Free vibration of a rectangular plate with an attached three-degree-of-freedom spring-mass system

Autores
Febbo, Mariano; Bambill, Diana Virginia; Rossi, Raul Edgardo
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The present paper studies the variation of the natural frequencies and mode shapes of rectangular plates carrying a three degree-of-freedom spring-mass system (subsystem), when the subsystem changes (stiffness, mass, moment of inertia, location). An analytical approach based on Lagrange multipliers as well as a finite element formulation are employed and compared. Numerically reliable results are presented for the first time, illustrating the convenience of using the present analytical method which requires only the solution of a linear eigenvalue problem. Results obtained through the variation of the mass, stiffness and moment of inertia of the 3-DOF system can be understood under the effective mass concept or Rayleigh’s statement. The analysis of frequency values of the whole system, when the 3-DOF system approaches or moves away from the center, shows that the variations depend on each particular mode of vibration. When the 3-DOF system is placed in the center of the plate, “new” modes are found to be a combination of the subsystem’s modes (two rotations, traslation) and the bare plate’s modes that possess the same symmetry. This situation no longer exists as the 3-DOF system moves away from the center of the plate, since different bare plate’s modes enable distinct motions of the 3-DOF system contributing differently to the “new’ modes as its location is modified. Also the natural frequencies of the compound system are nearly uncoupled have been calculated by means of a first order eigenvalue perturbation analysis.
Fil: Febbo, Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina
Fil: Bambill, Diana Virginia. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Rossi, Raul Edgardo. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
3-Dof Spring-Mass-System
Rectangular Plate
Frequencies
Mode Shapes
Linear Eigenvalue Problem
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:11336/67192
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/67192
network_acronym_str CONICETDig
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spelling Free vibration of a rectangular plate with an attached three-degree-of-freedom spring-mass systemFebbo, MarianoBambill, Diana VirginiaRossi, Raul Edgardo3-Dof Spring-Mass-SystemRectangular PlateFrequenciesMode ShapesLinear Eigenvalue Problemhttps://purl.org/becyt/ford/2.3https://purl.org/becyt/ford/2The present paper studies the variation of the natural frequencies and mode shapes of rectangular plates carrying a three degree-of-freedom spring-mass system (subsystem), when the subsystem changes (stiffness, mass, moment of inertia, location). An analytical approach based on Lagrange multipliers as well as a finite element formulation are employed and compared. Numerically reliable results are presented for the first time, illustrating the convenience of using the present analytical method which requires only the solution of a linear eigenvalue problem. Results obtained through the variation of the mass, stiffness and moment of inertia of the 3-DOF system can be understood under the effective mass concept or Rayleigh’s statement. The analysis of frequency values of the whole system, when the 3-DOF system approaches or moves away from the center, shows that the variations depend on each particular mode of vibration. When the 3-DOF system is placed in the center of the plate, “new” modes are found to be a combination of the subsystem’s modes (two rotations, traslation) and the bare plate’s modes that possess the same symmetry. This situation no longer exists as the 3-DOF system moves away from the center of the plate, since different bare plate’s modes enable distinct motions of the 3-DOF system contributing differently to the “new’ modes as its location is modified. Also the natural frequencies of the compound system are nearly uncoupled have been calculated by means of a first order eigenvalue perturbation analysis.Fil: Febbo, Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; ArgentinaFil: Bambill, Diana Virginia. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Rossi, Raul Edgardo. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaTechno-Press2011-12info: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/11336/67192Febbo, Mariano; Bambill, Diana Virginia; Rossi, Raul Edgardo; Free vibration of a rectangular plate with an attached three-degree-of-freedom spring-mass system; Techno-Press; Structural Engineering And Mechanics; 40; 5; 12-2011; 637-6541225-4568CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://koreascience.or.kr/article/JAKO201115541089340.pageinfo:eu-repo/semantics/altIdentifier/doi/10.12989/sem.2011.40.5.637info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:02:18Zoai:ri.conicet.gov.ar:11336/67192instacron: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:34982025-10-22 12:02:19.056CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Free vibration of a rectangular plate with an attached three-degree-of-freedom spring-mass system
title Free vibration of a rectangular plate with an attached three-degree-of-freedom spring-mass system
spellingShingle Free vibration of a rectangular plate with an attached three-degree-of-freedom spring-mass system
Febbo, Mariano
3-Dof Spring-Mass-System
Rectangular Plate
Frequencies
Mode Shapes
Linear Eigenvalue Problem
