Uma introdução à influência da interação modal nas oscilações não lineares de cascas cilíndricas

Detalhes bibliográficos
Autor(a) principal: Rodrigues, Lara
Data de Publicação: 2013
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Repositório Institucional da UFG
Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/3132
Resumo: The aim of this work is to investigate the interaction and modal coupling phenomena on the nonlinear vibrations of simply supported cylindrical shell subject to both harmonic axial and lateral loads. The equations of motion of the cylindrical shell are deduced from their energy functionals and the strain field is based on the nonlinear Donnell shallow shell theory. Finally, the problem is reduced to a system of nonlinear ordinary differential equations by the application of the standard Galerkin method. The modal expansion that describes the transverse displacement of the shell is obtained by applying perturbation techniques, which identifies the importance of each term in the modal expansion by the power of the perturbation parameter. The Karhunen-Loève method is applied in order to verify the importance of each term in the modal expansion, quantifying the contribution of each of these terms in the total energy of the system. The starting solution used in the perturbation procedure contains two modes of vibration with the same natural frequency and their respective companion modes, yielding a modal expansion able to describe the modal interaction between these two modes. Then, the influence of modal interaction on the nonlinear behavior of the cylindrical shell, subjected to both lateral and axial harmonic load is studied. From the analysis of the resonance curves, the parametric instability and escape boundaries, the bifurcation diagrams, the basins of attraction and phase portraits of the cylindrical shell is possible to identify situations in which the consideration of modal interaction is necessary.
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spelling Silva, Frederico Martins Alves dahttp://lattes.cnpq.br/9929132527197884Silva, Frederico Martins Alves daAlmeida, Sylvia Regina Mesquita dePrado, Zenón José Guzmán Núñez DelGonçalves, Paulo Batistahttp://lattes.cnpq.br/6482247758794733Rodrigues, Lara2014-09-23T15:24:03Z2013-02-14RODRIGUES, Lara. Uma introdução à influência da interação modal nas oscilações não lineares de cascas cilíndricas. 2013. 145 f. Dissertação (Mestrado em Engenharia Civil) - Universidade Federal de Goiás, Goiânia, 2013.http://repositorio.bc.ufg.br/tede/handle/tede/3132ark:/38995/001300000c7q7The aim of this work is to investigate the interaction and modal coupling phenomena on the nonlinear vibrations of simply supported cylindrical shell subject to both harmonic axial and lateral loads. The equations of motion of the cylindrical shell are deduced from their energy functionals and the strain field is based on the nonlinear Donnell shallow shell theory. Finally, the problem is reduced to a system of nonlinear ordinary differential equations by the application of the standard Galerkin method. The modal expansion that describes the transverse displacement of the shell is obtained by applying perturbation techniques, which identifies the importance of each term in the modal expansion by the power of the perturbation parameter. The Karhunen-Loève method is applied in order to verify the importance of each term in the modal expansion, quantifying the contribution of each of these terms in the total energy of the system. The starting solution used in the perturbation procedure contains two modes of vibration with the same natural frequency and their respective companion modes, yielding a modal expansion able to describe the modal interaction between these two modes. Then, the influence of modal interaction on the nonlinear behavior of the cylindrical shell, subjected to both lateral and axial harmonic load is studied. From the analysis of the resonance curves, the parametric instability and escape boundaries, the bifurcation diagrams, the basins of attraction and phase portraits of the cylindrical shell is possible to identify situations in which the consideration of modal interaction is necessary.Neste trabalho estudam-se as vibrações não lineares de cascas cilíndricas simplesmente apoiadas sujeitas a um carregamento lateral e a um carregamento axial, ambos harmônicos, com o objetivo de se analisar fenômenos como o acoplamento e a interação modal. As equações de movimento da casca cilíndrica são deduzidas a partir de seus funcionais de energia. O campo de deformações da casca cilíndrica é descrito com base na teoria não linear de Donnell para cascas esbeltas e o problema é reduzido a um sistema de equações diferenciais ordinárias não lineares a partir da aplicação do método de Galerkin. As expansões modais que descrevem o campo de deslocamento transversal