Aplicabilidade do polinômio de caos para a análise das oscilações não lineares de um sistema sujeito a flambagem

• Autor(a) principal: Silva, Michael Dowglas de Gois
• Data de Publicação: 2016
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• dARK ID: ark:/38995/001300000dmzk
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/7136
• topic: Flambagem; Bifurcação; Polinômio de caos; Fator de integridade; Buckilng; Bifurcation; Polynomial chaos; Integrity fator; ESTRUTURAS::MECANICA DAS ESTRUTURAS

In the present paper several configurations of static and dynamic equilibrium in the non-linear oscillations are studied through a simple structural system, given by a rigid bar-spring model with a degree of freedom, that depending on its parameters, can represent in a simplified way several structural elements such as portico, column, arch, shells and plaques, among others. Therefore, a bibliographical research about the instability regarding the static and dynamic equilibrium, the analysis of bifurcations, the phase plane and the basin of attraction of discrete models was made. The purpose of this study is to situate the problem, in order to evaluate in this dissertation, the influence of the uncertainties of the geometric parameters on the nonlinear vibrations and the stability of mechanical systems susceptible to buckling by comparing deterministic and nondeterministic responses. Legendre-Chaos polynomial is used to obtain the stochastic responses of the model studied. The equations of the system are deduced from their energy functionalities using the principle of stationary potential energy allowing the analysis of different bifurcation mechanisms from the chosen parameters. Two particularities are studied, the systems that present symmetrical bifurcation of the Butterfly type and the systems that present asymmetric Swallowtail bifurcation, in both cases the bifurcations present an initial unstable post critical path. For the systematic study of the nonlinear equilibrium equations, we used the symbolic algebra software, MAPLE, and computational codes written in the C language, allowing us to obtain the post-critical paths and the integration of the equilibrium equations for the analysis of the time responses, phase planes, attraction basins, and integrity factors.