Estudo do comportamento dinâmico de membranas retangulares hiperelásticas

• Ano de defesa: 2015
• Autor(a) principal: Silva, Renato de Sousa e
• Orientador(a): Soares, Renata Machado
• Banca de defesa: Soares, Renata Machado, Silva, Frederico Martins Alves da, Ávila, Suzana Moreira
• 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 hiperelástica; Análise dinâmica; Modelo Neo-Hookeano; Modelo de Mooney-Rivlin; Modelo de Yeoh
• Palavras-chave em Inglês: Hyperelastic membrane; Nonlinear dynamic analysis; Neo-Hookean model; Mooney-Rivlin model; Yeoh material model
• Área do conhecimento CNPq: ENGENHARIA CIVIL::GEOTECNICA
• Link de acesso: http://repositorio.bc.ufg.br/tede/handle/tede/4809

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.