Análise não linear de placas retangulares compostas de material viscoelástico
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFG |
Texto Completo: | http://repositorio.bc.ufg.br/tede/handle/tede/10830 |
Resumo: | Based on Kelvin-Voigt mechanical model, in this work the viscoelastic damping in nonlinear vibrations and dynamic instability of transversally and axially loaded rectangular plates is studied. Rectangular plates with initial geometric imperfections and with linear rotational springs at the edges are admitted in order to consider clamped boundary conditions. The non-linear Von-Kármán relations are used to describe the deformation relations of the plates and the system of non-linear dynamic equilibrium equations is found through the Hamilton principle by way of application of the Rayleigh-Ritz method, being solved later through of the fourth-order Runge-Kutta method. Initially, using the frequency-amplitude relations the influence of the viscoelasticity parameter on the plate’s non-linear mechanical behavior is investigated, observing that with the increase in the viscoelasticity parameter, the maximum amplitudes and non-linearity of the response decrease. The resonance curves, the post-critical path, the bifurcation diagrams, the attraction basins, the phase plans and the Poincaré maps were obtained for two different plates under distinct loading conditions. It is shown that, for all the amplitudes of the transverse loading studied, the plate presents periodic solutions of period 1T. When the plate is analyzed with higher levels of axial loading, this response may have periods of high order, and quasi-periodic and chaotic responses are also found. In all cases, a behavior of hardening of the plate is observed, however, in the study of effect of initial geometric imperfections, the response may become initially softened for high levels of imperfection. Finally, a nonlinear damping model is also used, which is compared with an equivalent viscous damping model. |
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Del Prado, Zenón José Guzmán Núñezhttp://lattes.cnpq.br/7703344458057759Soares, Renata Machadohttp://lattes.cnpq.br/1938664529309726Del Prado, Zenón José Guzmán NúñezSoares, Renata MachadoSilva, Frederico Martins Alves daOrlando, Diegohttp://lattes.cnpq.br/0787464545955553Dias, Phablo Veríssimo Inácio2020-10-02T11:24:43Z2020-10-02T11:24:43Z2020-06-19DIAS, P. V. I. Análise não linear de placas retangulares compostas de material viscoelástico. 2020. 103 f. Dissertação (Mestrado em Geotecnia, Estruturas e Construção Civil) - Universidade Federal de Goiás, Goiânia, 2020.http://repositorio.bc.ufg.br/tede/handle/tede/10830Based on Kelvin-Voigt mechanical model, in this work the viscoelastic damping in nonlinear vibrations and dynamic instability of transversally and axially loaded rectangular plates is studied. Rectangular plates with initial geometric imperfections and with linear rotational springs at the edges are admitted in order to consider clamped boundary conditions. The non-linear Von-Kármán relations are used to describe the deformation relations of the plates and the system of non-linear dynamic equilibrium equations is found through the Hamilton principle by way of application of the Rayleigh-Ritz method, being solved later through of the fourth-order Runge-Kutta method. Initially, using the frequency-amplitude relations the influence of the viscoelasticity parameter on the plate’s non-linear mechanical behavior is investigated, observing that with the increase in the viscoelasticity parameter, the maximum amplitudes and non-linearity of the response decrease. The resonance curves, the post-critical path, the bifurcation diagrams, the attraction basins, the phase plans and the Poincaré maps were obtained for two different plates under distinct loading conditions. It is shown that, for all the amplitudes of the transverse loading studied, the plate presents periodic solutions of period 1T. When the plate is analyzed with higher levels of axial loading, this response may have periods of high order, and quasi-periodic and chaotic responses are also found. In all cases, a behavior of hardening of the plate is observed, however, in the study of effect of initial geometric imperfections, the response may become initially softened for high levels of imperfection. Finally, a nonlinear damping model is also used, which is compared with an equivalent viscous damping model.Com base no modelo mecânico de Kelvin-Voigt, estuda-se neste trabalho o amortecimento viscoelástico nas vibrações não lineares e na instabilidade dinâmica de placas retangulares carregadas transversal e axialmente. São consideradas placas retangulares com imperfeições geométricas iniciais e com molas rotacionais lineares em todas as bordas de forma a considerar o engastamento. As relações não lineares de Von-Kármán são utilizadas para descrever as relações de deformação das placas e o sistema de equações não lineares de equilíbrio