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Dynamics of a two-degree-of freedom system with a rigid stop: Chattering-impact and subharmonic motions

Xifeng Zhu

The dynamic model of a two-degree-of-freedom system with a rigid stop is considered. The multi-impact motions of the one excitation period, subharmonic motions and chattering-impact characteristics of the system are analyzed by Runge-Kutta numerical simulation algorithm, and furthermore the saddle-node and grazing bifurcations between p/1 motions are revealed exactly. The research results show that a series of grazing bifurcations occur with decreasing frequency so that the impact number p of p/1 motions correspondingly increases one by one, a series of saddle-node bifurcations occur with increasing frequency so that the impact number p of p/1 motions correspondingly decreases one by one and there exists frequency hysteresis range and multiple coexistence attractors between p/1 and (p+1)/1 motions. In the low exciting frequency case, the impact number p of p/1 motions becomes big enough and chattering-impact characteristics will be appearing. The transition law from 1/1 motion to chattering-impact motion is summarized explicitly.