Free Vibrations of a Trapezoidal Plate with an Internal Line Hinge

Autores
Quintana, Maria Virginia; Grossi, Ricardo Oscar
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This paper deals with a general variational formulation for the determination of natural frequencies and mode shapes of free vibrations of laminated thin plates of trapezoidal shape with an internal line hinge restrained against rotation. The analysis was carried out by using the kinematics corresponding to the classical laminated plate theory (CLPT). The eigenvalue problem is obtained by employing a combination of the Ritz method and the Lagrange multipliers method. The domain of the plate is transformed into a rectangular domain in the computational space by using nonorthogonal triangular coordinates and the transverse displacements are approximated with a set of simple polynomials automatically generated and expressed in the triangular coordinates. The developed algorithm allows obtaining approximate analytical solutions for mentioned plate with different geometries, aspect ratio, position of the line hinge, and boundary conditions including translational and rotational elastically restrained edges. It allows studying the influence of the mentioned line on the vibration frequencies and respective mode shapes. The algorithm can easily be programmed and it is numerically stable. Additionally, as a particular case, the results of triangular plates can be easily generated.
Fil: Quintana, Maria Virginia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Salta. Instituto de Investigación Para la Industria Química (i); Argentina. Universidad Nacional de Salta; Argentina
Fil: Grossi, Ricardo Oscar. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Salta. Instituto de Investigación Para la Industria Química (i); Argentina. Universidad Nacional de Salta; Argentina
Materia
Free Vibrations
Trapezoidal Plates
Ritz Method
Internal Line Hinge
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/4750
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Free Vibrations of a Trapezoidal Plate with an Internal Line HingeQuintana, Maria VirginiaGrossi, Ricardo OscarFree VibrationsTrapezoidal PlatesRitz MethodInternal Line Hingehttps://purl.org/becyt/ford/2.3https://purl.org/becyt/ford/2This paper deals with a general variational formulation for the determination of natural frequencies and mode shapes of free vibrations of laminated thin plates of trapezoidal shape with an internal line hinge restrained against rotation. The analysis was carried out by using the kinematics corresponding to the classical laminated plate theory (CLPT). The eigenvalue problem is obtained by employing a combination of the Ritz method and the Lagrange multipliers method. The domain of the plate is transformed into a rectangular domain in the computational space by using nonorthogonal triangular coordinates and the transverse displacements are approximated with a set of simple polynomials automatically generated and expressed in the triangular coordinates. The developed algorithm allows obtaining approximate analytical solutions for mentioned plate with different geometries, aspect ratio, position of the line hinge, and boundary conditions including translational and rotational elastically restrained edges. It allows studying the influence of the mentioned line on the vibration frequencies and respective mode shapes. The algorithm can easily be programmed and it is numerically stable. Additionally, as a particular case, the results of triangular plates can be easily generated.Fil: Quintana, Maria Virginia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Salta. Instituto de Investigación Para la Industria Química (i); Argentina. Universidad Nacional de Salta; ArgentinaFil: Grossi, Ricardo Oscar. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Salta. Instituto de Investigación Para la Industria Química (i); Argentina. Universidad Nacional de Salta; ArgentinaHindawi Publishing Corporation2014-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/4750Quintana, Maria Virginia; Grossi, Ricardo Oscar; Free Vibrations of a Trapezoidal Plate with an Internal Line Hinge; Hindawi Publishing Corporation; The Scientific World Journal; 2014; 2-2014; 252084-2520842356-6140enginfo:eu-repo/semantics/altIdentifier/url/http://www.hindawi.com/journals/tswj/2014/252084/info:eu-repo/semantics/altIdentifier/doi/10.1155/2014/252084info:eu-repo/semantics/altIdentifier/issn/2356-6140info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:08:11Zoai:ri.conicet.gov.ar:11336/4750instacron: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 10:08:11.918CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Free Vibrations of a Trapezoidal Plate with an Internal Line Hinge
title Free Vibrations of a Trapezoidal Plate with an Internal Line Hinge
spellingShingle Free Vibrations of a Trapezoidal Plate with an Internal Line Hinge
Quintana, Maria Virginia
Free Vibrations
Trapezoidal Plates
