Análise dinâmica não-linear de uma membrana hiperelástica esférica

• Ano de defesa: 2018
• Autor(a) principal: Amaral, Pedro Felipe Tavares do
• Orientador(a): Soares, Renata Machado
• Banca de defesa: Soares, Renata Machado, Prado, Zenón José Guzmán Nunez del, Gavassoni Neto, Elvídio
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Goiás
• Programa de Pós-Graduação: Programa de Pós-graduação em Geotecnia, Estruturas e Construção Civil (EEC)
• Departamento: Escola de Engenharia Civil - EEC (RG)
• País: Brasil
• Palavras-chave em Português: Membrana esférica; Material hiperelástico; Mooney-Rivlin; Análise de estabilidade; Análise dinâmica
• Palavras-chave em Inglês: Spherical Membrane; Hyperelastic material; Mooney-Rivlin; Dynamic analysis; Stability analysis
• Área do conhecimento CNPq: ENGENHARIA CIVIL::ESTRUTURAS
• Link de acesso: http://repositorio.bc.ufg.br/tede/handle/tede/8420

In the present work, studies about the nonlinear static and dynamic behavior of a spherical membrane are presented. This membrane is composed by a hyperelastic, incompressible homogeneous and isotropic material, which is defined by either of the two distinct constitutive models: Mooney-Rivlin or the Neo-Hookean model. The equilibrium equations are obtained from the large-strain theory, by utilizing a variational formulation and by subjecting the membrane to an uniformly distributed internal radial pressure differential. From the nonlinear static analysis, internal membrane tensions and strains are obtained. From the dynamic analysis, the frequency-amplitude relation, the linear stability analysis, the time response, bifurcation diagrams, resonance curves and basins of attraction are obtained. As a first step, there is an analysis on a membrane composed by the same experimental material, which is described by the two different constitutive models presented in this work. It is observed that the dynamic responses are considerably distinct, due to the difference between the geometrical nonlinearities that each constitutive model insert on the equilibrium equation. The Neo-Hookean model has a lower pre-stretching limit, and its attraction basins are more eroded and irregular than the Mooney-Rivlin, that is still stable on regions of larger vibration amplitudes. Then, the influence of the Mooney-Rivlin parameter (α) is evaluated, and it is found that this parameter is the main source of the differences between the constitutive models, modifying the stability, nonlinear vibrations and also influencing on the loss or gain of the global rigidity of the membrane.