A variational approach to free vibration analysis of shear deformable polygonal plates with variable thickness

Autores
Quintana, Maria Virginia; Nallim, Liz
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This paper presents a simple and general variational approach for the study of the free vibration behaviour of polygonal isotropic plates with variable thickness. The Reissner-Mindlin plate theory is used to take into account the effects of shear deformation and rotary inertia in the analysis. Moreover, this theory allows obtaining greater accuracy of frequency coefficients corresponding to vibration higher modes, even for the thin plates. The governing eigenvalue equation is obtained employing the Ritz method. The plate geometry is approximated by using non-orthogonal triangular co-ordinates, while sets of independent polynomials, expressed in these co-ordinates, are employed to approximate the displacement and rotation fields. The developed algorithm allows obtaining approximated analytical solutions for plates with different aspect ratios, thickness variation and boundary conditions, including edges elastically restrained by both translational and rotational springs. Therefore, a unified program has been easily implemented. Convergence and comparison analyzes are carried out to verify the reliability and accuracy of the numerical solutions. Finally, sets of parametric studies are performed and the results are given in graphical and tabular form.
Fil: Quintana, Maria Virginia. 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
Elastically Restrained Edges
Free Vibration
Mindlin Plates
Ritz Method
Trapezoidal Plates
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:11336/74034
Acceder
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network_name_str CONICET Digital (CONICET)
spelling A variational approach to free vibration analysis of shear deformable polygonal plates with variable thicknessQuintana, Maria VirginiaNallim, LizElastically Restrained EdgesFree VibrationMindlin PlatesRitz MethodTrapezoidal Plateshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1This paper presents a simple and general variational approach for the study of the free vibration behaviour of polygonal isotropic plates with variable thickness. The Reissner-Mindlin plate theory is used to take into account the effects of shear deformation and rotary inertia in the analysis. Moreover, this theory allows obtaining greater accuracy of frequency coefficients corresponding to vibration higher modes, even for the thin plates. The governing eigenvalue equation is obtained employing the Ritz method. The plate geometry is approximated by using non-orthogonal triangular co-ordinates, while sets of independent polynomials, expressed in these co-ordinates, are employed to approximate the displacement and rotation fields. The developed algorithm allows obtaining approximated analytical solutions for plates with different aspect ratios, thickness variation and boundary conditions, including edges elastically restrained by both translational and rotational springs. Therefore, a unified program has been easily implemented. Convergence and comparison analyzes are carried out to verify the reliability and accuracy of the numerical solutions. Finally, sets of parametric studies are performed and the results are given in graphical and tabular form.Fil: Quintana, Maria Virginia. 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; ArgentinaElsevier2010-05info: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/11336/74034Quintana, Maria Virginia; Nallim, Liz; A variational approach to free vibration analysis of shear deformable polygonal plates with variable thickness; Elsevier; Applied Acoustics; 71; 5; 5-2010; 393-4010003-682XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0003682X09002801info:eu-repo/semantics/altIdentifier/doi/10.1016/j.apacoust.2009.12.002info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:09:11Zoai:ri.conicet.gov.ar:11336/74034instacron: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 10:09:11.317CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A variational approach to free vibration analysis of shear deformable polygonal plates with variable thickness
title A variational approach to free vibration analysis of shear deformable polygonal plates with variable thickness
spellingShingle A variational approach to free vibration analysis of shear deformable polygonal plates with variable thickness
Quintana, Maria Virginia
Elastically Restrained Edges
Free Vibration
Mindlin Plates
Ritz Method
Trapezoidal Plates
title_short A variational approach to free vibration analysis of shear deformable polygonal plates with variable thickness
title_full A variational approach to free vibration analysis of shear deformable polygonal plates with variable thickness
title_fullStr A variational approach to free vibration analysis of shear deformable polygonal plates with variable thickness
title_full_unstemmed A variational approach to free vibration analysis of shear deformable polygonal plates with variable thickness
title_sort A variational approach to free vibration analysis of shear deformable polygonal plates with variable thickness
dc.creator.none.fl_str_mv Quintana, Maria Virginia
Nallim, Liz
author Quintana, Maria Virginia
author_facet Quintana, Maria Virginia
Nallim, Liz
author_role author
author2 Nallim, Liz
author2_role author
dc.subject.none.fl_str_mv Elastically Restrained Edges
Free Vibration
Mindlin Plates
Ritz Method
Trapezoidal Plates
topic Elastically Restrained Edges
Free Vibration
Mindlin Plates
Ritz Method
Trapezoidal Plates
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv This paper presents a simple and general variational approach for the study of the free vibration behaviour of polygonal isotropic plates with variable thickness. The Reissner-Mindlin plate theory is used to take into account the effects of shear deformation and rotary inertia in the analysis. Moreover, this theory allows obtaining greater accuracy of frequency coefficients corresponding to vibration higher modes, even for the thin plates. The governing eigenvalue equation is obtained employing the Ritz method. The plate geometry is approximated by using non-orthogonal triangular co-ordinates, while sets of independent polynomials, expressed in these co-ordinates, are employed to approximate the displacement and rotation fields. The developed algorithm allows obtaining approximated analytical solutions for plates with different aspect ratios, thickness variation and boundary conditions, including edges elastically restrained by both translational and rotational springs. Therefore, a unified program has been easily implemented. Convergence and comparison analyzes are carried out to verify the reliability and accuracy of the numerical solutions. Finally, sets of parametric studies are performed and the results are given in graphical and tabular form.
Fil: Quintana, Maria Virginia. 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 This paper presents a simple and general variational approach for the study of the free vibration behaviour of polygonal isotropic plates with variable thickness. The Reissner-Mindlin plate theory is used to take into account the effects of shear deformation and rotary inertia in the analysis. Moreover, this theory allows obtaining greater accuracy of frequency coefficients corresponding to vibration higher modes, even for the thin plates. The governing eigenvalue equation is obtained employing the Ritz method. The plate geometry is approximated by using non-orthogonal triangular co-ordinates, while sets of independent polynomials, expressed in these co-ordinates, are employed to approximate the displacement and rotation fields. The developed algorithm allows obtaining approximated analytical solutions for plates with different aspect ratios, thickness variation and boundary conditions, including edges elastically restrained by both translational and rotational springs. Therefore, a unified program has been easily implemented. Convergence and comparison analyzes are carried out to verify the reliability and accuracy of the numerical solutions. Finally, sets of parametric studies are performed and the results are given in graphical and tabular form.
publishDate 2010
dc.date.none.fl_str_mv 2010-05
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/11336/74034
Quintana, Maria Virginia; Nallim, Liz; A variational approach to free vibration analysis of shear deformable polygonal plates with variable thickness; Elsevier; Applied Acoustics; 71; 5; 5-2010; 393-401
0003-682X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/74034
identifier_str_mv Quintana, Maria Virginia; Nallim, Liz; A variational approach to free vibration analysis of shear deformable polygonal plates with variable thickness; Elsevier; Applied Acoustics; 71; 5; 5-2010; 393-401
0003-682X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0003682X09002801
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.apacoust.2009.12.002
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
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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