Uniform stabilization for the transmission problem of the Timoshenko system with memory

Detalhes bibliográficos
Autor(a) principal: Alves, Margareth S.
Data de Publicação: 2010
Outros Autores: Raposo, Carlos Alberto, Rivera, Jaime E. Muñoz, Sepúlveda, Mauricio A., Villagrán, Octavio Paulo Vera
Tipo de documento: Artigo
Idioma: eng
Título da fonte: LOCUS Repositório Institucional da UFV
Texto Completo: https://doi.org/10.1016/j.jmaa.2010.02.045
http://www.locus.ufv.br/handle/123456789/22221
Resumo: In this paper we study the transmission for a partially viscoelastic beam, that is, a beam which is composed of two components, elastic and viscoelastic. In the rotation angle of the filaments of the beam, ψ1(x,t) and ψ2(x,t), the dissipation is occasioned by the memory effect. In the transverse vibrations ϕ1(x,t) and ϕ2(x,t) we do not have dissipation and the system is purely elastic. For this type of beam we show the uniform stabilization, i.e., the rate of decay has directly relation with the velocity of the relaxation function.
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spelling Alves, Margareth S.Raposo, Carlos AlbertoRivera, Jaime E. MuñozSepúlveda, Mauricio A.Villagrán, Octavio Paulo Vera2018-10-10T15:53:03Z2018-10-10T15:53:03Z2010-09-010022-247Xhttps://doi.org/10.1016/j.jmaa.2010.02.045http://www.locus.ufv.br/handle/123456789/22221In this paper we study the transmission for a partially viscoelastic beam, that is, a beam which is composed of two components, elastic and viscoelastic. In the rotation angle of the filaments of the beam, ψ1(x,t) and ψ2(x,t), the dissipation is occasioned by the memory effect. In the transverse vibrations ϕ1(x,t) and ϕ2(x,t) we do not have dissipation and the system is purely elastic. For this type of beam we show the uniform stabilization, i.e., the rate of decay has directly relation with the velocity of the relaxation function.engJournal of Mathematical Analysis and ApplicationsVolume 369, Issue 1, Pages 323-345, September 2010Elsevier B. V.info:eu-repo/semantics/openAccessTransmission problemExponential decayPolynomial decayPartially viscoelastic beamUniform stabilization for the transmission problem of the Timoshenko system with memoryinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfreponame:LOCUS Repositório Institucional da UFVinstname:Universidade Federal de Viçosa (UFV)instacron:UFVORIGINALartigo.pdfartigo.pdfTexto completoapplication/pdf326185https://locus.ufv.br//bitstream/123456789/22221/1/artigo.pdf35ecdf38be0ee3260fb193ce346ee97dMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://locus.ufv.br//bitstream/123456789/22221/2/license.txt8a4605be74aa9ea9d79846c1fba20a33MD52123456789/222212018-10-10 13:00:06.962oai:locus.ufv.br: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Repositório InstitucionalPUBhttps://www.locus.ufv.br/oai/requestfabiojreis@ufv.bropendoar:21452018-10-10T16:00:06LOCUS Repositório Institucional da UFV - Universidade Federal de Viçosa (UFV)false
dc.title.en.fl_str_mv Uniform stabilization for the transmission problem of the Timoshenko system with memory
title Uniform stabilization for the transmission problem of the Timoshenko system with memory
spellingShingle Uniform stabilization for the transmission problem of the Timoshenko system with memory
Alves, Margareth S.
Transmission problem
Exponential decay
Polynomial decay
Partially viscoelastic beam
title_short Uniform stabilization for the transmission problem of the Timoshenko system with memory
title_full Uniform stabilization for the transmission problem of the Timoshenko system with memory
title_fullStr Uniform stabilization for the transmission problem of the Timoshenko system with memory
title_full_unstemmed Uniform stabilization for the transmission problem of the Timoshenko system with memory
title_sort Uniform stabilization for the transmission problem of the Timoshenko system with memory
author Alves, Margareth S.
author_facet Alves, Margareth S.
Raposo, Carlos Alberto
Rivera, Jaime E. Muñoz
Sepúlveda, Mauricio A.
Villagrán, Octavio Paulo Vera
author_role author
author2 Raposo, Carlos Alberto
Rivera, Jaime E. Muñoz
Sepúlveda, Mauricio A.
Villagrán, Octavio Paulo Vera
author2_role author
author
author
author
dc.contributor.author.fl_str_mv Alves, Margareth S.
Raposo, Carlos Alberto
Rivera, Jaime E. Muñoz
Sepúlveda, Mauricio A.
Villagrán, Octavio Paulo Vera
dc.subject.pt-BR.fl_str_mv Transmission problem
Exponential decay
Polynomial decay
Partially viscoelastic beam
topic Transmission problem
Exponential decay
Polynomial decay
Partially viscoelastic beam
description In this paper we study the transmission for a partially viscoelastic beam, that is, a beam which is composed of two components, elastic and viscoelastic. In the rotation angle of the filaments of the beam, ψ1(x,t) and ψ2(x,t), the dissipation is occasioned by the memory effect. In the transverse vibrations ϕ1(x,t) and ϕ2(x,t) we do not have dissipation and the system is purely elastic. For this type of beam we show the uniform stabilization, i.e., the rate of decay has directly relation with the velocity of the relaxation function.
publishDate 2010
dc.date.issued.fl_str_mv 2010-09-01
dc.date.accessioned.fl_str_mv 2018-10-10T15:53:03Z
dc.date.available.fl_str_mv 2018-10-10T15:53:03Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://doi.org/10.1016/j.jmaa.2010.02.045
http://www.locus.ufv.br/handle/123456789/22221
dc.identifier.issn.none.fl_str_mv 0022-247X
identifier_str_mv 0022-247X
url https://doi.org/10.1016/j.jmaa.2010.02.045
http://www.locus.ufv.br/handle/123456789/22221
dc.language.iso.fl_str_mv eng
language eng
dc.relation.ispartofseries.pt-BR.fl_str_mv Volume 369, Issue 1, Pages 323-345, September 2010
dc.rights.driver.fl_str_mv Elsevier B. V.
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Elsevier B. V.
eu_rights_str_mv openAccess
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dc.publisher.none.fl_str_mv Journal of Mathematical Analysis and Applications
publisher.none.fl_str_mv Journal of Mathematical Analysis and Applications
dc.source.none.fl_str_mv reponame:LOCUS Repositório Institucional da UFV
instname:Universidade Federal de Viçosa (UFV)
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instname_str Universidade Federal de Viçosa (UFV)
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reponame_str LOCUS Repositório Institucional da UFV
collection LOCUS Repositório Institucional da UFV
bitstream.url.fl_str_mv https://locus.ufv.br//bitstream/123456789/22221/1/artigo.pdf
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