The transition conditions in the dynamics of elastically restrained beams

Autores
Grossi, Ricardo Oscar; Quintana, Maria Virginia
Año de publicación
2008
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This paper deals with the free transverse vibration of a non-homogeneous tapered beam subjected to general axial forces, with arbitrarily located internal hinge and elastics supports, and ends elastically restrained against rotation and translation. A rigorous and complete development is presented. First, a brief description of several papers previously published is included. Second, the Hamilton principle is rigorously stated by defining the domain D of the action integral and the space Da of admissible directions. The differential equations, boundary conditions, and particularly the transitions conditions, are obtained. Third, the transition conditions are analysed for several sets of restraints conditions. Fourth, the existence and uniqueness of the weak solutions of the boundary value problem and the eigenvalue problem which, respectively, govern the statical and dynamical behaviour of the mentioned beam is treated. Finally, the method of separation of variables is used for the determination of the exact frequencies and mode shapes and a modern application of the Ritz method to obtain approximate eigenvalues. In order to obtain an indication of the accuracy of the developed mathematical model, some cases available in the literature have been considered. New results are presented for different boundary conditions and restraint conditions in the internal hinge. © 2008 Elsevier Ltd. All rights reserved.
Fil: Grossi, Ricardo Oscar. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta; Argentina. Universidad Nacional de Salta. Facultad de Ingenieria; Argentina
Fil: Quintana, Maria Virginia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta; Argentina. Universidad Nacional de Salta. Facultad de Ingenieria; Argentina
Materia
Free Vibration
Beams
Hinge
Week Solutions
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/61695
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling The transition conditions in the dynamics of elastically restrained beamsGrossi, Ricardo OscarQuintana, Maria VirginiaFree VibrationBeamsHingeWeek Solutionshttps://purl.org/becyt/ford/2.1https://purl.org/becyt/ford/2This paper deals with the free transverse vibration of a non-homogeneous tapered beam subjected to general axial forces, with arbitrarily located internal hinge and elastics supports, and ends elastically restrained against rotation and translation. A rigorous and complete development is presented. First, a brief description of several papers previously published is included. Second, the Hamilton principle is rigorously stated by defining the domain D of the action integral and the space Da of admissible directions. The differential equations, boundary conditions, and particularly the transitions conditions, are obtained. Third, the transition conditions are analysed for several sets of restraints conditions. Fourth, the existence and uniqueness of the weak solutions of the boundary value problem and the eigenvalue problem which, respectively, govern the statical and dynamical behaviour of the mentioned beam is treated. Finally, the method of separation of variables is used for the determination of the exact frequencies and mode shapes and a modern application of the Ritz method to obtain approximate eigenvalues. In order to obtain an indication of the accuracy of the developed mathematical model, some cases available in the literature have been considered. New results are presented for different boundary conditions and restraint conditions in the internal hinge. © 2008 Elsevier Ltd. All rights reserved.Fil: Grossi, Ricardo Oscar. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta; Argentina. Universidad Nacional de Salta. Facultad de Ingenieria; ArgentinaFil: Quintana, Maria Virginia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta; Argentina. Universidad Nacional de Salta. Facultad de Ingenieria; ArgentinaAcademic Press Ltd - Elsevier Science Ltd2008-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/61695Grossi, Ricardo Oscar; Quintana, Maria Virginia; The transition conditions in the dynamics of elastically restrained beams; Academic Press Ltd - Elsevier Science Ltd; Journal of Sound and Vibration; 316; 1-5; 9-2008; 274-2970022-460XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jsv.2008.02.019info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022460X08001557info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:35:13Zoai:ri.conicet.gov.ar:11336/61695instacron: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 09:35:13.311CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The transition conditions in the dynamics of elastically restrained beams
title The transition conditions in the dynamics of elastically restrained beams
spellingShingle The transition conditions in the dynamics of elastically restrained beams
Grossi, Ricardo Oscar
Free Vibration
Beams
Hinge
Week Solutions
