关键词: 冲击振动, 分岔, 间隙, 稳定性, 周期运动, 板条马氏体, 断口形貌, 高应变速率, 双相钢, 微观变形机理

Abstract: A multi-degree-of-freedom vibratory system with a clearance is considered. The system consists of linear components, but the maximum displacement of one of the masses is limited to a threshold value by the symmetrical rigid stops. Such models play an important role in the studies of mechanical systems with clearances or gaps. Period one double-impact symmetrical motions are derived analytically according to the set of periodicity and matching conditions, and associated Poincaré map is established. Stability and local bifurcations of the fixed point of double-impact symmetrical motion is analyzed by us-ing the Poincaré map. A two-degree-of-freedom vibratory system with a clearance is used as an example to demonstrate the validity of the analysis. Stability of periodic-impact motions, bifurcations, grazing singularities and routes to chaos are ana-lyzed for the two-degree-of-freedom vibratory system with a clearance, in turn. Dynamics of the fundamental element in vehicle dynamics, a suspended, rolling wheelset is described. The diversity of dynamical behavior in this rolling wheelset with vibro-impact is demonstrated. Interesting features like both symmetric and asymmetric limit cycles, pitchfork bifurcation, period-doubling bifurcation, grazing boundary singularity and chaos, etc., are found.

Key words: Bifurcation, Clearance, Periodic motion, Stability, Vibro-impact