Análise de estabilidade em sistemas mecânicos não lineares com vistas a atenuação de vibrações

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Universidade Federal de Goiás


In the last years, there is a growing interest in the study of nonlinear phenomena that because with the modernization of the structures and employment of innovative and more flexible materials, the nonlinearities become more evident. In that sense, this work aims to study the behavior of a mechanical system with two degrees of freedom with non-linear characteristics in primary resonance. The structure consists of the main system connected to a secondary system to act as a Nonlinear Dynamic Vibration Absorber, which partially or fully absorbs the vibrational energy of the system. The numerical solutions of the problem are obtained using the Runge-Kutta methods of 4th order and approximate analytical solutions are obtained using the Multiple Scales Method, and then it turns out how close can be closer to the numerical solutions. Through the mentioned disturbance method, too, it is determined the answers for the ordinary differential equations of the first order, which describe the modulation amplitudes and phases. Thus, the solution in steady state and the stability are studied using the frequency response. Furthermore, the behavior of the main system and the absorber are investigated through numerical simulations, such as responses in the time domain, phase planes and Poincaré map; which show that the system displays periodic movements, quasi-periodic and chaotic.



Sistemas mecânicos não lineares, Solução numérica, Método das múltiplas escalas, Estabilidade, Caos, Mechanical systems nonlinear, Numerical integration of multiple scales method, stability


PURCINA, A. B. Análise de estabilidade em sistemas mecânicos não lineares com vistas a atenuação de vibrações. 2016. 84 f. Dissertação (Mestrado em Modelagem e Otimização) - Universidade Federal de Goiás, Catalão, 2016.