Uma introdução à influência da interação modal nas oscilações não lineares de cascas cilíndricas

• Ano de defesa: 2013
• Autor(a) principal: Rodrigues, Lara
• Orientador(a): Silva, Frederico Martins Alves da
• Banca de defesa: Silva, Frederico Martins Alves da, Almeida, Sylvia Regina Mesquita de, Prado, Zenón José Guzmán Núñez Del, Gonçalves, Paulo Batista
• 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 Engenharia Civil (EEC)
• Departamento: Escola de Engenharia Civil - EEC (RG)
• País: Brasil
• Palavras-chave em Português: Cascas cilíndricas; Acoplamento modal; Interação modal; Método da perturbação; Karhunen-Loève; Análise não linear
• Palavras-chave em Inglês: Cylindrical shells; Modal coupling; Modal interaction; Perturbation techniques; Nonlinear analysis
• Área do conhecimento CNPq: ESTRUTURAS::MECANICA DAS ESTRUTURAS
• Link de acesso: http://repositorio.bc.ufg.br/tede/handle/tede/3132

The aim of this work is to investigate the interaction and modal coupling phenomena on the nonlinear vibrations of simply supported cylindrical shell subject to both harmonic axial and lateral loads. The equations of motion of the cylindrical shell are deduced from their energy functionals and the strain field is based on the nonlinear Donnell shallow shell theory. Finally, the problem is reduced to a system of nonlinear ordinary differential equations by the application of the standard Galerkin method. The modal expansion that describes the transverse displacement of the shell is obtained by applying perturbation techniques, which identifies the importance of each term in the modal expansion by the power of the perturbation parameter. The Karhunen-Loève method is applied in order to verify the importance of each term in the modal expansion, quantifying the contribution of each of these terms in the total energy of the system. The starting solution used in the perturbation procedure contains two modes of vibration with the same natural frequency and their respective companion modes, yielding a modal expansion able to describe the modal interaction between these two modes. Then, the influence of modal interaction on the nonlinear behavior of the cylindrical shell, subjected to both lateral and axial harmonic load is studied. From the analysis of the resonance curves, the parametric instability and escape boundaries, the bifurcation diagrams, the basins of attraction and phase portraits of the cylindrical shell is possible to identify situations in which the consideration of modal interaction is necessary.