Abstract:Based on impact damper, a dynamic model of the unconstrained collision system was established. Using coefficient of restitution as the primary control parameter, it analyzed the system periodical movement and its bifurcation region, revealed the chattering movement characteristic of the system, and obtained the coefficient of restitution interval during the chattering of collision system under various mass and frequency ratio conditions. The results showed: there was obvious bifurcation phenomena in the collision system when the coefficient of restitution was over 0.5; The coefficient of restitution for chattering is in the range of 0.5 to 0.9, and as the mass ratio decreased, the coefficient of restitution interval constantly increased; as the frequency increased, the coefficient of restitution interval dropped.
杜妍辰,张洪源,林俊文. 碰撞阻尼器中颤振发生的恢复系数区间研究[J]. 振动与冲击, 2021, 40(24): 154-162.
DU Yanchen,ZHANG Hongyuan,LIN Junwen. A study on the coefficient of restitution interval for chattering in an impact damper. JOURNAL OF VIBRATION AND SHOCK, 2021, 40(24): 154-162.
[1] CHENG J, XU H. Inner mass impact damper for attenuating structure vibration[J]. International Journal of Solids and Structures,2006, 43: 5355-5369.
[2] PARK J, WANG S, CROCKER MJ. Mass loaded resonance of a single unit impact damper caused by impacts and the resulting kinetic energy influx[J]. Journal of Sound and Vibration, 2009, 323: 877-895.
[3] DU Y, Investigation of chattering behavior of impact damper[J]. Advances in Mechanical Engineering, 2017, 9(12): 1–8.
[4]BUDD C, DUX F. Chattering and related behaviour in impact oscillators [J]. Philosophical Transactions of the Royal Society of London A, 1994, 347: 365-389.
[5] TOULEMONDE C, GONTIER C. Sticking motions of impact oscillators [J]. European Journal of Mechanics-A/Solids, 1998, 17: 339-366.
[6] WAGG DJ, BISHOP SR. Chatter, sticking and chaotic impacting motion in a two degree of freedom impact oscillator [J]. International Journal of Bifurcation and Chaos, 2011,11(1): 57-71.
[7] WAGG DJ. Rising phenomena and the multi-sliding bifurcation in a two-degree of freedom impact oscillator [J]. Chaos, Solitons and Fractals, 2004, 22: 541-548.
[8] WAGG DJ. Multiple non-smooth events in multi-degree-of-freedom vibro-impact systems[J]. Nonlinear Dynamics, 2006, 43:137-148.
[9] WAGG DJ, BISHOP SR. Dynamics of a two degree of freedom vibro-impact systems with multiple motion limiting constraints [J]. International Journal of Bifurcation and Chaos, 2004, 14(1): 119-140.
[10] DEMEIO L, LENCI S. Asymptotic analysis of chattering oscillations for an impacting inverted pendulum[J]. Quarterly Journal of Mechanics and Applied Mathematics, 2006, 59(3):419-434.
[11] ALZATE R, BERNARDO MD, MONTANARO U, et al. Experimental and numerical verification of bifurcations and chaos in cam-follower impacting systems[J]. Nonlinear Dynamics, 2007, 50(3):409-429.
[12] NORDMARK AB, PIIROINEN PT. Simulation and stability analysis of impacting systems with complete chattering [J]. Nonlinear Dynamics, 2009, 58: 85-106.
[13] QUINTANA G, CIURANA J. Chatter in machining processes: A review[J]. International Journal of Machine Tools & Manufacture, 2011, 51(5):363–376.
[14] HŐS C, CHAMPNEYS AR. Grazing bifurcations and chatter in a pressure relief valve model[J]. Physica D, 2012, 241(22): 2068-2076
[15] 杨智春, 赵令诚, 姜节胜. 碰撞阻尼器抑制机翼/外挂颤振的研究[J]. 振动工程学报, 1995, (1):1-7.
YANG Zhichun, ZHAO Lingcheng, JIANG Jiesheng. Investigation of wing/store flutter suppression with impact damper[J]. Journal ofVibratiom Engineering, 1995, (1):1-7.
[16] YIN XC, QIN Y, ZOU H. Transient responses of repeated impact of a beam against a stop[J]. International Journal of Solids and Structures, 2007, 44(22-23):7323-7339.
[17] LUO G W, MA L, LV X H. Dynamic analysis suppressing chaotic impacts of a two-degree-of-freedom oscillator with a clearance[J]. Non-linear Analysis: Real World Applications, 2009, 10(2):756-778.
[18] 冯进钤, 徐伟, 牛玉俊. Duffing单边碰撞系统的颤振分岔[J]. 物理学报, 2010, 59(1):157-163.
FENG Jinqian, XU Wei, NIU Yujun. Chattering bifurcations in a Duffing unilateral vibro-impact system[J].ActaPhysicaSinica, 2010, 59(1):157-163.
[19] 李飞, 丁旺才. 多约束碰撞振动系统的粘滞运动分析[J]. 振动与冲击, 2010, 29(5):150-156.
LI Fei, DING Wangcai. Analysis of sticking motion in a vibro-impact system with multiple constraints [J].JournalofVibrationandShock, 2010, 29(5):150-156.
[20] 张惠, 丁旺才, 李飞. 两自由度含间隙和预紧弹簧碰撞振动系统动力学分析[J]. 工程力学, 2011, 28(3):209-217.
ZHANG Hui, DING Wangcai, LI Fei. Dynamics of a two-degree-of-freedom impact system with clearance and pre-compressed spring[J]. Engineering Mechanics, 2011, 28(3):209-217.
[21] 苏芳,王晨升.两自由度单边刚性约束碰撞系统的混沌演化[J].机械研究与应用,2012(4):69-71.
SU Fang, WANGChensheng. Chaos evolution of two-degree-of-freedom impact system with unilateral rigid constraints[J].Mechanical Research & Application,2012, (4):69-71.
[22] 王小斌, 周鹏, 张亚兵. 一类双自由度碰撞振动系统的颤振及擦边研究[J]. 宁夏大学学报:自然科学版, 2014(2):97-103.
WANG Xiaobin, ZHOU Peng, ZHANG Yabing. Chattering analysis of two-degree-of-freedom vibration system[J].Journal of Ningxia University(Natural Science Edition),2014(2):97-103.
[23] 朱喜锋, 曹兴潇. 两自由度弹性碰撞系统的颤碰运动及转迁规律[J]. 兰州交通大学学报, 2014, 33(4): 191-195.
ZHU Xifeng, CAO Xingxiao. Chattering-impact motion and its transition law of a two-degree-of-freedom system with soft impacts[J]. Journal of Lanzhou Jiaotong University, 2014, 33(4): 191-195.
[24] 朱喜锋,罗冠炜. 两自由度含间隙弹性碰撞系统的颤碰运动分析[J]. 振动与冲击, 2015, 34(15): 195-200.
ZHU Xifeng, LUO Guanwei. Chattering-impact motion of a 2-DOF system with clearance and soft impacts[J]. JournalofVibrationandShock, 2015, 34(15): 195-200.