一类两自由度分段线性非光滑系统的分岔与混沌

Bifurcation and chaos of a two-degree-of-freedom non-smooth system with piecewise-linearity

研究了一类两自由度分段线性非光滑系统周期运动的分岔现象和混沌行为。求出系统在各分界面处的切换矩阵,应用Floquet理论分析了该系统周期运动发生Neimark-Sacker分岔和倍化分岔的条件,然后建立Poincaré映射,通过数值方法进一步揭示了系统发生的Neimark-Sacker分岔,倍化分岔和亚谐分岔现象。对该系统分岔和混沌的研究,有助于工程中此类弹性碰撞系统的优化设计。

In this paper, the bifurcation and chaos of periodic motions of a two-degree-of-freedom non-smooth system with piecewise-linearity is studied. The switching matrix is given out at the switching boundaries and the Neimark-Sacker bifurcation and period-doubling bifurcation of periodic motions of the system are investigated by the Floquet theory. We establish Poincare map is established as well as further study of Neimark-Sacker bifurcation, in other words, period-doubling bifurca- tion and subharmonic bifurcation in the non-smooth system by means of numerical simulations. It is possible to optimize the parameters of the practical system by investigation of bifurcation and chaos in the soft impact system.