含碰撞和摩擦振动系统黏滞-黏着运动转迁机理研究

Viscous-adhesive motion transition mechanism of vibration system with collision and friction

针对一类含碰撞和摩擦的单自由度振动系统,通过分析相空间内自由滑动、碰撞、黏着和黏滞四种不同性质运动的发生条件,结合四种不同的Poincaré映射截面对其周期运动进行辨识,研究参数域内系统周期运动分布规律。采用参数延续算法和胞映射算法,并结合系统稳定性判定条件,揭示了系统周期黏滞-黏着运动分布及转迁规律。研究结果表明:周期黏滞-黏着运动主要集中在低频小间隙区,系统向着周期黏滞-黏着运动转迁过程中,在擦边分岔(grazing bifurcation,GR)诱导下碰撞次数增加,碰撞速度逐渐减小,同时周期运动的周期带逐渐变窄;相邻周期运动转迁过程中主要受到GR、鞍结分岔(saddle node bifurcation,SN)和滑移分岔(sliding bifurcation,SL)的诱导,由于转迁相互不可逆性,形成GR-SN和(GR-SL)-SN等不同形式的多态共存区。系统间隙和恢复系数减小,黏滞-黏着运动频带变宽,起始点向高频方向延伸。

Here,aiming at a kind of single-DOF vibration system with collision and friction,by analyzing occurrence conditions of 4 different motions including free sliding,collision,adhesion and viscosity in phase space,and combining 4 different Poincarémapping sections to identify the system’s periodic motion,distribution laws of the system’s periodic motion in parametric domain were studied.By using the parameter continuation algorithm and the cell mapping algorithm,combined with the system stability criteria,the system periodic viscous-adhesive motion’s distribution and transition laws were revealed.The results showed that periodic viscous-adhesive motion is mainly concentrated in regions of low-frequency with small gaps,in transition process of the system towards periodic viscous-adhesive motion,number of collisions increases and collision speed decreases gradually under guidance of grazing bifurcation(GR),while periodic band of periodic motion narrows down gradually;in transition process,adjacent periodic motion is mainly induced by grazing bifurcation(GR),saddle node bifurcation(SN)and sliding bifurcation(SL);due to the mutual irreversibility of transitions,polymorphic coexistence zones with different forms of GR-SN,and(GR-SL)-SN,etc.are formed;when system gap and recovery coefficient decrease,frequency band of viscous-adhesive motion widens,and starting point extends to high frequency direction.