Pattern types and bifurcation characteristics of the low frequency periodic impact vibration of a periodically forced system with a clearance

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Journal of Vibration and Shock ›› 2019, Vol. 38 ›› Issue (6) : 218-225.

SHI Yuqing1, DU Sanshan2, L Xiaohong1, LUO Guanwei2

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Abstract

Two periodically-forced systems with single rigid stop and single elastic stop respectively were considered. Pattern types, diversity, regularity and bifurcation characteristics of the fundamental group of impact motions and subharmonic impact motions in the parameter plan, in low frequency range, were analyzed. The transition irreversibility of adjacent impact motions with fundamental period and two types of transition regions, narrow hysteresis and tongues-shaped regions, were found by using the multi-target and multi-parameter co-simulation analysis. The occurrence mechanism and distribution characteristics of the two types of transition regions (hysteresis and tongue-shaped regions), as well as the pattern types and regularity of subharmonic impact motions in the tongue-shaped regions were studied. The transition law from impact motions with fundamental period to incomplete and complete chattering-impact vibrations was studied.

Key words

clearance / impact / low frequency vibration / bifurcation.

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SHI Yuqing1, DU Sanshan2, L Xiaohong1, LUO Guanwei2. Pattern types and bifurcation characteristics of the low frequency periodic impact vibration of a periodically forced system with a clearance[J]. Journal of Vibration and Shock, 2019, 38(6): 218-225

