave solutions obtained by the reciprocity theorem
•Surface wave motions generated by a time-harmonic point load are investigated.•Expressions for the displacements are determined by the reciprocity theorem.•Wave motions due to a horizontal load are obtained by the use of Hankel transform.•The solutions by using reciprocity, Hankel transform, and by...
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Published in: | Ultrasonics 2014-09, Vol.54 (7), p.1891-1894 |
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creator | Phan, Haidang Cho, Younho Achenbach, Jan D. |
description | •Surface wave motions generated by a time-harmonic point load are investigated.•Expressions for the displacements are determined by the reciprocity theorem.•Wave motions due to a horizontal load are obtained by the use of Hankel transform.•The solutions by using reciprocity, Hankel transform, and by Lamb are the same.
Surface wave motions generated by a time-harmonic point load applied at the surface of an isotropic linearly elastic half-space are conventionally solved by the use of integral transform techniques. The inverse transforms, are often complicated and will not always yield closed-form solutions. In this paper expressions for the displacements for surface wave motions radiated from point-load excitation are determined in a simple manner by the use of the elastodynamic reciprocity theorem. It is shown that the radiated amplitudes of the surface displacements obtained by the reciprocity approach are identical to the corresponding results obtained by the use of Hankel transform and by Lamb in his classical paper. |
doi_str_mv | 10.1016/j.ultras.2014.05.003 |
format | article |
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Surface wave motions generated by a time-harmonic point load applied at the surface of an isotropic linearly elastic half-space are conventionally solved by the use of integral transform techniques. The inverse transforms, are often complicated and will not always yield closed-form solutions. In this paper expressions for the displacements for surface wave motions radiated from point-load excitation are determined in a simple manner by the use of the elastodynamic reciprocity theorem. It is shown that the radiated amplitudes of the surface displacements obtained by the reciprocity approach are identical to the corresponding results obtained by the use of Hankel transform and by Lamb in his classical paper.</description><identifier>ISSN: 0041-624X</identifier><identifier>EISSN: 1874-9968</identifier><identifier>DOI: 10.1016/j.ultras.2014.05.003</identifier><identifier>PMID: 24928810</identifier><language>eng</language><publisher>Netherlands: Elsevier B.V</publisher><subject>Half-space ; Hankel transform ; Point load ; Reciprocity ; Surface wave</subject><ispartof>Ultrasonics, 2014-09, Vol.54 (7), p.1891-1894</ispartof><rights>2014 Elsevier B.V.</rights><rights>Copyright © 2014 Elsevier B.V. All rights reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c395t-8736fbc0b6a9357a1994763b2e9ac5147a574e0d115040c94a1ea127df0a33863</citedby><cites>FETCH-LOGICAL-c395t-8736fbc0b6a9357a1994763b2e9ac5147a574e0d115040c94a1ea127df0a33863</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>315,786,790,27957,27958</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/24928810$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Phan, Haidang</creatorcontrib><creatorcontrib>Cho, Younho</creatorcontrib><creatorcontrib>Achenbach, Jan D.</creatorcontrib><title>Verification of surface wave solutions obtained by the reciprocity theorem</title><title>Ultrasonics</title><addtitle>Ultrasonics</addtitle><description>•Surface wave motions generated by a time-harmonic point load are investigated.•Expressions for the displacements are determined by the reciprocity theorem.•Wave motions due to a horizontal load are obtained by the use of Hankel transform.•The solutions by using reciprocity, Hankel transform, and by Lamb are the same.
