Estudo do comportamento dinâmico de membranas retangulares hiperelásticas

Detalhes bibliográficos
Autor(a) principal: Silva, Renato de Sousa e
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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spelling 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
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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
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dc.publisher.none.fl_str_mv Universidade Federal de Goiás
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dc.publisher.initials.fl_str_mv UFG
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dc.publisher.department.fl_str_mv Escola de Engenharia Civil - EEC (RG)
publisher.none.fl_str_mv Universidade Federal de Goiás
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