Elastic waveguides: history and the state of the art. II
In this paper, the normal modes of an elastic rectangular waveguide are analyzed. We retrace the key aspects of the almost 150-year history of this problem. Using the superposition method, we have obtained an analytical solution of the problem for four types of symmetry of the wave field. In additio...
Gespeichert in:
| Veröffentlicht in: | Journal of mathematical sciences (New York, N.Y.) N.Y.), 2010-05, Vol.167 (2), p.197-216 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 216 |
|---|---|
| container_issue | 2 |
| container_start_page | 197 |
| container_title | Journal of mathematical sciences (New York, N.Y.) |
| container_volume | 167 |
| creator | Meleshko, V. V. Bondarenko, A. A. Trofimchuk, A. N. Abasov, R. Z. |
| description | In this paper, the normal modes of an elastic rectangular waveguide are analyzed. We retrace the key aspects of the almost 150-year history of this problem. Using the superposition method, we have obtained an analytical solution of the problem for four types of symmetry of the wave field. In addition, we have established important differences of the dispersion characteristics of normal modes in a rectangle from the Rayleigh–Lamb modes for an infinite plate and the Pochhammer–Chree modes for a cylinder. We give also an estimate of a series of approximate theories for a rectangular waveguide.
The numerical interpretation of the results of analysis is however necessary, and it is a degree of perfection which it would be very important to give to every application of analysis to the natural sciences. So long as it is not obtained, the solutions may be said to remain incomplete and useless, and the truth which it is proposed to discover is no less hidden in the formulas of analysis than it was in the physical problem itself.
J. Fourier [28, Sec. 13] |
| doi_str_mv | 10.1007/s10958-010-9915-z |
| format | Article |
| fullrecord | <record><control><sourceid>gale_cross</sourceid><recordid>TN_cdi_gale_infotracmisc_A366176925</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><galeid>A366176925</galeid><sourcerecordid>A366176925</sourcerecordid><originalsourceid>FETCH-LOGICAL-c342z-b181313933b1558711110acedbd16fb461e4b776bc54db1b542de1e11f5042713</originalsourceid><addsrcrecordid>eNp9kc9LwzAUx4soOKd_gLeCJw-ZeU3TtN7GmFoYCP44h7R97TK6VpJM3f56M-tlMHw5vPfC55NDvkFwDXQClIo7CzTjKaFASZYBJ7uTYARcMJKKjJ_6mYqIMCbi8-DC2hX1TpKyUZDOW2WdLsMv9YnNRldo78Oltq4321B1VeiWGFqnHIZ9_bso4yZhnl8GZ7VqLV799XHw_jB_mz2RxfNjPpsuSMniaEcKSIEByxgrgPNUgC-qSqyKCpK6iBPAuBAiKUoeVwUUPI4qBASoOY0jAWwc3AzvNqpFqbu6d0aVa21LOWVJAiLJIu4pcoRqsEOj2r7DWvvrA35yhPenwrUujwq3B4JnHH67Rm2slfnryyELA1ua3lqDtfwweq3MVgKV-7TkkJb0acl9WnLnnWhwrGe7Bo1c9RvT-Z_9R_oBv3GTeA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Elastic waveguides: history and the state of the art. II</title><source>SpringerLink Journals - AutoHoldings</source><creator>Meleshko, V. V. ; Bondarenko, A. A. ; Trofimchuk, A. N. ; Abasov, R. Z.</creator><creatorcontrib>Meleshko, V. V. ; Bondarenko, A. A. ; Trofimchuk, A. N. ; Abasov, R. Z.</creatorcontrib><description>In this paper, the normal modes of an elastic rectangular waveguide are analyzed. We retrace the key aspects of the almost 150-year history of this problem. Using the superposition method, we have obtained an analytical solution of the problem for four types of symmetry of the wave field. In addition, we have established important differences of the dispersion characteristics of normal modes in a rectangle from the Rayleigh–Lamb modes for an infinite plate and the Pochhammer–Chree modes for a cylinder. We give also an estimate of a series of approximate theories for a rectangular waveguide.
The numerical interpretation of the results of analysis is however necessary, and it is a degree of perfection which it would be very important to give to every application of analysis to the natural sciences. So long as it is not obtained, the solutions may be said to remain incomplete and useless, and the truth which it is proposed to discover is no less hidden in the formulas of analysis than it was in the physical problem itself.
J. Fourier [28, Sec. 13]</description><identifier>ISSN: 1072-3374</identifier><identifier>EISSN: 1573-8795</identifier><identifier>DOI: 10.1007/s10958-010-9915-z</identifier><language>eng</language><publisher>Boston: Springer US</publisher><subject>Analysis ; Mathematics ; Mathematics and Statistics ; Waveguides</subject><ispartof>Journal of mathematical sciences (New York, N.Y.), 2010-05, Vol.167 (2), p.197-216</ispartof><rights>Springer Science+Business Media, Inc. 2010</rights><rights>COPYRIGHT 2010 Springer</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c342z-b181313933b1558711110acedbd16fb461e4b776bc54db1b542de1e11f5042713</citedby><cites>FETCH-LOGICAL-c342z-b181313933b1558711110acedbd16fb461e4b776bc54db1b542de1e11f5042713</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10958-010-9915-z$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10958-010-9915-z$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>315,781,785,27929,27930,41493,42562,51324</link.rule.ids></links><search><creatorcontrib>Meleshko, V. V.</creatorcontrib><creatorcontrib>Bondarenko, A. A.</creatorcontrib><creatorcontrib>Trofimchuk, A. N.</creatorcontrib><creatorcontrib>Abasov, R. Z.</creatorcontrib><title>Elastic waveguides: history and the state of the art. II</title><title>Journal of mathematical sciences (New York, N.Y.)</title><addtitle>J Math Sci</addtitle><description>In this paper, the normal modes of an elastic rectangular waveguide are analyzed. We retrace the key aspects of the almost 150-year history of this problem. Using the superposition method, we have obtained an analytical solution of the problem for four types of symmetry of the wave field. In addition, we have established important differences of the dispersion characteristics of normal modes in a rectangle from the Rayleigh–Lamb modes for an infinite plate and the Pochhammer–Chree modes for a cylinder. We give also an estimate of a series of approximate theories for a rectangular waveguide.