da casca são obtidas através da aplicação do método da perturbação, que identifica a importância de cada termo da expansão modal a partir da potência do parâmetro de perturbação. O método de Karhunen-Loève é aplicado a fim de se verificar a importância de cada termo da expansão modal, quantificando a participação de cada um desses termos na energia total do sistema. Utilizam-se, como solução inicial do método da perturbação, dois modos de vibração com frequência natural igual e com seus respectivos companion modes, obtendo-se uma expansão modal capaz de descrever a interação modal entre esses dois modos. Em seguida, analisa-se a influência da interação modal no comportamento não linear da casca cilíndrica submetidas a cargas laterais e axiais harmônicas. A partir da análise das curvas de ressonância, das fronteiras de instabilidade paramétrica, dos diagramas de bifurcação, das bacias de atração e dos planosfase da casca cilíndrica é possível identificar em quais situações de carregamento a consideração da interação modal se faz necessária.Submitted by Erika Demachki (erikademachki@gmail.com) on 2014-09-22T20:32:01Z No. of bitstreams: 2 Lara Rodrigues.pdf: 17878503 bytes, checksum: a51778a9fbf6a31b2a71fe0c9c462105 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2014-09-23T15:24:03Z (GMT) No. of bitstreams: 2 Lara Rodrigues.pdf: 17878503 bytes, checksum: a51778a9fbf6a31b2a71fe0c9c462105 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)Made available in DSpace on 2014-09-23T15:24:03Z (GMT). No. of bitstreams: 2 Lara Rodrigues.pdf: 17878503 bytes, checksum: a51778a9fbf6a31b2a71fe0c9c462105 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2013-02-14Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESapplication/pdfhttp://repositorio.bc.ufg.br/tede/retrieve/8371/Lara%20Rodrigues.pdf.jpgporUniversidade Federal de GoiásPrograma de Pós-graduação em Engenharia Civil (EEC)UFGBrasilEscola de Engenharia Civil - EEC (RG)ABE, A.; KOBAYASHI, Y.; YAMADA, G. Nonlinear dynamic behaviors of clamped laminated shallow shells with one-to-one internal resonance. Journal of Sound and Vibration, [s. l.], v. 304, p. 957-968, 2007. AMABILI, M. Nonlinear vibrations and stability of shells and plates. 1 ed. England: Cambridge University Press, 2008. 374 p. AMABILI, M. Internal resonances in non-linear vibrations of laminated circular cylindrical shell. Nonlinear Dynamics, [s. l.], v. 69, p. 755-770, 2012. 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Dissertação (Mestrado em Engenharia Mecânica) – Departamento de Engenharia Mecânica, Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, 2001.-6536446489817675175600600600600724087251626315585-22971529077907822172075167498588264571http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessCascas cilíndricasAcoplamento modalInteração modalMétodo da perturbaçãoKarhunen-LoèveAnálise não linearCylindrical shellsModal couplingModal interactionPerturbation techniquesNonlinear analysisESTRUTURAS::MECANICA DAS ESTRUTURASUma introdução à influência da interação modal nas oscilações não lineares de cascas cilíndricasAn introduction to the influence of modal interactions in non-linear oscillations of cylindrical shellsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisreponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGLICENSElicense.txtlicense.txttext/plain; charset=utf-82165http://repositorio.bc.ufg.br/tede/bitstreams/2717de59-9b76-43bb-863f-fd99f883ef7d/downloadbd3efa91386c1718a7f26a329fdcb468MD51CC-LICENSElicense_urllicense_urltext/plain; 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dc.title.por.fl_str_mv Uma introdução à influência da interação modal nas oscilações não lineares de cascas cilíndricas
dc.title.alternative.eng.fl_str_mv An introduction to the influence of modal interactions in non-linear oscillations of cylindrical shells
title Uma introdução à influência da interação modal nas oscilações não lineares de cascas cilíndricas
spellingShingle Uma introdução à influência da interação modal nas oscilações não lineares de cascas cilíndricas
Rodrigues, Lara
Cascas cilíndricas
Acoplamento modal
Interação modal
Método da perturbação
Karhunen-Loève
Análise não linear
Cylindrical shells
Modal coupling
Modal interaction
Perturbation techniques
Nonlinear analysis
ESTRUTURAS::MECANICA DAS ESTRUTURAS
title_short Uma introdução à influência da interação modal nas oscilações não lineares de cascas cilíndricas
title_full Uma introdução à influência da interação modal nas oscilações não lineares de cascas cilíndricas
title_fullStr Uma introdução à influência da interação modal nas oscilações não lineares de cascas cilíndricas
title_full_unstemmed Uma introdução à influência da interação modal nas oscilações não lineares de cascas cilíndricas
title_sort Uma introdução à influência da interação modal nas oscilações não lineares de cascas cilíndricas
