Estudo do comportamento dinâmico de membranas retangulares hiperelásticas
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFG |
dARK ID: | ark:/38995/0013000003h0g |
Texto Completo: | http://repositorio.bc.ufg.br/tede/handle/tede/4809 |
Resumo: | Structural elements with large deformation capacity as hyperelastic membranes are gaining prominence in several engineering branches and have applications in biomechanics, thus the study of the dynamic behavior of hyperelastic structures is very important to minimize effects as the loss of the stability and undesirable vibrations. In this paper the elasticity theory for large deformations in the development of membrane theory, in order to investigate the linear and nonlinear dynamic behavior of hyperelastic membrane is used. A rectangular membrane composed of an elastomeric material, isotropic, homogeneous, incompressible and consisting of neo-Hookeano, Mooney-Rivlin and Yeoh models is considered. To model the membrane, the energy and work of external forces are used together with the application of the Hamilton on the Lagrange function. The Galerkin method is applied to obtain a discretized system of nonlinear Partial Differential Equations (PDE) and the Runge-Kutta method of 4th order is used to obtain its time response. Finally, the Brute Force and Continuation methods are applied to investigate the nonlinear dynamic behavior of the membrane. A parametric analysis is carried out looking to evaluate the influence of the material, geometry and initial tensions on the natural frequencies of the membrane. It is noted that increasing the size of a tensioned membrane, it is also increased the natural frequency for a given amplitude, and increasing the strength of a pre-tensioned membrane, the smaller the value of the frequency in relation to a range. Small differences are perceived in the behavior of the membrane for the three constitutive models of material, which are calibrated to represent the same material. Moreover, the main bifurcations of the analyzed membranes are of cyclic bending type, known as saddle-node bifurcation. |
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Soares, Renata Machadohttp://lattes.cnpq.br/1938664529309726Prado, Zenón José Guzmán Núñezhttp://lattes.cnpq.br/7703344458057759Soares, Renata MachadoSilva, Frederico Martins Alves daÁvila, Suzana Moreirahttp://lattes.cnpq.br/7911057390921183Silva, Renato de Sousa e2015-10-28T14:29:10Z2015-06-12SILVA, R. S. Estudo do comportamento dinâmico de membranas retangulares hiperelásticas. 2015. 92 f. Dissertação (Mestrado em Geotecnia, Estruturas e Construção Civil) - Universidade Federal de Goiás, Goiânia, 2015.http://repositorio.bc.ufg.br/tede/handle/tede/4809ark:/38995/0013000003h0gStructural elements with large deformation capacity as hyperelastic membranes are gaining prominence in several engineering branches and have applications in biomechanics, thus the study of the dynamic behavior of hyperelastic structures is very important to minimize effects as the loss of the stability and undesirable vibrations. In this paper the elasticity theory for large deformations in the development of membrane theory, in order to investigate the linear and nonlinear dynamic behavior of hyperelastic membrane is used. A rectangular membrane composed of an elastomeric material, isotropic, homogeneous, incompressible and consisting of neo-Hookeano, Mooney-Rivlin and Yeoh models is considered. To model the membrane, the energy and work of external forces are used together with the application of the Hamilton on the Lagrange function. The Galerkin method is applied to obtain a discretized system of nonlinear Partial Differential Equations (PDE) and the Runge-Kutta method of 4th order is used to obtain its time response. Finally, the Brute Force and Continuation methods are applied to investigate the nonlinear dynamic behavior of the membrane. A parametric analysis is carried out looking to evaluate the influence of the material, geometry and initial tensions on the natural frequencies of the membrane. It is noted that increasing the size of a tensioned membrane, it is also increased the natural frequency for a given amplitude, and increasing the strength of a pre-tensioned membrane, the smaller the value of the frequency in relation to a range. Small differences are perceived in the behavior of the membrane for the three constitutive models of material, which are calibrated to represent the same material. Moreover, the main bifurcations of the analyzed membranes are of cyclic bending type, known as