Polynomial stability of a joint-leg-beam system with local damping

Autores
Burns, J. A.; Cliff, E. M.; Liu, Z.; Spies, Ruben Daniel
Año de publicación
2007
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Recent advances in the design and construction of large inflatable/rigidizable space structures and potential new applications of such structures have produced a demand for better analysis and computational tools to deal with the new class of structures. Understanding stability and damping properties of truss systems composed of these materials is central to the successful operation of future systems. In this paper, we consider a mathematical model for an assembly of two elastic beams connected to a joint through legs. The dynamic joint model is composed of two rigid bodies (the joint-legs) with an internal moment. In an ideal design all struts and joints will have identical material and geometric properties. In this case we previously established exponential stability of the beam-joint system. However, in order to apply theoretical stability estimates to realistic systems one must deal with the case where the individual truss components are not identical and still be able to analyze damping. We consider a problem of this type where one beam is assumed to have a small Kelvin-Voigt damping parameter and the second beam has no damping. In this case, we prove that the component system is only polynomially damped even if additional rotational damping is assumed in the joint.
Fil: Burns, J. A.. Virginia Polytechnic Institute; Estados Unidos
Fil: Cliff, E. M.. Virginia Polytechnic Institute; Estados Unidos
Fil: Liu, Z.. University of Minnesota; Estados Unidos
Fil: Spies, Ruben Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
Materia
BEAM
DAMPING
POLYNOMIAL DECAY RATE
SEMIGROUP
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/84242
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Polynomial stability of a joint-leg-beam system with local dampingBurns, J. A.Cliff, E. M.Liu, Z.Spies, Ruben DanielBEAMDAMPINGPOLYNOMIAL DECAY RATESEMIGROUPhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Recent advances in the design and construction of large inflatable/rigidizable space structures and potential new applications of such structures have produced a demand for better analysis and computational tools to deal with the new class of structures. Understanding stability and damping properties of truss systems composed of these materials is central to the successful operation of future systems. In this paper, we consider a mathematical model for an assembly of two elastic beams connected to a joint through legs. The dynamic joint model is composed of two rigid bodies (the joint-legs) with an internal moment. In an ideal design all struts and joints will have identical material and geometric properties. In this case we previously established exponential stability of the beam-joint system. However, in order to apply theoretical stability estimates to realistic systems one must deal with the case where the individual truss components are not identical and still be able to analyze damping. We consider a problem of this type where one beam is assumed to have a small Kelvin-Voigt damping parameter and the second beam has no damping. In this case, we prove that the component system is only polynomially damped even if additional rotational damping is assumed in the joint.Fil: Burns, J. A.. Virginia Polytechnic Institute; Estados UnidosFil: Cliff, E. M.. Virginia Polytechnic Institute; Estados UnidosFil: Liu, Z.. University of Minnesota; Estados UnidosFil: Spies, Ruben Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; ArgentinaElsevier2007-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/84242Burns, J. A.; Cliff, E. M.; Liu, Z.; Spies, Ruben Daniel; Polynomial stability of a joint-leg-beam system with local damping; Elsevier; Mathematical And Computer Modelling; 46; 9-10; 11-2007; 1236-12460895-7177CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.mcm.2006.11.037info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0895717707000519info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:39:23Zoai:ri.conicet.gov.ar:11336/84242instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:39:23.452CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Polynomial stability of a joint-leg-beam system with local damping
title Polynomial stability of a joint-leg-beam system with local damping
spellingShingle Polynomial stability of a joint-leg-beam system with local damping
Burns, J. A.
BEAM
DAMPING
POLYNOMIAL DECAY RATE
SEMIGROUP
title_short Polynomial stability of a joint-leg-beam system with local damping
title_full Polynomial stability of a joint-leg-beam system with local damping
title_fullStr Polynomial stability of a joint-leg-beam system with local damping
title_full_unstemmed Polynomial stability of a joint-leg-beam system with local damping
title_sort Polynomial stability of a joint-leg-beam system with local damping
dc.creator.none.fl_str_mv Burns, J. A.
Cliff, E. M.
Liu, Z.
Spies, Ruben Daniel
author Burns, J. A.
author_facet Burns, J. A.
Cliff, E. M.
Liu, Z.
Spies, Ruben Daniel
author_role author
author2 Cliff, E. M.
Liu, Z.
Spies, Ruben Daniel
author2_role author
author
author
dc.subject.none.fl_str_mv BEAM
DAMPING
POLYNOMIAL DECAY RATE
SEMIGROUP
topic BEAM
DAMPING
POLYNOMIAL DECAY RATE
SEMIGROUP
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Recent advances in the design and construction of large inflatable/rigidizable space structures and potential new applications of such structures have produced a demand for better analysis and computational tools to deal with the new class of structures. Understanding stability and damping properties of truss systems composed of these materials is central to the successful operation of future systems. In this paper, we consider a mathematical model for an assembly of two elastic beams connected to a joint through legs. The dynamic joint model is composed of two rigid bodies (the joint-legs) with an internal moment. In an ideal design all struts and joints will have identical material and geometric properties. In this case we previously established exponential stability of the beam-joint system. However, in order to apply theoretical stability estimates to realistic systems one must deal with the case where the individual truss components are not identical and still be able to analyze damping. We consider a problem of this type where one beam is assumed to have a small Kelvin-Voigt damping parameter and the second beam has no damping. In this case, we prove that the component system is only polynomially damped even if additional rotational damping is assumed in the joint.
Fil: Burns, J. A.. Virginia Polytechnic Institute; Estados Unidos
Fil: Cliff, E. M.. Virginia Polytechnic Institute; Estados Unidos
Fil: Liu, Z.. University of Minnesota; Estados Unidos
Fil: Spies, Ruben Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina
description Recent advances in the design and construction of large inflatable/rigidizable space structures and potential new applications of such structures have produced a demand for better analysis and computational tools to deal with the new class of structures. Understanding stability and damping properties of truss systems composed of these materials is central to the successful operation of future systems. In this paper, we consider a mathematical model for an assembly of two elastic beams connected to a joint through legs. The dynamic joint model is composed of two rigid bodies (the joint-legs) with an internal moment. In an ideal design all struts and joints will have identical material and geometric properties. In this case we previously established exponential stability of the beam-joint system. However, in order to apply theoretical stability estimates to realistic systems one must deal with the case where the individual truss components are not identical and still be able to analyze damping. We consider a problem of this type where one beam is assumed to have a small Kelvin-Voigt damping parameter and the second beam has no damping. In this case, we prove that the component system is only polynomially damped even if additional rotational damping is assumed in the joint.
publishDate 2007
dc.date.none.fl_str_mv 2007-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/84242
Burns, J. A.; Cliff, E. M.; Liu, Z.; Spies, Ruben Daniel; Polynomial stability of a joint-leg-beam system with local damping; Elsevier; Mathematical And Computer Modelling; 46; 9-10; 11-2007; 1236-1246
0895-7177
CONICET Digital
CONICET
url http://hdl.handle.net/11336/84242
identifier_str_mv Burns, J. A.; Cliff, E. M.; Liu, Z.; Spies, Ruben Daniel; Polynomial stability of a joint-leg-beam system with local damping; Elsevier; Mathematical And Computer Modelling; 46; 9-10; 11-2007; 1236-1246
0895-7177
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.mcm.2006.11.037
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0895717707000519
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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