含对称间隙互碰振动系统的动力学分析

Dynamic Analysis of the Vibro-impact System with Two Symmetric-clearance

本文分析了一类含对称间隙的两自由度互碰振动系统的周期运动,建立该碰撞振动系统的Poincaré映射,确定了周期运动的稳定性。根据Poincaré映射在不动点处的特征多项式和根与系数的关系,确定了两参数同时变化时所有满足鞍结分岔和Hopf分岔的临界参数。最后给出了两参数变化时系统的动力学特性图。

The periodic motion of a two-degree-of-freedom vibro-impact system with two symmetric-clearance is analyzed in this paper. And the poincaré map is also established, so the stability of the periodic motion is determined . Based on the characteristic polynomial of Poincaré map at the fixed point, the critical parameters of saddle node bifurcation and hopf bifurcation are determined when two control parameters change simuhaneously. At last, the dynamic behavior of system is analyzed using numerical simulation, the validity of theoretical derivation is also verified.