saddle-node bifurcation.Elementos estruturais com grande capacidade de deformação como membranas hiperelásticas vêm ganhando destaque em diversas áreas da engenharia e têm várias aplicações na biomecânica, assim, o estudo do comportamento dinâmico de estruturas hiperelásticas é de grande importância visando minimizar os efeitos, como à perda de estabilidade e vibrações indesejáveis. No presente trabalho é utilizada a teoria da elasticidade para grandes deformações no desenvolvimento da teoria de membranas com o objetivo de investigar o comportamento dinâmico linear e não linear de membranas hiperelásticas. Considera-se a membrana retangular composta por um material elastomérico, isotrópico, homogêneo, incompressível e descrito pelos modelos constitutivos de neo-Hookeano, Mooney-Rivlin e Yeoh. Para obter as equações de equilíbrio estático e dinâmico da estrutura são utilizadas as energias e trabalhos atuantes, bem como o princípio de Hamilton aplicado na função de Lagrange. O Método de Galerkin é utilizado para discretizar as Equações Diferenciais Parciais (EDP) em um sistema de Equações Diferenciais Ordinárias (EDO). Para resolver esse sistema, utiliza-se o Método de Runge-Kutta de quarta ordem e utiliza-se o Método da Força Bruta e o Método da Continuação para investigar o comportamento dinâmico da membrana. É realizada uma análise paramétrica visando avaliar a influência do material e da geometria da membrana nas frequências naturais e nas tensões inicias. Constata-se que as bifurcações das membranas analisadas são do tipo Dobra Cíclica, conhecida como Nó-Sela. Além de verificar que quanto menor o nível de tração, maior será a não linearidade da curva de frequênciaamplitude da membrana e que há leves divergências no comportamento da membrana em relação aos três modelos constitutivos do material adotados.Submitted by Cláudia Bueno (claudiamoura18@gmail.com) on 2015-10-27T18:16:56Z No. of bitstreams: 2 Dissertação - Renato de Sousa e Silva - 2015.pdf: 7212801 bytes, checksum: 41d5a93b0ae749a6418b871cd4fea683 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-10-28T14:29:10Z (GMT) No. of bitstreams: 2 Dissertação - Renato de Sousa e Silva - 2015.pdf: 7212801 bytes, checksum: 41d5a93b0ae749a6418b871cd4fea683 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)Made available in DSpace on 2015-10-28T14:29:10Z (GMT). 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dc.title.por.fl_str_mv |
Estudo do comportamento dinâmico de membranas retangulares hiperelásticas |
dc.title.alternative.eng.fl_str_mv |
Analysis of the dynamic behavior of rectangular membranes hyperelástic |
title |
Estudo do comportamento dinâmico de membranas retangulares hiperelásticas |
spellingShingle |
Estudo do comportamento dinâmico de membranas retangulares hiperelásticas Silva, Renato de Sousa e Membrana hiperelástica Análise dinâmica Modelo Neo-Hookeano Modelo de Mooney-Rivlin Modelo de Yeoh Hyperelastic membrane Nonlinear dynamic analysis Neo-Hookean model Mooney-Rivlin model Yeoh material model ENGENHARIA CIVIL::GEOTECNICA |
title_short |
Estudo do comportamento dinâmico de membranas retangulares hiperelásticas |
title_full |
Estudo do comportamento dinâmico de membranas retangulares hiperelásticas |
title_fullStr |
Estudo do comportamento dinâmico de membranas retangulares hiperelásticas |
title_full_unstemmed |
Estudo do comportamento dinâmico de membranas retangulares hiperelásticas |
title_sort |
Estudo do comportamento dinâmico de membranas retangulares hiperelásticas |
author |
Silva, Renato de Sousa e |
author_facet |
Silva, Renato de Sousa e |
author_role |
author |
dc.contributor.advisor1.fl_str_mv |
Soares, Renata Machado |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/1938664529309726 |
dc.contributor.advisor-co1.fl_str_mv |
Prado, Zenón José Guzmán Núñez |
dc.contributor.advisor-co1Lattes.fl_str_mv |
http://lattes.cnpq.br/7703344458057759 |
dc.contributor.referee1.fl_str_mv |
Soares, Renata Machado |
dc.contributor.referee2.fl_str_mv |
Silva, Frederico Martins Alves da |
dc.contributor.referee3.fl_str_mv |
Ávila, Suzana Moreira |
dc.contributor.authorLattes.fl_str_mv |
http://lattes.cnpq.br/7911057390921183 |
dc.contributor.author.fl_str_mv |
Silva, Renato de Sousa e |
contributor_str_mv |
Soares, Renata Machado Prado, Zenón José Guzmán Núñez Soares, Renata Machado Silva, Frederico Martins Alves da Ávila, Suzana Moreira |
dc.subject.por.fl_str_mv |
Membrana hiperelástica Análise dinâmica Modelo Neo-Hookeano Modelo de Mooney-Rivlin Modelo de Yeoh |
topic |