Ritz Method
Internal Line Hinge
title_short Free Vibrations of a Trapezoidal Plate with an Internal Line Hinge
title_full Free Vibrations of a Trapezoidal Plate with an Internal Line Hinge
title_fullStr Free Vibrations of a Trapezoidal Plate with an Internal Line Hinge
title_full_unstemmed Free Vibrations of a Trapezoidal Plate with an Internal Line Hinge
title_sort Free Vibrations of a Trapezoidal Plate with an Internal Line Hinge
dc.creator.none.fl_str_mv Quintana, Maria Virginia
Grossi, Ricardo Oscar
author Quintana, Maria Virginia
author_facet Quintana, Maria Virginia
Grossi, Ricardo Oscar
author_role author
author2 Grossi, Ricardo Oscar
author2_role author
dc.subject.none.fl_str_mv Free Vibrations
Trapezoidal Plates
Ritz Method
Internal Line Hinge
topic Free Vibrations
Trapezoidal Plates
Ritz Method
Internal Line Hinge
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.3
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv This paper deals with a general variational formulation for the determination of natural frequencies and mode shapes of free vibrations of laminated thin plates of trapezoidal shape with an internal line hinge restrained against rotation. The analysis was carried out by using the kinematics corresponding to the classical laminated plate theory (CLPT). The eigenvalue problem is obtained by employing a combination of the Ritz method and the Lagrange multipliers method. The domain of the plate is transformed into a rectangular domain in the computational space by using nonorthogonal triangular coordinates and the transverse displacements are approximated with a set of simple polynomials automatically generated and expressed in the triangular coordinates. The developed algorithm allows obtaining approximate analytical solutions for mentioned plate with different geometries, aspect ratio, position of the line hinge, and boundary conditions including translational and rotational elastically restrained edges. It allows studying the influence of the mentioned line on the vibration frequencies and respective mode shapes. The algorithm can easily be programmed and it is numerically stable. Additionally, as a particular case, the results of triangular plates can be easily generated.
Fil: Quintana, Maria Virginia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Salta. Instituto de Investigación Para la Industria Química (i); Argentina. Universidad Nacional de Salta; Argentina
Fil: Grossi, Ricardo Oscar. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Salta. Instituto de Investigación Para la Industria Química (i); Argentina. Universidad Nacional de Salta; Argentina
description This paper deals with a general variational formulation for the determination of natural frequencies and mode shapes of free vibrations of laminated thin plates of trapezoidal shape with an internal line hinge restrained against rotation. The analysis was carried out by using the kinematics corresponding to the classical laminated plate theory (CLPT). The eigenvalue problem is obtained by employing a combination of the Ritz method and the Lagrange multipliers method. The domain of the plate is transformed into a rectangular domain in the computational space by using nonorthogonal triangular coordinates and the transverse displacements are approximated with a set of simple polynomials automatically generated and expressed in the triangular coordinates. The developed algorithm allows obtaining approximate analytical solutions for mentioned plate with different geometries, aspect ratio, position of the line hinge, and boundary conditions including translational and rotational elastically restrained edges. It allows studying the influence of the mentioned line on the vibration frequencies and respective mode shapes. The algorithm can easily be programmed and it is numerically stable. Additionally, as a particular case, the results of triangular plates can be easily generated.
publishDate 2014
dc.date.none.fl_str_mv 2014-02
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/11336/4750
Quintana, Maria Virginia; Grossi, Ricardo Oscar; Free Vibrations of a Trapezoidal Plate with an Internal Line Hinge; Hindawi Publishing Corporation; The Scientific World Journal; 2014; 2-2014; 252084-252084
2356-6140
url http://hdl.handle.net/11336/4750
identifier_str_mv Quintana, Maria Virginia; Grossi, Ricardo Oscar; Free Vibrations of a Trapezoidal Plate with an Internal Line Hinge; Hindawi Publishing Corporation; The Scientific World Journal; 2014; 2-2014; 252084-252084
2356-6140
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.hindawi.com/journals/tswj/2014/252084/
info:eu-repo/semantics/altIdentifier/doi/10.1155/2014/252084
info:eu-repo/semantics/altIdentifier/issn/2356-6140
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Hindawi Publishing Corporation
publisher.none.fl_str_mv Hindawi Publishing Corporation
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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