dinâmico é encontrado por meio do princípio de Hamilton através da aplicação do método de Rayleigh-Ritz, sendo resolvido posteriormente através do método de Runge-Kutta de quarta ordem. Inicialmente investiga-se, por meio das relações frequência-amplitude, a influência do parâmetro de viscoelasticidade no comportamento mecânico não linear da placa, observando-se que com o aumento do parâmetro de viscoelasticidade, as amplitudes máximas e a não linearidade da resposta diminuem. Foram obtidas as curvas de ressonância, o caminho pós-crítico, os diagramas de bifurcação, os planos fase e os mapeamentos de Poincaré para duas placas diferentes em condições distintas de carregamento. Mostra-se que, para todas as amplitudes estudadas do carregamento transversal, a placa apresenta soluções periódicas de período 1T. No entanto, quando se analisa a placa com níveis mais altos de carregamento axial, essa resposta pode possuir períodos de alta ordem, sendo encontradas também respostas quase-periódicas e caóticas. Para todos os casos observa-se um comportamento de endurecimento (hardening) da placa, porém, no estudo do efeito de imperfeições geométricas iniciais, a resposta pode se tornar inicialmente amolecida (softening) para níveis altos da imperfeição. Por fim, é utilizado também um modelo de amortecimento não-linear, o qual é comparado com um modelo de amortecimento viscoso equivalente.Submitted by Franciele Moreira (francielemoreyra@gmail.com) on 2020-10-01T17:13:21Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Dissertação - Phablo Veríssimo Inácio Dias - 2020.pdf: 17298466 bytes, checksum: 193c9774c83a15f9c0d0f256f1464c45 (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2020-10-02T11:24:42Z (GMT) No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Dissertação - Phablo Veríssimo Inácio Dias - 2020.pdf: 17298466 bytes, checksum: 193c9774c83a15f9c0d0f256f1464c45 (MD5)Made available in DSpace on 2020-10-02T11:24:43Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Dissertação - Phablo Veríssimo Inácio Dias - 2020.pdf: 17298466 bytes, checksum: 193c9774c83a15f9c0d0f256f1464c45 (MD5) Previous issue date: 2020-06-19Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESporUniversidade Federal de GoiásPrograma de Pós-graduação em Geotecnia, Estruturas e Construção Civil (EEC)UFGBrasilEscola de Engenharia Civil e Ambiental - EECA (RG)Attribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessPlacas viscoelásticasModelo de Kelvin-VoigtVibrações não linearesViscoelastic platesKelvin-Voigt modelNonlinear vibrationsENGENHARIAS::ENGENHARIA CIVIL::ESTRUTURASAnálise não linear de placas retangulares compostas de material viscoelásticoNonlinear analysis of viscoelastic rectangular platesinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesis6050050050050033991reponame:Repositório Institucional da UFGinstname:Universidade Federal de Goiás (UFG)instacron:UFGCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811http://repositorio.bc.ufg.br/tede/bitstreams/ba8b70d2-5438-44e0-8b80-6ebbf322f916/downloade39d27027a6cc9cb039ad269a5db8e34MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://repositorio.bc.ufg.br/tede/bitstreams/fb7150d9-4d76-4191-9afe-b843729ffb8d/download8a4605be74aa9ea9d79846c1fba20a33MD51ORIGINALDissertação - Phablo Veríssimo Inácio Dias - 2020.pdfDissertação - Phablo Veríssimo Inácio Dias - 2020.pdfapplication/pdf17298466http://repositorio.bc.ufg.br/tede/bitstreams/bbfe259c-e394-423e-a0f4-226fe2e46220/download193c9774c83a15f9c0d0f256f1464c45MD53tede/108302020-10-02 08:24:44.705http://creativecommons.org/licenses/by-nc-nd/3.0/br/Attribution-NonCommercial-NoDerivs 3.0 Brazilopen.accessoai:repositorio.bc.ufg.br:tede/10830http://repositorio.bc.ufg.br/tedeRepositório InstitucionalPUBhttp://repositorio.bc.ufg.br/oai/requesttasesdissertacoes.bc@ufg.bropendoar:2020-10-02T11:24:44Repositório Institucional da UFG - Universidade Federal de Goiás (UFG)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 |
dc.title.pt_BR.fl_str_mv |
Análise não linear de placas retangulares compostas de material viscoelástico |
dc.title.alternative.eng.fl_str_mv |
Nonlinear analysis of viscoelastic rectangular plates |
title |
Análise não linear de placas retangulares compostas de material viscoelástico |
spellingShingle |
Análise não linear de placas retangulares compostas de material viscoelástico Dias, Phablo Veríssimo Inácio Placas viscoelásticas Modelo de Kelvin-Voigt Vibrações não lineares Viscoelastic plates Kelvin-Voigt model Nonlinear vibrations ENGENHARIAS::ENGENHARIA CIVIL::ESTRUTURAS |
title_short |
Análise não linear de placas retangulares compostas de material viscoelástico |
title_full |
Análise não linear de placas retangulares compostas de material viscoelástico |
title_fullStr |
Análise não linear de placas retangulares compostas de material viscoelástico |
title_full_unstemmed |
Análise não linear de placas retangulares compostas de material viscoelástico |
title_sort |
Análise não linear de placas retangulares compostas de material viscoelástico |
