A variational Ritz formulation for vibration analysis of thick quadrilateral laminated plates

Autores
Rango, Rita Fernanda; Bellomo, Facundo Javier; Nallim, Liz
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In the present study, a variational Ritz approach for vibration analysis of thick arbitrarily quadrilateral laminated plates, based on the trigonometric shear deformation theory (TSDT) is developed. In this theory, shear stresses are vanished at the top and bottom surfaces of the laminate and shear correction factors are no longer required. A general straight-sided quadrilateral domain is mapped into a square domain in the computational space using a four-node master plate, employing a geometric transformation. The displacement field components are approximated by sets of beam characteristic orthogonal polynomials generated using the Gram–Schmidt procedure. The use of Ritz method allows a high spectral accuracy and faster convergence rates than local methods such as finite element. The algorithm developed is quite general, free of shear locking and can be used to obtain natural frequencies and modal shapes of laminated plates having various material parameters, geometrical planforms, length-to-thickness ratios and any combinations of free, simply supported and clamped edge support conditions. Through several numerical examples, the capability, efficiency and accuracy of the formulation are demonstrated. Convergence studies and comparison with other existing solutions in the literature suggest that the present algorithm is robust and computationally efficient.
Fil: Rango, Rita Fernanda. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta. Instituto de Investigaciones Para la Industria Química. Universidad Nacional de Salta. Facultad de Ingeniería. Instituto de Investigaciones Para la Industria Química; Argentina
Fil: Bellomo, Facundo Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta. Instituto de Investigaciones Para la Industria Química. Universidad Nacional de Salta. Facultad de Ingeniería. Instituto de Investigaciones Para la Industria Química; Argentina
Fil: Nallim, Liz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta. Instituto de Investigaciones Para la Industria Química. Universidad Nacional de Salta. Facultad de Ingeniería. Instituto de Investigaciones Para la Industria Química; Argentina
Materia
Thick Plates
Quadrilateral Plates
Ritz Method
Free Vibration
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:11336/22137
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/22137
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A variational Ritz formulation for vibration analysis of thick quadrilateral laminated platesRango, Rita FernandaBellomo, Facundo JavierNallim, LizThick PlatesQuadrilateral PlatesRitz MethodFree Vibrationhttps://purl.org/becyt/ford/2.1https://purl.org/becyt/ford/2In the present study, a variational Ritz approach for vibration analysis of thick arbitrarily quadrilateral laminated plates, based on the trigonometric shear deformation theory (TSDT) is developed. In this theory, shear stresses are vanished at the top and bottom surfaces of the laminate and shear correction factors are no longer required. A general straight-sided quadrilateral domain is mapped into a square domain in the computational space using a four-node master plate, employing a geometric transformation. The displacement field components are approximated by sets of beam characteristic orthogonal polynomials generated using the Gram–Schmidt procedure. The use of Ritz method allows a high spectral accuracy and faster convergence rates than local methods such as finite element. The algorithm developed is quite general, free of shear locking and can be used to obtain natural frequencies and modal shapes of laminated plates having various material parameters, geometrical planforms, length-to-thickness ratios and any combinations of free, simply supported and clamped edge support conditions. Through several numerical examples, the capability, efficiency and accuracy of the formulation are demonstrated. Convergence studies and comparison with other existing solutions in the literature suggest that the present algorithm is robust and computationally efficient.Fil: Rango, Rita Fernanda. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta. Instituto de Investigaciones Para la Industria Química. Universidad Nacional de Salta. Facultad de Ingeniería. Instituto de Investigaciones Para la Industria Química; ArgentinaFil: Bellomo, Facundo Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta. Instituto de Investigaciones Para la Industria Química. Universidad Nacional de Salta. Facultad de Ingeniería. Instituto de Investigaciones Para la Industria Química; ArgentinaFil: Nallim, Liz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta. Instituto de Investigaciones Para la Industria Química. Universidad Nacional de Salta. Facultad de Ingeniería. Instituto de Investigaciones Para la Industria Química; ArgentinaElsevier2015-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/22137Rango, Rita Fernanda; Bellomo, Facundo Javier; Nallim, Liz; A variational Ritz formulation for vibration analysis of thick quadrilateral laminated plates; Elsevier; International Journal Of Mechanical Sciences; 104; 10-2015; 60-740020-7403CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.ijmecsci.2015.09.018info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0020740315003458info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:18:33Zoai:ri.conicet.gov.ar:11336/22137instacron: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 10:18:33.368CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A variational Ritz formulation for vibration analysis of thick quadrilateral laminated plates