Membrana hiperelástica Análise dinâmica Modelo Neo-Hookeano Modelo de Mooney-Rivlin Modelo de Yeoh Hyperelastic membrane Nonlinear dynamic analysis Neo-Hookean model Mooney-Rivlin model Yeoh material model ENGENHARIA CIVIL::GEOTECNICA |
dc.subject.eng.fl_str_mv |
Hyperelastic membrane Nonlinear dynamic analysis Neo-Hookean model Mooney-Rivlin model Yeoh material model |
dc.subject.cnpq.fl_str_mv |
ENGENHARIA CIVIL::GEOTECNICA |
description |
Structural elements with large deformation capacity as hyperelastic membranes are gaining prominence in several engineering branches and have applications in biomechanics, thus the study of the dynamic behavior of hyperelastic structures is very important to minimize effects as the loss of the stability and undesirable vibrations. In this paper the elasticity theory for large deformations in the development of membrane theory, in order to investigate the linear and nonlinear dynamic behavior of hyperelastic membrane is used. A rectangular membrane composed of an elastomeric material, isotropic, homogeneous, incompressible and consisting of neo-Hookeano, Mooney-Rivlin and Yeoh models is considered. To model the membrane, the energy and work of external forces are used together with the application of the Hamilton on the Lagrange function. The Galerkin method is applied to obtain a discretized system of nonlinear Partial Differential Equations (PDE) and the Runge-Kutta method of 4th order is used to obtain its time response. Finally, the Brute Force and Continuation methods are applied to investigate the nonlinear dynamic behavior of the membrane. A parametric analysis is carried out looking to evaluate the influence of the material, geometry and initial tensions on the natural frequencies of the membrane. It is noted that increasing the size of a tensioned membrane, it is also increased the natural frequency for a given amplitude, and increasing the strength of a pre-tensioned membrane, the smaller the value of the frequency in relation to a range. Small differences are perceived in the behavior of the membrane for the three constitutive models of material, which are calibrated to represent the same material. Moreover, the main bifurcations of the analyzed membranes are of cyclic bending type, known as saddle-node bifurcation. |
publishDate |
2015 |
dc.date.accessioned.fl_str_mv |
2015-10-28T14:29:10Z |
dc.date.issued.fl_str_mv |
2015-06-12 |
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 |
SILVA, R. S. Estudo do comportamento dinâmico de membranas retangulares hiperelásticas. 2015. 92 f. Dissertação (Mestrado em Geotecnia, Estruturas e Construção Civil) - Universidade Federal de Goiás, Goiânia, 2015. |
dc.identifier.uri.fl_str_mv |
http://repositorio.bc.ufg.br/tede/handle/tede/4809 |
dc.identifier.dark.fl_str_mv |
ark:/38995/0013000003h0g |
identifier_str_mv |
SILVA, R. S. Estudo do comportamento dinâmico de membranas retangulares hiperelásticas. 2015. 92 f. Dissertação (Mestrado em Geotecnia, Estruturas e Construção Civil) - Universidade Federal de Goiás, Goiânia, 2015. ark:/38995/0013000003h0g |
url |
http://repositorio.bc.ufg.br/tede/handle/tede/4809 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.program.fl_str_mv |
6915322422128222104 |
dc.relation.confidence.fl_str_mv |
600 600 600 600 |
dc.relation.department.fl_str_mv |
724087251626315585 |
dc.relation.cnpq.fl_str_mv |
8794820169253231856 |
dc.relation.sponsorship.fl_str_mv |
-961409807440757778 |
dc.rights.driver.fl_str_mv |
http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
http://creativecommons.org/licenses/by-nc-nd/4.0/ |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
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 - EEC (RG) |
publisher.none.fl_str_mv |
Universidade Federal de Goiás |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFG instname:Universidade Federal de Goiás (UFG) instacron:UFG |
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UFG |
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Repositório Institucional da UFG |
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bitstream.checksum.fl_str_mv |
bd3efa91386c1718a7f26a329fdcb468 4afdbb8c545fd630ea7db775da747b2f 683d9883b2ad62ac3b8bafc566b2e600 9da0b6dfac957114c6a7714714b86306 41d5a93b0ae749a6418b871cd4fea683 db75dcf99b304e4e63566f51559f0abc 6793d43e846b2b0444da9fa9aaad547f |
bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 MD5 MD5 MD5 |
repository.name.fl_str_mv |
Repositório Institucional da UFG - Universidade Federal de Goiás (UFG) |
repository.mail.fl_str_mv |
tasesdissertacoes.bc@ufg.br |
_version_ |
1815172546232844288 |