一类Filippov碰摩转子系统的非光滑分析

The Non-Smooth Analysis of Filippov Rub-Impact Rotor System

摘要: 针对两端刚性支撑的Jeffcott转子，建立了一个三自由度、弯扭耦合的Filippov碰摩转子系统。通过对比有无考虑扭振的碰摩转子的振幅和激励及响应相位差随转动角速度变化的分岔图及转子的时间历程图、相图、Poincaré截面图，数值分析了弯扭耦合的Filippov碰摩转子系统的碰摩响应相位特征和非光滑动力学行为。分析表明：对于弯扭耦合的Filippov碰摩转子系统，振动响应具有确定的相位特征；两类方程分叉图的变化过程基本相同；扭转现象明显；在一定参数下，系统会出现stick-slip现象。

Abstract: A three-degree-of-freedom lateral-torsional coupled Filippov differential system for a Jeffcott rotor supported rigidly is established. Comparing the lateral-torsional coupled rub-impact rotor and the lateral rub-impact rotor through bifurcation diagrams of amplitude and the phase difference, time trajectories, phase portraits, Poincaré maps, time-history diagram, the phase characteristic and the non-smooth dynamic behavior of the Filippov rub-impact system are analyzed numerically. It is shown that the rub-impact response has the definite phase characteristic; the two models have a similar bifurcation process in their bifurcation figures; the torsional vibration is obvious, and the stick-slip phenomena will happen in this system in a certain parameter.