塑性冲击振动系统的非光滑分岔

NON⁃SMOOTH BIFURCATION OF A PLASTIC IMPACTING OSCILLATOR

考虑塑性碰撞工况下的单自由度冲击振动系统,推导了擦边分岔和余维一滑动分岔的条件。结合二维参数和单参数分岔分析,研究了单冲击周期运动的分岔特征,揭示了冲击振动系统的穿越滑动分岔、切换滑动分岔和余维二滑动分岔等非光滑分岔以及擦边分岔和混沌激变等不连续分岔行为。非黏滞型周期运动与黏滞型周期运动经穿越滑动分岔相互转迁。在二维参数平面的低频小间隙区域,(1,1,1)周期运动与(1,2,1)周期运动交替出现。两类周期运动的临界线为切换滑动分岔线。混沌边界激变导致混沌吸引子及其吸引域突然消失。

A single degree⁃of⁃freedom plastic impacting oscillator was considered under the conditions of grazing and codimension⁃1 bifurcations.Based on the two⁃and one⁃dimensional parameters bifurcation analysis,the bifurcation characteristics of single⁃impact periodic motions was studied.The non⁃smooth bifurcations such as crossing⁃sliding,switching⁃sliding and codimension⁃2 sliding bifurcations as well as the discontinuous bifurcations such as grazing bifurcation and boundary crisis were revealed.The non⁃sticking periodic motion and sticking periodic motion transit into each other via a crossing⁃sliding bifurcation.In the two⁃dimensional parameter region of the low frequency and small clearance,the periodic motions(1,1,1)and(1,2,1)are distributed alternately.The boundary between the two types of periodic motions is a switching⁃sliding bifurcation curve.The boundary crisis of chaos occurs leading the chaotic attractor and its basin to vanish.