Surface wave motions generated by a time-harmonic point load applied at the surface of an isotropic linearly elastic half-space are conventionally solved by the use of integral transform techniques. The inverse transforms, are often complicated and will not always yield closed-form solutions. In this paper expressions for the displacements for surface wave motions radiated from point-load excitation are determined in a simple manner by the use of the elastodynamic reciprocity theorem. It is shown that the radiated amplitudes of the surface displacements obtained by the reciprocity approach are identical to the corresponding results obtained by the use of Hankel transform and by Lamb in his classical paper.</description><subject>Half-space</subject><subject>Hankel transform</subject><subject>Point load</subject><subject>Reciprocity</subject><subject>Surface wave</subject><issn>0041-624X</issn><issn>1874-9968</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAQhoMoun78A5EevbTONGnaXARZ_ETwouItpOkUs3Q3a9Ku7L-366pHT8Mwz8zLPIydImQIKC9m2dD1wcQsBxQZFBkA32ETrEqRKiWrXTYBEJjKXLwdsMMYZzCCFfJ9dpALlVcVwoQ9vFJwrbOmd36R-DaJQ2iNpeTTrCiJvhs2g5j4ujduQU1Sr5P-nZJA1i2Dt67_7n2g-THba00X6eSnHrGXm-vn6V36-HR7P716TC1XRZ9WJZdtbaGWRvGiNKiUKCWvc1LGFihKU5SCoEEsQIBVwiAZzMumBcN5JfkRO9_eHfM_Boq9nrtoqevMgvwQNRZCYYVSihEVW9QGH2OgVi-Dm5uw1gh6Y1HP9Nai3ljUUOjR4rh29pMw1HNq_pZ-tY3A5Rag8c-Vo6CjdbSw1LhRTK8b7_5P-AIw2YVI</recordid><startdate>20140901</startdate><enddate>20140901</enddate><creator>Phan, Haidang</creator><creator>Cho, Younho</creator><creator>Achenbach, Jan D.</creator><general>Elsevier B.V</general><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope></search><sort><creationdate>20140901</creationdate><title>Verification of surface wave solutions obtained by the reciprocity theorem</title><author>Phan, Haidang ; Cho, Younho ; Achenbach, Jan D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c395t-8736fbc0b6a9357a1994763b2e9ac5147a574e0d115040c94a1ea127df0a33863</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Half-space</topic><topic>Hankel transform</topic><topic>Point load</topic><topic>Reciprocity</topic><topic>Surface wave</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Phan, Haidang</creatorcontrib><creatorcontrib>Cho, Younho</creatorcontrib><creatorcontrib>Achenbach, Jan D.</creatorcontrib><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><jtitle>Ultrasonics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Phan, Haidang</au><au>Cho, Younho</au><au>Achenbach, Jan D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Verification of surface wave solutions obtained by the reciprocity theorem</atitle><jtitle>Ultrasonics</jtitle><addtitle>Ultrasonics</addtitle><date>2014-09-01</date><risdate>2014</risdate><volume>54</volume><issue>7</issue><spage>1891</spage><epage>1894</epage><pages>1891-1894</pages><issn>0041-624X</issn><eissn>1874-9968</eissn><notes>ObjectType-Article-1</notes><notes>SourceType-Scholarly Journals-1</notes><notes>ObjectType-Feature-2</notes><notes>content type line 23</notes><abstract>•Surface wave motions generated by a time-harmonic point load are investigated.•Expressions for the displacements are determined by the reciprocity theorem.•Wave motions due to a horizontal load are obtained by the use of Hankel transform.•The solutions by using reciprocity, Hankel transform, and by Lamb are the same.
Surface wave motions generated by a time-harmonic point load applied at the surface of an isotropic linearly elastic half-space are conventionally solved by the use of integral transform techniques. The inverse transforms, are often complicated and will not always yield closed-form solutions. In this paper expressions for the displacements for surface wave motions radiated from point-load excitation are determined in a simple manner by the use of the elastodynamic reciprocity theorem. It is shown that the radiated amplitudes of the surface displacements obtained by the reciprocity approach are identical to the corresponding results obtained by the use of Hankel transform and by Lamb in his classical paper.</abstract><cop>Netherlands</cop><pub>Elsevier B.V</pub><pmid>24928810</pmid><doi>10.1016/j.ultras.2014.05.003</doi><tpages>4</tpages></addata></record> |
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subjects | Half-space Hankel transform Point load Reciprocity Surface wave |
title | Verification of surface wave solutions obtained by the reciprocity theorem |
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