title_short Free vibration of a rectangular plate with an attached three-degree-of-freedom spring-mass system
title_full Free vibration of a rectangular plate with an attached three-degree-of-freedom spring-mass system
title_fullStr Free vibration of a rectangular plate with an attached three-degree-of-freedom spring-mass system
title_full_unstemmed Free vibration of a rectangular plate with an attached three-degree-of-freedom spring-mass system
title_sort Free vibration of a rectangular plate with an attached three-degree-of-freedom spring-mass system
dc.creator.none.fl_str_mv Febbo, Mariano
Bambill, Diana Virginia
Rossi, Raul Edgardo
author Febbo, Mariano
author_facet Febbo, Mariano
Bambill, Diana Virginia
Rossi, Raul Edgardo
author_role author
author2 Bambill, Diana Virginia
Rossi, Raul Edgardo
author2_role author
author
dc.subject.none.fl_str_mv 3-Dof Spring-Mass-System
Rectangular Plate
Frequencies
Mode Shapes
Linear Eigenvalue Problem
topic 3-Dof Spring-Mass-System
Rectangular Plate
Frequencies
Mode Shapes
Linear Eigenvalue Problem
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.3
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv The present paper studies the variation of the natural frequencies and mode shapes of rectangular plates carrying a three degree-of-freedom spring-mass system (subsystem), when the subsystem changes (stiffness, mass, moment of inertia, location). An analytical approach based on Lagrange multipliers as well as a finite element formulation are employed and compared. Numerically reliable results are presented for the first time, illustrating the convenience of using the present analytical method which requires only the solution of a linear eigenvalue problem. Results obtained through the variation of the mass, stiffness and moment of inertia of the 3-DOF system can be understood under the effective mass concept or Rayleigh’s statement. The analysis of frequency values of the whole system, when the 3-DOF system approaches or moves away from the center, shows that the variations depend on each particular mode of vibration. When the 3-DOF system is placed in the center of the plate, “new” modes are found to be a combination of the subsystem’s modes (two rotations, traslation) and the bare plate’s modes that possess the same symmetry. This situation no longer exists as the 3-DOF system moves away from the center of the plate, since different bare plate’s modes enable distinct motions of the 3-DOF system contributing differently to the “new’ modes as its location is modified. Also the natural frequencies of the compound system are nearly uncoupled have been calculated by means of a first order eigenvalue perturbation analysis.
Fil: Febbo, Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina
Fil: Bambill, Diana Virginia. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Rossi, Raul Edgardo. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description The present paper studies the variation of the natural frequencies and mode shapes of rectangular plates carrying a three degree-of-freedom spring-mass system (subsystem), when the subsystem changes (stiffness, mass, moment of inertia, location). An analytical approach based on Lagrange multipliers as well as a finite element formulation are employed and compared. Numerically reliable results are presented for the first time, illustrating the convenience of using the present analytical method which requires only the solution of a linear eigenvalue problem. Results obtained through the variation of the mass, stiffness and moment of inertia of the 3-DOF system can be understood under the effective mass concept or Rayleigh’s statement. The analysis of frequency values of the whole system, when the 3-DOF system approaches or moves away from the center, shows that the variations depend on each particular mode of vibration. When the 3-DOF system is placed in the center of the plate, “new” modes are found to be a combination of the subsystem’s modes (two rotations, traslation) and the bare plate’s modes that possess the same symmetry. This situation no longer exists as the 3-DOF system moves away from the center of the plate, since different bare plate’s modes enable distinct motions of the 3-DOF system contributing differently to the “new’ modes as its location is modified. Also the natural frequencies of the compound system are nearly uncoupled have been calculated by means of a first order eigenvalue perturbation analysis.
publishDate 2011
dc.date.none.fl_str_mv 2011-12
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/11336/67192
Febbo, Mariano; Bambill, Diana Virginia; Rossi, Raul Edgardo; Free vibration of a rectangular plate with an attached three-degree-of-freedom spring-mass system; Techno-Press; Structural Engineering And Mechanics; 40; 5; 12-2011; 637-654
1225-4568
CONICET Digital
CONICET
url http://hdl.handle.net/11336/67192
identifier_str_mv Febbo, Mariano; Bambill, Diana Virginia; Rossi, Raul Edgardo; Free vibration of a rectangular plate with an attached three-degree-of-freedom spring-mass system; Techno-Press; Structural Engineering And Mechanics; 40; 5; 12-2011; 637-654
1225-4568
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://koreascience.or.kr/article/JAKO201115541089340.page
info:eu-repo/semantics/altIdentifier/doi/10.12989/sem.2011.40.5.637
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 Techno-Press
publisher.none.fl_str_mv Techno-Press
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 12.982451

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