Aiming at a single-degree-of-freedom vibration system with friction and impact, the periodic motion of the four different types of motions including free sliding, collision, adhesion and viscous in the phase space is analyzed . Identify and study the distribution of periodic motion of the system in the parameter domain combined with four different Poincaré mapping sections. Using the parameter continuation algorithm and the cell mapping algorithm, combined with the system stability judgment conditions, the system's periodic viscous-adhesive motion distribution and transition law are revealed. The research results show that the periodic viscous-adhesive motion is mainly concentrated in the low-frequency small gap area. During the transition of the system to the periodic viscous-adhesive motion, the number of collisions increases and the collision speed gradually decreases under the induction of the grazing bifurcation (GR). At the same time, the periodic band of periodic motion gradually narrows. The transition process of adjacent periodic motions is mainly induced by rubbing bifurcation (GR), saddle knot bifurcation (SN) and sliding bifurcation (SL). Due to the mutual irreversibility of transitions, GR-SN and (GR- SL)-SN and other different forms of polymorphic coexistence areas. The system gap and recovery coefficient are reduced, the viscous-adhesive movement frequency band becomes wider, and the starting point extends in the direction of high frequency.
Key words
impact and friction；viscosity-adhesion /
grazing bifurcation；saddle node bifurcation；sliding bifurcation
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