title A variational Ritz formulation for vibration analysis of thick quadrilateral laminated plates
spellingShingle A variational Ritz formulation for vibration analysis of thick quadrilateral laminated plates
Rango, Rita Fernanda
Thick Plates
Quadrilateral Plates
Ritz Method
Free Vibration
title_short A variational Ritz formulation for vibration analysis of thick quadrilateral laminated plates
title_full A variational Ritz formulation for vibration analysis of thick quadrilateral laminated plates
title_fullStr A variational Ritz formulation for vibration analysis of thick quadrilateral laminated plates
title_full_unstemmed A variational Ritz formulation for vibration analysis of thick quadrilateral laminated plates
title_sort A variational Ritz formulation for vibration analysis of thick quadrilateral laminated plates
dc.creator.none.fl_str_mv Rango, Rita Fernanda
Bellomo, Facundo Javier
Nallim, Liz
author Rango, Rita Fernanda
author_facet Rango, Rita Fernanda
Bellomo, Facundo Javier
Nallim, Liz
author_role author
author2 Bellomo, Facundo Javier
Nallim, Liz
author2_role author
author
dc.subject.none.fl_str_mv Thick Plates
Quadrilateral Plates
Ritz Method
Free Vibration
topic Thick Plates
Quadrilateral Plates
Ritz Method
Free Vibration
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.1
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv In the present study, a variational Ritz approach for vibration analysis of thick arbitrarily quadrilateral laminated plates, based on the trigonometric shear deformation theory (TSDT) is developed. In this theory, shear stresses are vanished at the top and bottom surfaces of the laminate and shear correction factors are no longer required. A general straight-sided quadrilateral domain is mapped into a square domain in the computational space using a four-node master plate, employing a geometric transformation. The displacement field components are approximated by sets of beam characteristic orthogonal polynomials generated using the Gram–Schmidt procedure. The use of Ritz method allows a high spectral accuracy and faster convergence rates than local methods such as finite element. The algorithm developed is quite general, free of shear locking and can be used to obtain natural frequencies and modal shapes of laminated plates having various material parameters, geometrical planforms, length-to-thickness ratios and any combinations of free, simply supported and clamped edge support conditions. Through several numerical examples, the capability, efficiency and accuracy of the formulation are demonstrated. Convergence studies and comparison with other existing solutions in the literature suggest that the present algorithm is robust and computationally efficient.
Fil: Rango, Rita Fernanda. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta. Instituto de Investigaciones Para la Industria Química. Universidad Nacional de Salta. Facultad de Ingeniería. Instituto de Investigaciones Para la Industria Química; Argentina
Fil: Bellomo, Facundo Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta. Instituto de Investigaciones Para la Industria Química. Universidad Nacional de Salta. Facultad de Ingeniería. Instituto de Investigaciones Para la Industria Química; Argentina
Fil: Nallim, Liz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta. Instituto de Investigaciones Para la Industria Química. Universidad Nacional de Salta. Facultad de Ingeniería. Instituto de Investigaciones Para la Industria Química; Argentina
description In the present study, a variational Ritz approach for vibration analysis of thick arbitrarily quadrilateral laminated plates, based on the trigonometric shear deformation theory (TSDT) is developed. In this theory, shear stresses are vanished at the top and bottom surfaces of the laminate and shear correction factors are no longer required. A general straight-sided quadrilateral domain is mapped into a square domain in the computational space using a four-node master plate, employing a geometric transformation. The displacement field components are approximated by sets of beam characteristic orthogonal polynomials generated using the Gram–Schmidt procedure. The use of Ritz method allows a high spectral accuracy and faster convergence rates than local methods such as finite element. The algorithm developed is quite general, free of shear locking and can be used to obtain natural frequencies and modal shapes of laminated plates having various material parameters, geometrical planforms, length-to-thickness ratios and any combinations of free, simply supported and clamped edge support conditions. Through several numerical examples, the capability, efficiency and accuracy of the formulation are demonstrated. Convergence studies and comparison with other existing solutions in the literature suggest that the present algorithm is robust and computationally efficient.
publishDate 2015
dc.date.none.fl_str_mv 2015-10
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/11336/22137
Rango, Rita Fernanda; Bellomo, Facundo Javier; Nallim, Liz; A variational Ritz formulation for vibration analysis of thick quadrilateral laminated plates; Elsevier; International Journal Of Mechanical Sciences; 104; 10-2015; 60-74
0020-7403
CONICET Digital
CONICET
url http://hdl.handle.net/11336/22137
identifier_str_mv Rango, Rita Fernanda; Bellomo, Facundo Javier; Nallim, Liz; A variational Ritz formulation for vibration analysis of thick quadrilateral laminated plates; Elsevier; International Journal Of Mechanical Sciences; 104; 10-2015; 60-74
0020-7403
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.ijmecsci.2015.09.018
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0020740315003458
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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