Influência do acoplamento modal no comportamento estático não linear de painéis cilíndricos

• Autor(a) principal: Morais, Jordana Lopes
• Data de Publicação: 2017
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/7679
• topic: Painel cilíndrico; Acoplamento modal; Estabilidade estática; Modelo de baixa dimensão; Imperfeição; Geométrica; Cylindrical panel; Modular coupling; Static stability; Low-size model; Geometric imperfection; ENGENHARIA CIVIL::ESTRUTURAS

The objective of this work is the study of modal coupling in the field of transversal displacement and the search for the least amount of degrees of freedom possible to compose the modal expansion, in order to correctly represent the nonlinear behavior in cylindrical panels simply supported and submitted to a static axial loading. Nonlinear equations are deduced from their energy functionals, represented by the Airy stress function and the the strain field is based on the nonlinear Donnell shallow shell theory. The transverse displacement field is determined by the perturbation method, obtaining the non-linear modes that couple to the linear mode of vibration, then the non-linear equilibrium equations are discretized by the Galerkin method. Linear and non-linear analyzes were developed for many types of cylindrical panel geometries, varying values for radius, circumferential length and axial length. The linear analyzes aim to find the buckling modes with their respective buckling loads. In the nonlinear analysis the behavior of the cylindrical panels and the influences of the nonlinear couplings present in the transverse displacement field are studied in order to find a modal expansion that represents the correct behavior of the cylindrical panel with the least amount of possible coupled modes. The most appropriate modal solution is formed by a vibration mode described by sine-type harmonic functions, and a mode composed of harmonic functions of the cosine type. Then, from the modal expansion found, we study the static stability of the cylindrical panels by means of the equilibrium paths and the surfaces of total potential energy. In order to confirm the validity of the modal expansion that is presented as the most adequate, we investigate the static stability of cylindrical panels for two other models of modal solution. Also, the influence of initial geometric imperfections on the nonlinear behavior of cylindrical panels and the static stability of their equilibrium paths is verified.