Invariant properties of Timoshenko beam equations

The Lie groups theory is applied to study the invariant properties of the Timoshenko beam equations. A group classification with respect to the external load is performed and the full symmetry groups are determined. Then, the most general form of the solutions to the Timoshenko beam equations, invar...

Full description

Saved in:
Bibliographic Details
Published in:International journal of engineering science 1995-11, Vol.33 (14), p.2103-2114
Main Author: Djondjorov, Peter A.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Physics
Solid mechanics
Static elasticity
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c395t-643579e3d5268e0ac4a0ec90655b84188067e3a11020a9ad975b0c12a44ccb0c3
cites cdi_FETCH-LOGICAL-c395t-643579e3d5268e0ac4a0ec90655b84188067e3a11020a9ad975b0c12a44ccb0c3
container_end_page 2114
container_issue 14
container_start_page 2103
container_title International journal of engineering science
container_volume 33
creator Djondjorov, Peter A.
description The Lie groups theory is applied to study the invariant properties of the Timoshenko beam equations. A group classification with respect to the external load is performed and the full symmetry groups are determined. Then, the most general form of the solutions to the Timoshenko beam equations, invariant under an arbitrary one-parameter symmetry group is obtained. As an example, invariant solutions, representing travelling waves along the beam are discussed. Next, for each case of external loads, specified during the group classification procedure, the variational and divergence symmetries of the governing equations are determined. Finally, eight conservation laws for the solutions to the Timoshenko beam equations are derived via the Noether theorem, each being valid for a particular choice of the external load.
doi_str_mv 10.1016/0020-7225(95)00056-4
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_27479775</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>0020722595000564</els_id><sourcerecordid>27475584</sourcerecordid><originalsourceid>FETCH-LOGICAL-c395t-643579e3d5268e0ac4a0ec90655b84188067e3a11020a9ad975b0c12a44ccb0c3</originalsourceid><addsrcrecordid>eNqNkD1PwzAQhi0EEqXwDxgyIARD4JzYcbwgoYqPSpVYymxdnYswpHFrp5X49yS06oiY7obnfe_0MHbJ4Y4DL-4BMkhVlskbLW8BQBapOGIjXiqdZlyrYzY6IKfsLMbPAcq1HjE-bbcYHLZdsgp-RaFzFBNfJ3O39PGD2i-fLAiXCa032DnfxnN2UmMT6WI_x-z9-Wk-eU1nby_TyeMstbmWXVqIXCpNeSWzoiRAKxDIaiikXJSClyUUinLkvH8MNVZayQVYnqEQ1vZbPmbXu97-r_WGYmeWLlpqGmzJb6LJlFBaKfkvUMpS9KDYgTb4GAPVZhXcEsO34WAGkWawZAZLRkvzK9IMsat9P0aLTR2wtS4esrmCPlv22MMOo17K1lEw0TpqLVUukO1M5d3fd34AxGuE5A</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>27475584</pqid></control><display><type>article</type><title>Invariant properties of Timoshenko beam equations</title><source>ScienceDirect Freedom Collection</source><creator>Djondjorov, Peter A.</creator><creatorcontrib>Djondjorov, Peter A.</creatorcontrib><description>The Lie groups theory is applied to study the invariant properties of the Timoshenko beam equations. A group classification with respect to the external load is performed and the full symmetry groups are determined. Then, the most general form of the solutions to the Timoshenko beam equations, invariant under an arbitrary one-parameter symmetry group is obtained. As an example, invariant solutions, representing travelling waves along the beam are discussed. Next, for each case of external loads, specified during the group classification procedure, the variational and divergence symmetries of the governing equations are determined. Finally, eight conservation laws for the solutions to the Timoshenko beam equations are derived via the Noether theorem, each being valid for a particular choice of the external load.</description><identifier>ISSN: 0020-7225</identifier><identifier>EISSN: 1879-2197</identifier><identifier>DOI: 10.1016/0020-7225(95)00056-4</identifier><identifier>CODEN: IJESAN</identifier><language>eng</language><publisher>Oxford: Elsevier Ltd</publisher><subject>Exact sciences and technology ; Fundamental areas of phenomenology (including applications) ; Physics ; Solid mechanics ; Static elasticity ; Static elasticity (thermoelasticity...) ; Structural and continuum mechanics</subject><ispartof>International journal of engineering science, 1995-11, Vol.33 (14), p.2103-2114</ispartof><rights>1995</rights><rights>1995 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c395t-643579e3d5268e0ac4a0ec90655b84188067e3a11020a9ad975b0c12a44ccb0c3</citedby><cites>FETCH-LOGICAL-c395t-643579e3d5268e0ac4a0ec90655b84188067e3a11020a9ad975b0c12a44ccb0c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&amp;idt=3701018$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Djondjorov, Peter A.