Diversity and transition characteristics of sticking and non-sticking periodic impact motions of periodically forced impact systems with large dissipation

Abstract

A forced vibration system with dual bodies and an endstop is considered in this paper. A large energy loss is considered as one of the mass blocks of the system hits the endstop, and the impact associated with the large energy loss is first assumed to be completely plastic. The plastic impact may bring about the occurrence of the sticking phase, which is equivalent to a change in the structure of the forced vibration system at a certain stage after the impact. The incidence relation between dynamical characteristics and model parameters is studied through the multi-target and multi-parameter collaborative simulation analysis for determining the reasonable matching range of parameters. Pattern types, occurrence regions, distribution regularities and bifurcation characteristics of periodic and subharmonic impact vibrations are presented on a series of parameter planes. The key features of Poincare mapping, associated with the plastic impacts, are primarily manifested in piecewise continuity caused by sliding bifurcation and grazing discontinuity induced by grazing bifurcation. Integrative effects of these two nonstandard bifurcations can bring about some abnormal transitions to occur. The large dissipation case associated with small collision recovery coefficient is briefly analyzed, and the induced mechanism of chatter-sticking motion and the incidence relation between the sticking characteristics and the restitution coefficient R are discussed. The nonstandard dynamic characteristics associated with the plastic impacts are further demonstrated by dynamic mechanical behaviors of two practical impact machines applied in engineering.