STABILITY ANALYSIS IN NONLINEAR MECHANICAL SYSTEM
Alcione Borges Purcina1; Tatiane Nunes da Costa2; Romes Antonio Borges2
1 Universidade Federal de Goiás - Regional Catalão‏; 2 Universidade Federal de Goiás - Regional Catalão
doi:10.20906/CPS/CILAMCE2015-0815
Resumo
In this work, the behavior of a nonlinear system with nonlinear absorber will be investigated for the case of primary resonance. The system consists of the main system connected to a mechanical device called dynamic vibration absorber, which are widely used to attenuate undesirable vibrations in a given structure. For the integration of equations of motion will be used Fourth-Order Runge-Kutta Method. Approximate solutions to the first order, are obtained using the multiple scales method, in order to verify how close is achieved to approach of the numerical solution. The method of multiple scales, also, is used to derive a system of first-order nonlinear ordinary-differential equations that describe the modulation of the amplitude and the phase of the response. The steady state solution and stability will be studied. The stability of the system will be investigated using frequency response curve, time domain response, phase plan, Poincare map and Lyapunov exponent. Numerical Simulations show that the system presents periodic and chaotic movements. Such behavior should be demonstrated by applying the Routh-Hurwitz criterion and analysis of Lyapunov exponent. In general, the main characteristics of a dynamic system that experiences the chaotic response will be identified.
Palavras-chave: Nonlinear dynamical absorber; Multiple Scales Methods; Runge-kutta; Bifurcations; Chaotic dynamics