Two-parameter bifurcation analysis for an impact progressive vibration system

The mechanical model of an impact progressive vibration system was established. Impact types between a vibration exciter and a cushion, and progressive motion conditions of a slider were analyzed. Judgment conditions and dynamic equations for 4 possible motion states of the system were derived. Based on bifurcation analysis in a 2-D parametric plane, periodic vibration types of the system were obtained at all points in the parametric plane of (ω, l). The bifurcation characteristics of the fundamental impact motions of 1/1 and 2/1 were analyzed in detail. The relations among system parameters, impact velocity and slider's progressive motion rate were studied. It was shown that the fundamental impact motion of 1/1 produces the periodic vibration of 2/2 through period-doubling bifurcation, and it produces the fundamental impact motion of 2/1 through virtual erasure bifurcation or multi-slip one; the fundamental impact motion of 2/1 produces the fundamental impact motion of 3/1 through real erasure bifurcation, virtual erasure one or multi-slip one; due to virtual erasure bifurcation of the fundamental impact motion of p/1(p=1, 2), an intermediate transition region appears in the transition process from the fundamental impact motion of p/1 to the stable fundamental impact motion of (p+1)/1; the system exhibits a quasi-periodic motion and a periodic bubble phenomenon of the fundamental impact motion of 1/1 under certain parametric conditions. © 2019, Editorial Office of Journal of Vibration and Shock. All right reserved.