一类含间隙振动系统的周期运动稳定性、分岔与混沌形成过程研究

RESEARCHES ON STABILITY OF PERIODIC MOTION, BIFURCATIONS AND CHAOS IN A VIBR ATORY SYSTEM WITH A CLEARANCE OR GAP

建立了两自由度含间隙振动系统对称周期碰撞运动的Poincar啨映射方程 ,讨论了该映射不动点的稳定性与局部分岔 .通过数值仿真研究了含间隙振动系统对称周期碰撞运动经叉式分岔、倍化分岔、“擦边”

A two-degree-of-freedom vibratory system with a clear an ce or gap is considered. Symmetrical periodic motion and its Poincaré map are e stablished analytically. Stability and local bifurcations of the fixed point of periodic impact are analyzed. The routes from periodic impact motions to chaos, via pitchfork bifurcation, period-doubling bifurcation and grazing boundary, ar e studied by numerical simulation.\;