The numerical interpretation of the results of analysis is however necessary, and it is a degree of perfection which it would be very important to give to every application of analysis to the natural sciences. So long as it is not obtained, the solutions may be said to remain incomplete and useless, and the truth which it is proposed to discover is no less hidden in the formulas of analysis than it was in the physical problem itself.
J. Fourier [28, Sec. 13]</description><subject>Analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Waveguides</subject><issn>1072-3374</issn><issn>1573-8795</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp9kc9LwzAUx4soOKd_gLeCJw-ZeU3TtN7GmFoYCP44h7R97TK6VpJM3f56M-tlMHw5vPfC55NDvkFwDXQClIo7CzTjKaFASZYBJ7uTYARcMJKKjJ_6mYqIMCbi8-DC2hX1TpKyUZDOW2WdLsMv9YnNRldo78Oltq4321B1VeiWGFqnHIZ9_bso4yZhnl8GZ7VqLV799XHw_jB_mz2RxfNjPpsuSMniaEcKSIEByxgrgPNUgC-qSqyKCpK6iBPAuBAiKUoeVwUUPI4qBASoOY0jAWwc3AzvNqpFqbu6d0aVa21LOWVJAiLJIu4pcoRqsEOj2r7DWvvrA35yhPenwrUujwq3B4JnHH67Rm2slfnryyELA1ua3lqDtfwweq3MVgKV-7TkkJb0acl9WnLnnWhwrGe7Bo1c9RvT-Z_9R_oBv3GTeA</recordid><startdate>20100515</startdate><enddate>20100515</enddate><creator>Meleshko, V. V.</creator><creator>Bondarenko, A. A.</creator><creator>Trofimchuk, A. N.</creator><creator>Abasov, R. Z.</creator><general>Springer US</general><general>Springer</general><scope>AAYXX</scope><scope>CITATION</scope><scope>ISR</scope></search><sort><creationdate>20100515</creationdate><title>Elastic waveguides: history and the state of the art. II</title><author>Meleshko, V. V. ; Bondarenko, A. A. ; Trofimchuk, A. N. ; Abasov, R. Z.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c342z-b181313933b1558711110acedbd16fb461e4b776bc54db1b542de1e11f5042713</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Waveguides</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Meleshko, V. V.</creatorcontrib><creatorcontrib>Bondarenko, A. A.</creatorcontrib><creatorcontrib>Trofimchuk, A. N.</creatorcontrib><creatorcontrib>Abasov, R. Z.</creatorcontrib><collection>CrossRef</collection><collection>Gale In Context: Science</collection><jtitle>Journal of mathematical sciences (New York, N.Y.)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Meleshko, V. V.</au><au>Bondarenko, A. A.</au><au>Trofimchuk, A. N.</au><au>Abasov, R. Z.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Elastic waveguides: history and the state of the art. II</atitle><jtitle>Journal of mathematical sciences (New York, N.Y.)</jtitle><stitle>J Math Sci</stitle><date>2010-05-15</date><risdate>2010</risdate><volume>167</volume><issue>2</issue><spage>197</spage><epage>216</epage><pages>197-216</pages><issn>1072-3374</issn><eissn>1573-8795</eissn><abstract>In this paper, the normal modes of an elastic rectangular waveguide are analyzed. We retrace the key aspects of the almost 150-year history of this problem. Using the superposition method, we have obtained an analytical solution of the problem for four types of symmetry of the wave field. In addition, we have established important differences of the dispersion characteristics of normal modes in a rectangle from the Rayleigh–Lamb modes for an infinite plate and the Pochhammer–Chree modes for a cylinder. We give also an estimate of a series of approximate theories for a rectangular waveguide.
The numerical interpretation of the results of analysis is however necessary, and it is a degree of perfection which it would be very important to give to every application of analysis to the natural sciences. So long as it is not obtained, the solutions may be said to remain incomplete and useless, and the truth which it is proposed to discover is no less hidden in the formulas of analysis than it was in the physical problem itself.
J. Fourier [28, Sec. 13]</abstract><cop>Boston</cop><pub>Springer US</pub><doi>10.1007/s10958-010-9915-z</doi><tpages>20</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1072-3374 |
| ispartof | Journal of mathematical sciences (New York, N.Y.), 2010-05, Vol.167 (2), p.197-216 |
| issn | 1072-3374 1573-8795 |
| language | eng |
| recordid | cdi_gale_infotracmisc_A366176925 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Analysis Mathematics Mathematics and Statistics Waveguides |
| title | Elastic waveguides: history and the state of the art. II |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-13T03%3A50%3A35IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-gale_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Elastic%20waveguides:%20history%20and%20the%20state%20of%20the%20art.%20II&rft.jtitle=Journal%20of%20mathematical%20sciences%20(New%20York,%20N.Y.)&rft.au=Meleshko,%20V.%20V.&rft.date=2010-05-15&rft.volume=167&rft.issue=2&rft.spage=197&rft.epage=216&rft.pages=197-216&rft.issn=1072-3374&rft.eissn=1573-8795&rft_id=info:doi/10.1007/s10958-010-9915-z&rft_dat=%3Cgale_cross%3EA366176925%3C/gale_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_galeid=A366176925&rfr_iscdi=true |