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、粘着和粘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,揭示了系统周期粘滞—粘着运动分布及转迁规律。研究结果表明:周期粘滞-粘着运动主要集中在低频小间隙区,系统向着周期粘滞-粘着运动转迁过程中,在擦边分岔(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擦边分岔(GR)、鞍结分岔(SN)和Sliding分岔(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,粘滞-粘着运动频带变宽,起始点向高频方向延伸。
Abstract
Aiming at a single-degree-of-freedom vibration system with friction and impact, the periodic motion of the four different types of motions including free sliding, collision, adhesion and viscous in the phase space is analyzed . Identify and study the distribution of periodic motion of the system in the parameter domain combined with four different Poincaré mapping sections. Using the parameter continuation algorithm and the cell mapping algorithm, combined with the system stability judgment conditions, the system's periodic viscous-adhesive motion distribution and transition law are revealed. The research results show that the periodic viscous-adhesive motion is mainly concentrated in the low-frequency small gap area. During the transition of the system to the periodic viscous-adhesive motion, the number of collisions increases and the collision speed gradually decreases under the induction of the grazing bifurcation (GR). At the same time, the periodic band of periodic motion gradually narrows. The transition process of adjacent periodic motions is mainly induced by rubbing bifurcation (GR), saddle knot bifurcation (SN) and sliding bifurcation (SL). Due to the mutual irreversibility of transitions, GR-SN and (GR- SL)-SN and other different forms of polymorphic coexistence areas. The system gap and recovery coefficient are reduced, the viscous-adhesive movement frequency band becomes wider, and the starting point extends in the direction of high frequency.
关键词
碰撞和摩擦 /
粘滞-粘着 /
擦边分岔 /
鞍结分岔 /
Sliding分岔
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Key words
impact and friction;viscosity-adhesion /
grazing bifurcation;saddle node bifurcation;sliding bifurcation
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参考文献
[1] Ahmadian M, Shao Pu Y. Effect of System Nonlinearitieson Locomotive Bogie Hunting Stability[J]. Vehicle System Dynamics,1998,29(6):365-384.
[2] 黄彩虹,曾京. 利用粘滑机理分析铁道车辆盘形制动颤振[J]. 现代制造工程,2009(5):26-28.
HUANG Cai-hong, ZENG Jing. Analysis of rolling stockdisc brake flutter by stick slip mechanism[J]. Modern Manufacturing Engineering,2009(5):26-28.
[3] 丁旺才,谢建华. 碰撞振动系统分岔与混沌的研究进展[J]. 力学进展,2005,35(4):513-524.
DING Wang-cai, XIE Jian-hua. Research Progress on Bifurcation and chaos of collision vibration system[J]. Advances in Mechanics,2005,35(4):513-524.
[4] Shaw S W,Holmes P J ,Periodically forced linear oscillator with impacts:Chaos and long-period motions[J]. Physical Review Letters,1983,51(8):623-626.
[5] Whiston G S. Global dynamics of a vibro-impacting linear oscillator[J]. Journal of Sound and vibration,1987,118(3):395-429.
[6] Wagg D J,Bishop S R. Dynamics of a two degree of freedom vibro-impact system with multiple motion limiting constraints[J]. International Journal of Bifurcation and Chaos,2004,14(01):119-140.
[7] Wagg D J. Periodic sticking motion in a two-degree-freedom impact oscillator[J]. International Journal of Bifurcation and Chaos,2005,40:1076-1087.
[8] 李飞,丁旺才.多约束碰撞系统的粘滞运动分析.[J]. 振动与冲击,2010,29(5):150-156.
LI Fei, DING Wang-cai. Viscous motion analysis of multiconstraint collision system.[J]. Journal of Vibration And Shock,2010,29(5):150-156.
[9] Virgin L N, Begley C J. Grazing bifurcations and basins of attraction in an impact friction oscillator. Physic D,1999,130:43-57.
[10] 李健,张思进.非光滑动力系统胞映射计算方法.[J]固体力学学报,2007,28(1):93-96.
LI JIAN, ZHANG Si-Jin. Cell-mapping computation on method for non-smooth dynamical systems[J]. Acta mechanica Solid Sinica ,2007,28(1):93-96.
[11] Pierpaolo Belardinelli, Stefano Lenci. An efficient parallel implementation of cell mapping methods for MDOF systems. Nonlinear Dynamics (2016) 86:2279–2290.
[12] Pierpaolo Belardinelli,Stefano Lenci. A first parallel programming approach in basins of attraction computation.[J]. International Journal of Non-Linear Mechanics 80 (2016) 76-81.
[13] Sun J Q, Xiong F R. Cell mapping methods-beyond global analysis of nonlinear dynamic systems[J]. Advances in Mechanics,2017,47:201705.
[14] Guofang Li, Wangcai Ding. Global Behavior of a vibro-impact system with asymmetric clearances[J]. J.Sound Vib.423,180–194 (2018).
[15] Guofang Li, Jie Sun, Wangcai Ding. Dynamics of a vibro-impact system by the global analysis method in parameter-state space [J]. Nonlinear Dynamics (2019) 97:541–557.
[16] Guofang Li, Shaopei Wu, Wangcai Ding. Global dynamics of a non-smooth system with elastic and rigid impacts and dry friction. [J]. Commun Nonlinear Sci Numer Simulat (2021) 95:105603.
[17] Luo G W,Lv X H,Shi Y. Vibro-impact dynamics of a two-degree-of freedom periodically-forced system with a clearance: diversity and parameter matching of periodic-impact motions[J]. International Journal of Non-Linear Mechanics,2014,65:173-195.
[18] 丁杰,王超.双侧不同约束碰振系统的周期运动转迁规律[J]. 华中科技大学学报(自然科学版),2021,49(1):06-11.
Ding Jie, WANG Chao. The transition law of periodic motions of the vibro-impact systems with different constraints on both sides[J]. Huazhong Univ.of Sci.&Tech.(Natural Science Tdition),2021,49(1):06-11.
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脚注
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