一类双约束单自由度碰振系统的擦边运动分析

The Analysis of Grazing Periodic Motions in a Single Degree of Freedom Vibro-Impact System with Double Constrains

摘要: 本文分析了一类单自由度双侧约束碰振系统的擦边周期运动的稳定性。利用不连续映射的方法建立了擦边周期轨道的局部Poincaré映射。在此基础上得到了双擦周期轨道的稳定性判据。根据此判据，可知系统在双擦周期轨道附近不存在局部吸引子，即，发生不连续擦边分岔。最后，用数值结果验证了理论方法的可行性。

Abstract: The stability of grazing periodic motion in a single degree of freedom vibro-impact system with double constrains is analyzed. The Poincaré mapping near the grazing trajectory is established by using the discontinuity mapping method. And the stability criterion of double grazing periodic motion is obtained. According to the criterion, it is demonstrated that local attractors do not exist near the double grazing trajectory, i.e., the grazing bifurcation is discontinuous. Finally, validity of the theoretical analysis is verified by the numerical results.