Periodic motions and bifurcations of a vibro-impact system with progressive motions

The mechanical model of a vibro-impact system with progressive motions was established. The probable motion states presented by the system between two consecutive impacts were analyzed, and their judgement conditions as well as motion equations were put forward. Numerical simulations were used to examine the bifurcation characteristics of the system with two types of periodic motions, including single-impact periodic motions and p/1(p≥1) fundamental motions, and the periodic motion forms corresponding to the best progression. The results indicate that the best progression occurs in 1/1 motion, near the peak value of the impact velocity of the mass M1. Due to its own specific grazing singularity, the system presents two forms of non-smooth bifurcations, namely, the real-grazing or bare-grazing bifurcation and saddle-node bifurcation, in the process of transition from 1/n(n≥2) single-impact subharmonic motion with progression to chaos, and in the process of mutual transition between adjacent p/1(p≥1) fundamental motions with progression. © 2018, Editorial Office of Journal of Vibration and Shock. All right reserved.