author |
Dias, Phablo Veríssimo Inácio |
author_facet |
Dias, Phablo Veríssimo Inácio |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Del Prado, Zenón José Guzmán Núñez |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/7703344458057759 |
dc.contributor.advisor-co1.fl_str_mv |
Soares, Renata Machado |
dc.contributor.advisor-co1Lattes.fl_str_mv |
http://lattes.cnpq.br/1938664529309726 |
dc.contributor.referee1.fl_str_mv |
Del Prado, Zenón José Guzmán Núñez |
dc.contributor.referee2.fl_str_mv |
Soares, Renata Machado |
dc.contributor.referee3.fl_str_mv |
Silva, Frederico Martins Alves da |
dc.contributor.referee4.fl_str_mv |
Orlando, Diego |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/0787464545955553 |
dc.contributor.author.fl_str_mv |
Dias, Phablo Veríssimo Inácio |
contributor_str_mv |
Del Prado, Zenón José Guzmán Núñez Soares, Renata Machado Del Prado, Zenón José Guzmán Núñez Soares, Renata Machado Silva, Frederico Martins Alves da Orlando, Diego |
dc.subject.por.fl_str_mv |
Placas viscoelásticas Modelo de Kelvin-Voigt Vibrações não lineares |
topic |
Placas viscoelásticas Modelo de Kelvin-Voigt Vibrações não lineares Viscoelastic plates Kelvin-Voigt model Nonlinear vibrations ENGENHARIAS::ENGENHARIA CIVIL::ESTRUTURAS |
dc.subject.eng.fl_str_mv |
Viscoelastic plates Kelvin-Voigt model Nonlinear vibrations |
dc.subject.cnpq.fl_str_mv |
ENGENHARIAS::ENGENHARIA CIVIL::ESTRUTURAS |
description |
Based on Kelvin-Voigt mechanical model, in this work the viscoelastic damping in nonlinear vibrations and dynamic instability of transversally and axially loaded rectangular plates is studied. Rectangular plates with initial geometric imperfections and with linear rotational springs at the edges are admitted in order to consider clamped boundary conditions. The non-linear Von-Kármán relations are used to describe the deformation relations of the plates and the system of non-linear dynamic equilibrium equations is found through the Hamilton principle by way of application of the Rayleigh-Ritz method, being solved later through of the fourth-order Runge-Kutta method. Initially, using the frequency-amplitude relations the influence of the viscoelasticity parameter on the plate’s non-linear mechanical behavior is investigated, observing that with the increase in the viscoelasticity parameter, the maximum amplitudes and non-linearity of the response decrease. The resonance curves, the post-critical path, the bifurcation diagrams, the attraction basins, the phase plans and the Poincaré maps were obtained for two different plates under distinct loading conditions. It is shown that, for all the amplitudes of the transverse loading studied, the plate presents periodic solutions of period 1T. When the plate is analyzed with higher levels of axial loading, this response may have periods of high order, and quasi-periodic and chaotic responses are also found. In all cases, a behavior of hardening of the plate is observed, however, in the study of effect of initial geometric imperfections, the response may become initially softened for high levels of imperfection. Finally, a nonlinear damping model is also used, which is compared with an equivalent viscous damping model. |
publishDate |
2020 |
dc.date.accessioned.fl_str_mv |
2020-10-02T11:24:43Z |
dc.date.available.fl_str_mv |
2020-10-02T11:24:43Z |
dc.date.issued.fl_str_mv |
2020-06-19 |
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 |
DIAS, P. V. I. Análise não linear de placas retangulares compostas de material viscoelástico. 2020. 103 f. Dissertação (Mestrado em Geotecnia, Estruturas e Construção Civil) - Universidade Federal de Goiás, Goiânia, 2020. |
dc.identifier.uri.fl_str_mv |
http://repositorio.bc.ufg.br/tede/handle/tede/10830 |
identifier_str_mv |
DIAS, P. V. I. Análise não linear de placas retangulares compostas de material viscoelástico. 2020. 103 f. Dissertação (Mestrado em Geotecnia, Estruturas e Construção Civil) - Universidade Federal de Goiás, Goiânia, 2020. |
url |
http://repositorio.bc.ufg.br/tede/handle/tede/10830 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.program.fl_str_mv |
60 |
dc.relation.confidence.fl_str_mv |
500 500 500 500 |
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3 |
dc.relation.cnpq.fl_str_mv |
399 |
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1 |
dc.rights.driver.fl_str_mv |
Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/openAccess |
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Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Goiás |
dc.publisher.program.fl_str_mv |
Programa de Pós-graduação em Geotecnia, Estruturas e Construção Civil (EEC) |
dc.publisher.initials.fl_str_mv |
UFG |
dc.publisher.country.fl_str_mv |
Brasil |
dc.publisher.department.fl_str_mv |
Escola de Engenharia Civil e Ambiental - EECA (RG) |
publisher.none.fl_str_mv |
Universidade Federal de Goiás |
dc.source.none.fl_str_mv |
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