</creatorcontrib><title>Invariant properties of Timoshenko beam equations</title><title>International journal of engineering science</title><description>The Lie groups theory is applied to study the invariant properties of the Timoshenko beam equations. A group classification with respect to the external load is performed and the full symmetry groups are determined. Then, the most general form of the solutions to the Timoshenko beam equations, invariant under an arbitrary one-parameter symmetry group is obtained. As an example, invariant solutions, representing travelling waves along the beam are discussed. Next, for each case of external loads, specified during the group classification procedure, the variational and divergence symmetries of the governing equations are determined. Finally, eight conservation laws for the solutions to the Timoshenko beam equations are derived via the Noether theorem, each being valid for a particular choice of the external load.</description><subject>Exact sciences and technology</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>Physics</subject><subject>Solid mechanics</subject><subject>Static elasticity</subject><subject>Static elasticity (thermoelasticity...)</subject><subject>Structural and continuum mechanics</subject><issn>0020-7225</issn><issn>1879-2197</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1995</creationdate><recordtype>article</recordtype><recordid>eNqNkD1PwzAQhi0EEqXwDxgyIARD4JzYcbwgoYqPSpVYymxdnYswpHFrp5X49yS06oiY7obnfe_0MHbJ4Y4DL-4BMkhVlskbLW8BQBapOGIjXiqdZlyrYzY6IKfsLMbPAcq1HjE-bbcYHLZdsgp-RaFzFBNfJ3O39PGD2i-fLAiXCa032DnfxnN2UmMT6WI_x-z9-Wk-eU1nby_TyeMstbmWXVqIXCpNeSWzoiRAKxDIaiikXJSClyUUinLkvH8MNVZayQVYnqEQ1vZbPmbXu97-r_WGYmeWLlpqGmzJb6LJlFBaKfkvUMpS9KDYgTb4GAPVZhXcEsO34WAGkWawZAZLRkvzK9IMsat9P0aLTR2wtS4esrmCPlv22MMOo17K1lEw0TpqLVUukO1M5d3fd34AxGuE5A</recordid><startdate>19951101</startdate><enddate>19951101</enddate><creator>Djondjorov, Peter A.</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SM</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>L7M</scope></search><sort><creationdate>19951101</creationdate><title>Invariant properties of Timoshenko beam equations</title><author>Djondjorov, Peter A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c395t-643579e3d5268e0ac4a0ec90655b84188067e3a11020a9ad975b0c12a44ccb0c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1995</creationdate><topic>Exact sciences and technology</topic><topic>Fundamental areas of phenomenology (including applications)</topic><topic>Physics</topic><topic>Solid mechanics</topic><topic>Static elasticity</topic><topic>Static elasticity (thermoelasticity...)</topic><topic>Structural and continuum mechanics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Djondjorov, Peter A.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Earthquake Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>International journal of engineering science</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Djondjorov, Peter A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Invariant properties of Timoshenko beam equations</atitle><jtitle>International journal of engineering science</jtitle><date>1995-11-01</date><risdate>1995</risdate><volume>33</volume><issue>14</issue><spage>2103</spage><epage>2114</epage><pages>2103-2114</pages><issn>0020-7225</issn><eissn>1879-2197</eissn><coden>IJESAN</coden><abstract>The Lie groups theory is applied to study the invariant properties of the Timoshenko beam equations. A group classification with respect to the external load is performed and the full symmetry groups are determined. Then, the most general form of the solutions to the Timoshenko beam equations, invariant under an arbitrary one-parameter symmetry group is obtained. As an example, invariant solutions, representing travelling waves along the beam are discussed. Next, for each case of external loads, specified during the group classification procedure, the variational and divergence symmetries of the governing equations are determined. Finally, eight conservation laws for the solutions to the Timoshenko beam equations are derived via the Noether theorem, each being valid for a particular choice of the external load.</abstract><cop>Oxford</cop><pub>Elsevier Ltd</pub><doi>10.1016/0020-7225(95)00056-4</doi><tpages>12</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0020-7225
ispartof International journal of engineering science, 1995-11, Vol.33 (14), p.2103-2114
issn 0020-7225
1879-2197
language eng
recordid cdi_proquest_miscellaneous_27479775
source ScienceDirect Freedom Collection
subjects Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Physics
Solid mechanics
Static elasticity
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
title Invariant properties of Timoshenko beam equations
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-31T23%3A09%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=Invariant%20properties%20of%20Timoshenko%20beam%20equations&rft.jtitle=International%20journal%20of%20engineering%20science&rft.au=Djondjorov,%20Peter%20A.&rft.date=1995-11-01&rft.volume=33&rft.issue=14&rft.spage=2103&rft.epage=2114&rft.pages=2103-2114&rft.issn=0020-7225&rft.eissn=1879-2197&rft.coden=IJESAN&rft_id=info:doi/10.1016/0020-7225(95)00056-4&rft_dat=%3Cproquest_cross%3E27475584%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c395t-643579e3d5268e0ac4a0ec90655b84188067e3a11020a9ad975b0c12a44ccb0c3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=27475584&rft_id=info:pmid/&rfr_iscdi=true