title_short The transition conditions in the dynamics of elastically restrained beams
title_full The transition conditions in the dynamics of elastically restrained beams
title_fullStr The transition conditions in the dynamics of elastically restrained beams
title_full_unstemmed The transition conditions in the dynamics of elastically restrained beams
title_sort The transition conditions in the dynamics of elastically restrained beams
dc.creator.none.fl_str_mv Grossi, Ricardo Oscar
Quintana, Maria Virginia
author Grossi, Ricardo Oscar
author_facet Grossi, Ricardo Oscar
Quintana, Maria Virginia
author_role author
author2 Quintana, Maria Virginia
author2_role author
dc.subject.none.fl_str_mv Free Vibration
Beams
Hinge
Week Solutions
topic Free Vibration
Beams
Hinge
Week Solutions
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.1
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv This paper deals with the free transverse vibration of a non-homogeneous tapered beam subjected to general axial forces, with arbitrarily located internal hinge and elastics supports, and ends elastically restrained against rotation and translation. A rigorous and complete development is presented. First, a brief description of several papers previously published is included. Second, the Hamilton principle is rigorously stated by defining the domain D of the action integral and the space Da of admissible directions. The differential equations, boundary conditions, and particularly the transitions conditions, are obtained. Third, the transition conditions are analysed for several sets of restraints conditions. Fourth, the existence and uniqueness of the weak solutions of the boundary value problem and the eigenvalue problem which, respectively, govern the statical and dynamical behaviour of the mentioned beam is treated. Finally, the method of separation of variables is used for the determination of the exact frequencies and mode shapes and a modern application of the Ritz method to obtain approximate eigenvalues. In order to obtain an indication of the accuracy of the developed mathematical model, some cases available in the literature have been considered. New results are presented for different boundary conditions and restraint conditions in the internal hinge. © 2008 Elsevier Ltd. All rights reserved.
Fil: Grossi, Ricardo Oscar. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta; Argentina. Universidad Nacional de Salta. Facultad de Ingenieria; Argentina
Fil: Quintana, Maria Virginia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta; Argentina. Universidad Nacional de Salta. Facultad de Ingenieria; Argentina
description This paper deals with the free transverse vibration of a non-homogeneous tapered beam subjected to general axial forces, with arbitrarily located internal hinge and elastics supports, and ends elastically restrained against rotation and translation. A rigorous and complete development is presented. First, a brief description of several papers previously published is included. Second, the Hamilton principle is rigorously stated by defining the domain D of the action integral and the space Da of admissible directions. The differential equations, boundary conditions, and particularly the transitions conditions, are obtained. Third, the transition conditions are analysed for several sets of restraints conditions. Fourth, the existence and uniqueness of the weak solutions of the boundary value problem and the eigenvalue problem which, respectively, govern the statical and dynamical behaviour of the mentioned beam is treated. Finally, the method of separation of variables is used for the determination of the exact frequencies and mode shapes and a modern application of the Ritz method to obtain approximate eigenvalues. In order to obtain an indication of the accuracy of the developed mathematical model, some cases available in the literature have been considered. New results are presented for different boundary conditions and restraint conditions in the internal hinge. © 2008 Elsevier Ltd. All rights reserved.
publishDate 2008
dc.date.none.fl_str_mv 2008-09
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/11336/61695
Grossi, Ricardo Oscar; Quintana, Maria Virginia; The transition conditions in the dynamics of elastically restrained beams; Academic Press Ltd - Elsevier Science Ltd; Journal of Sound and Vibration; 316; 1-5; 9-2008; 274-297
0022-460X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/61695
identifier_str_mv Grossi, Ricardo Oscar; Quintana, Maria Virginia; The transition conditions in the dynamics of elastically restrained beams; Academic Press Ltd - Elsevier Science Ltd; Journal of Sound and Vibration; 316; 1-5; 9-2008; 274-297
0022-460X
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.jsv.2008.02.019
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022460X08001557
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Ltd - Elsevier Science Ltd
publisher.none.fl_str_mv Academic Press Ltd - Elsevier Science Ltd
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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