References

[1] S.W. Shaw, P.J. Holmes. A periodically forced piecewise linear oscillator [J]. Journal of Sound and Vibration, 1983, 90(1): 129–155.
[2] J.O. Aidanpää, B.R. Gupta. Periodic and chaotic behaviour of a threshold-limited two-degree-of-freedom system [J]. Journal of Sound and Vibration, 1993, 165(2): 305–327.
[3] F. Peterka, J. Vacik. Transition to chaotic motion in mechanical systems with impacts [J]. Journal of Sound and Vibration, 1992, 154 (1): 95–115.
[4] Hu Haiyan. Controlling chaos of a periodically forced non-smooth mechanical system [J]. Acta Mechanica Sinica 1995, 11(3): 251–258.
[5] D.P. Jin, H.Y.Hu. Periodic vibro-impacts and their stability of a dual component system [J]. Acta Mech Sin. 1997, 13(4): 366–376.
[6] W.C. Ding, J.H. Xie, Q.G. Sun. Interaction of Hopf and period doubling bifurcations of a vibro-impact system [J]. Journal of Sound and Vibration, 2004, 275(1-2): 27–45.
[7] Jianhua Xie, Wangcai Ding. Hopf–Hopf bifurcation and invariant torus T2 of a vibro-impact system [J]. International Journal of Non-Linear Mechanics, 2005, 40(4): 531–543.
[8] Guilin Wen. Criterion to identify Hopf bifurcations in maps of arbitrary dimension [J]. Physical Review E, 2005, 72, 026201.
[9] R.I. Leine, Non-smooth stability analysis of the parametrically excited impact oscillator [J]. International Journal of Non-Linear Mechanics, 2012, 47(9): 1020–1032.
[10] Yang Liu, Ekaterina Pavlovskaia, David Hendry, Marian Wiercigroch. Vibro-impact responses of capsule system with various friction models [J]. International Journal of Mechanical Sciences, 2013, 72: 39–54.
[11] Yue, Yuan, Miao, Pengcheng, Xie, Jianhua. Coexistence of strange nonchaotic attractors and a special mixed attractor caused by a new intermittency in a periodically driven vibro-impact system [J]. Nonlinear Dynamics, 2017, 87(2): 1187–1207.
[12] Yongxiang Zhang, Guanwei Luo. Detecting unstable periodic orbits and unstable quasiperiodic orbits in vibro-impact systems [J]. International Journal of Non-Linear Mechanics, 2017, 96: 12–21.
[13] A.B. Nordmark. Non-periodic motion caused by grazing incidence in an impact oscillator [J]. Journal of Sound and Vibration, 1991, 145 (2): 279–297.
[14] G.S. Whiston. Singularities in vibro-impact dynamics [J], Journal of Sound and Vibration, 1992, 152 (3) 427–460.
[15] A.P. Ivanov. Stabilization of an impact oscillator near grazing incidence owing to resonance [J]. Journal of Sound and Vibration 1993, 162 (3): 562–565.
[16] H.Y. Hu. Detection of grazing orbits and incident bifurcations of a forced continuous, piecewise-linear oscillator [J]. Journal of Sound and Vibration, 1994, 187(3): 485–493.
[17] J. de Weger, W. van de Water, J. Molenaar. Grazing impact oscillations [J]. Physics Review E, 2000, 62 (2B): 2030–2041.
[18] M. di Bernardo, C.J. Budd, A.R. Champneys. Grazing and border-collision in piecewise-smooth systems: a unified analytical framework [J]. Physical Review Letters, 2001, 86 (12): 2553–2556.
[19] X. H. Long, G. J. Lin, B. Balachandran. Grazing bifurcations in an elastic structure excited by harmonic impactor motions [J]. Physica D, 2008, 237 (8): 1129–1138.
[20] Jieqiong Xu, Qunhong Li, Nan Wang. Existence and stability of the grazing periodic trajectory in a two-degree-of-freedom vibro-impact system [J]. Applied Mathematics and Computation, 2011, 217 (12): 5537–5546.
[21] D. Chillingworth. Dynamics of an impact oscillator near a degenerate graze [J]. Nonlinearity, 2010, 23 (11): 2723–2748.
[22] 高尚晗，龙新华，孟光. 主轴-滚动轴承系统三种分岔形式 [J]. 振动与冲击, 2009, 28(4): 59-65.
    GAO Shang-han, LONG Xin-hua, MENG Guang. Three types of bifurcation in a spindle-ball bearing system [J]. Journal of Vibration and Shock, 2009, 28(4): 59-65.
[23] 黄甫玉高，李群宏. 一类单侧碰撞悬臂振动系统的擦边分岔分析 [J]. 力学学报, 2008, 40(6): 812-819.
    Huangfu Yugao, Li Qunhong. GRAZING BIFURCATION OF A VIBRATING CANTILEVER SYSTEM WITH ONE-SIDED IMPACT [J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(6): 812-819.
[24] 高尚晗，龙新华，孟光. 主轴-滚动轴承系统三种分岔形式 [J]. 振动与冲击, 2009, 28(4): 59-65.
    GAO Shang-han, LONG Xin-hua, MENG Guang. Three types of bifurcation in a spindle-ball bearing system [J]. Journal of Vibration and Shock, 2009, 28(4): 59-65.
[25] C.J. Budd, F. Dux. Chattering and related behaviour in impact oscillators [J]. Philosophical Transactions Physical Sciences & Engineering, 1994, 347: 365–389.
[26] C. Toulemonde, C. Gontier. Sticking motions of impact oscillators [J]. European Journal of Mechanics A/Solids, 1998, 17 (2): 339–366.
[27] D. J. Wagg. Multiple non-smooth events in multi-degree-of- freedom vibro-impact systems [J]. Nonlinear Dynamics, 2006, 43: 137–148.
[28] A.B. Nordmark, P.T. Piiroinen. Simulation and stability analysis of impacting systems with complete chattering [J]. Nonlinear Dynamics, 2009, 58: 85–106.
[29] Csaba Hős, Alan R. Champneys. Grazing bifurcations and chatter in a pressure relief valve model [J]. Physica D Nonlinear Phenomena, 2012, 241: 2068–2076.
[30] 朱文骅，许跃敏，叶贵如. 非线性边界约束下梁的弯曲振动 [J]. 固体力学学报, 1990, 11(2): 181-189.
Zhu Wenhua, Xu Yuemin, Ye Guiru. VIBRATIONS OF BEAM UNDER NONLINEAR BOUNDARY CONSTRAINS [J]. ACT MECHANICA SOLIDA SINICA, 1990, 11(2): 181-189.
[31] 金栋平，胡海岩. 两柔性梁碰撞振动类型的实验研究 [J]. 实验力学, 1999, 12(2): 129-135.
JIN Dongping, HU Haiyan. An Experimental Study on Possible Types of Vibro-Impacts between Two Elastic Beams [J]. JOURNAL OF EXPERIMENTAL MECHANICS, 1999, 14(2): 129-135.
[32] 国家自然科学基金委员会工程与材料科学部, 机械工程学科发展战略报告(2011‒2022) [M]. 北京：科学出版社, 2011
National Natural Science Foundation of China, Ministry of engineering and Materials Science, Report of the mechanical engineering discipline development strategy (2011‒ 2022) [M]. Beijing: Science Press, 2011.