摘要
运用Poincaré映射理论与计算机仿真,研究了三自由度含间隙碰振系统的分岔和向混沌演化的道路.结果表明,在Hopf-flip余维二分岔点附近存在倍化分岔和Hopf分岔,不动点先发生倍化分岔形成周期2点,又经过Hopf分岔形成了概周期运动.Hopf-Hopf余维二分岔通过数值仿真展现了Hopf分岔、环面分岔以及由"近正方形"概周期吸引子转迁为混沌的奇异过程.通过对该类系统的研究,可以为工程实际中的含间隙碰振系统的优化设计提供理论参考.
The bifurcation and the routes to chaos of the three-degree-of-freedom vibro-impact system with clear- ance are investigated using Poincare mapping and the computer simulation in this paper. The results show that flip bifurcation and Hopf bifurcation exist close to the bifurcation point of the Hopf-flip codimension two bifurca- tion. In the fixed point, the period two point is formed when Flip bifurcation firstly takes place, and the quasi- periodic motion occurs after Hopf bifurcation. It is revealed that Hopf bifurcation, torus bifurcation and the chaos evolution of the ＂subquadrate＂ quasi-period attractor through the numerical simulations are exhibited in Hopf- Hopf codimension two bifurcations. The study on this vibro-impact system with clearance provides the essential reference for its future optimize design.
出处
《动力学与控制学报》
2016年第5期401-406,共6页
Journal of Dynamics and Control
