含间隙振动系统的周期运动和分岔

研究了一类多自由度含间隙振动系统的动态响应,根据碰撞条件和由碰撞规律所确定的衔接条件求得系统的对称型周期碰撞运动及相关Poincare映射,讨论了该映射不动点的稳定性与局部分岔。用一个2自由度含间隙振动系统阐述了方法的有效性,分析了对称型周期碰撞运动稳定性、分岔、擦边奇异性和混沌形成过程。通过数值仿真研究了铁道车辆轮对的横向周期碰撞振动,分析了轮对对称型周期碰撞运动的叉式分岔和擦边映射奇异性。

PERIODIC-IMPACT MOTIONS AND BIFURCATIONS OF THE VIBRATORY SYSTEM WITH A CLEARANCE

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 Poincare map is established. Stability and local bifurcations of the fixed point of double-impact symmetrical motion is analyzed by using the Poincare 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 analyzed 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.