author Rodrigues, Lara
author_facet Rodrigues, Lara
author_role author
dc.contributor.advisor1.fl_str_mv Silva, Frederico Martins Alves da
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/9929132527197884
dc.contributor.referee1.fl_str_mv Silva, Frederico Martins Alves da
dc.contributor.referee2.fl_str_mv Almeida, Sylvia Regina Mesquita de
dc.contributor.referee3.fl_str_mv Prado, Zenón José Guzmán Núñez Del
dc.contributor.referee4.fl_str_mv Gonçalves, Paulo Batista
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/6482247758794733
dc.contributor.author.fl_str_mv Rodrigues, Lara
contributor_str_mv Silva, Frederico Martins Alves da
Silva, Frederico Martins Alves da
Almeida, Sylvia Regina Mesquita de
Prado, Zenón José Guzmán Núñez Del
Gonçalves, Paulo Batista
dc.subject.por.fl_str_mv Cascas cilíndricas
Acoplamento modal
Interação modal
Método da perturbação
Karhunen-Loève
Análise não linear
topic Cascas cilíndricas
Acoplamento modal
Interação modal
Método da perturbação
Karhunen-Loève
Análise não linear
Cylindrical shells
Modal coupling
Modal interaction
Perturbation techniques
Nonlinear analysis
ESTRUTURAS::MECANICA DAS ESTRUTURAS
dc.subject.eng.fl_str_mv Cylindrical shells
Modal coupling
Modal interaction
Perturbation techniques
Nonlinear analysis
dc.subject.cnpq.fl_str_mv ESTRUTURAS::MECANICA DAS ESTRUTURAS
description The aim of this work is to investigate the interaction and modal coupling phenomena on the nonlinear vibrations of simply supported cylindrical shell subject to both harmonic axial and lateral loads. The equations of motion of the cylindrical shell are deduced from their energy functionals and the strain field is based on the nonlinear Donnell shallow shell theory. Finally, the problem is reduced to a system of nonlinear ordinary differential equations by the application of the standard Galerkin method. The modal expansion that describes the transverse displacement of the shell is obtained by applying perturbation techniques, which identifies the importance of each term in the modal expansion by the power of the perturbation parameter. The Karhunen-Loève method is applied in order to verify the importance of each term in the modal expansion, quantifying the contribution of each of these terms in the total energy of the system. The starting solution used in the perturbation procedure contains two modes of vibration with the same natural frequency and their respective companion modes, yielding a modal expansion able to describe the modal interaction between these two modes. Then, the influence of modal interaction on the nonlinear behavior of the cylindrical shell, subjected to both lateral and axial harmonic load is studied. From the analysis of the resonance curves, the parametric instability and escape boundaries, the bifurcation diagrams, the basins of attraction and phase portraits of the cylindrical shell is possible to identify situations in which the consideration of modal interaction is necessary.
publishDate 2013
dc.date.issued.fl_str_mv 2013-02-14
dc.date.accessioned.fl_str_mv 2014-09-23T15:24:03Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.citation.fl_str_mv RODRIGUES, Lara. Uma introdução à influência da interação modal nas oscilações não lineares de cascas cilíndricas. 2013. 145 f. Dissertação (Mestrado em Engenharia Civil) - Universidade Federal de Goiás, Goiânia, 2013.
dc.identifier.uri.fl_str_mv http://repositorio.bc.ufg.br/tede/handle/tede/3132
dc.identifier.dark.fl_str_mv ark:/38995/001300000c7q7
identifier_str_mv RODRIGUES, Lara. Uma introdução à influência da interação modal nas oscilações não lineares de cascas cilíndricas. 2013. 145 f. Dissertação (Mestrado em Engenharia Civil) - Universidade Federal de Goiás, Goiânia, 2013.
ark:/38995/001300000c7q7
url http://repositorio.bc.ufg.br/tede/handle/tede/3132
dc.language.iso.fl_str_mv por
language por
dc.relation.program.fl_str_mv -6536446489817675175
dc.relation.confidence.fl_str_mv 600
600
600
600
dc.relation.department.fl_str_mv 724087251626315585
dc.relation.cnpq.fl_str_mv -2297152907790782217
dc.relation.sponsorship.fl_str_mv 2075167498588264571
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G. N. Effect of nonlinear modal interaction on the dynamics behavior of cylindrical shells. In: Congresso Ibero-Latino- Americano de Métodos Computacionais em Engenharia, 2011, Ouro Preto. Anais... Ouro Preto: Universidade Federal de Ouro Preto, 2011c, v. 01, p. 1-10. VARADAN, T. K.; PRATHAP, G.; RAMANI, H. V. Nonlinear free flexural vibrations of thin circular cylindrical shells. AIAA Journal, [s. l.], v. 27, n. 9, p. 1303-1304, 1989. WOLTER, C. Uma introdução à redução de modelos através da expansão de Karhunen- Loève. 2001.54 f. Dissertação (Mestrado em Engenharia Mecânica) – Departamento de Engenharia Mecânica, Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, 2001.
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