|
|
|
| Diversity and regularity of periodic vibro-impact of a vibration system with clearance-elastic constraints |
| YIN Fengwei1,2,LUO Guanwei1,2,TONG Changhong3 |
1.School of Mechatronic Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China;
2.Gansu Provincial Key Laboratory of System Dynamics and Reliability of Rail Transport Equipment, Lanzhou 730070, China;
3.School of Bailie Mechanical Engineering, Lanzhou City University, Lanzhou 730070, China |
|
|
|
|
Abstract Based on the mechanical model of a two-degree-of-freedom forced vibration system with clearance-elastic constraints, the diversity and bifurcation characteristics of periodic impulsive vibration of this kind of non-smooth vibration system were studied by multi-objective and multi-parameter co-simulation analysis.The results reveals the relationship between the dynamic characteristics of the system and the parameters of the model.The fundamental periodic vibro-impact groups and its distribution characteristics in small frequency domain of a vibration system with the same clearance threshold constraints were discussed.The singularities, hysteretic and non-hysteretic transition regions induced by the irreversibility of the mutual transition of adjacent fundamental periodic vibro-impact were analyzed, and the mode types and regularities of sub-harmonic vibro-impact in non-hysteretic transition region were revealed.The difference of mode type and distribution regularity of periodic vibro-impact with the same clearance threshold and different clearance threshold constraints was compared.Furthermore, the mode types and emergence rules of fundamental vibro-impact groups in small frequency domain of elastically constrained vibration systems with different clearance thresholds were revealed.The calculation and analysis above may be provided scientific basis for dynamic design and collaborative optimization of mechanical systems with clearances and constraints.
|
|
Received: 23 July 2019
Published: 15 December 2020
|
|
|
|
[1] Shaw S W , Holmes P J. A periodically forced piecewise linear oscillator [J]. Journal of Sound and Vibration, 1983, 90(1): 129-155.
[2] Peterka F . Behaviour of impact oscillator with soft and preloaded stop[J]. Chaos, Solitons and Fractals, 2003, 18(1):79-88.
[3] 乐源, 缪鹏程. 一类碰撞振动系统的激变和拟周期-拟周期阵发性[J]. 振动与冲击, 2017, 36(07): 1-7+20.
LE Yuan, MIAO Pengcheng. Catastrophe and quasi-periodic quasi-periodic paroxysms of a class of impact vibration systems [J]. Journal of Vibration and Shock, 2017, 36(07): 1-7+20.
[4] Zhang Y X, Luo G W. Detecting unstable periodic orbits and unstable quasiperiodic orbits in vibro-impact systems [J]. International Journal of Non-Linear Mechanics, 2017, 96: 12-21.
[5] Peterka F , Vacík J. Transition to chaotic motion in mechanical systems with impacts[J]. Journal of Sound and Vibration, 1992, 154(1):95-115.
[6] Nordmark A B. Non-periodic motion caused by grazing incidence in an impact oscillator [J]. Journal of Sound and Vibration, 1991, 145(2): 279-297.
[7] Luo G W, Lv X H. Controlling bifurcation and chaos of a plastic impact oscillator [J]. Nonlinear Analysis: Real World Applications, 2009, 10(4): 2047-2061.
[8] Luo G W, Zhu X F, Shi Y Q. Dynamics of a two–degree–of freedom periodically–forced system with a rigid stop: diversity and evolution of periodic–impact motions[J]. Journal of Sound and Vibration, 2015, 334: 338–362.
[9] 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.
[10] Wagg D J . Rising phenomena and the multi-sliding bifurcation in a two-degree of freedom impact oscillator[J]. Chaos, Solitons and Fractals, 2004, 22(3):541-548.
[11] Wagg D J . Multiple non-smooth events in multi-degree-of- freedom vibro-impact systems[J]. Nonlinear Dynamics, 2006, 43(1-2):137-148.
[12] Wagg D J . Periodic sticking motion in a two-degree-of- freedom impact oscillator[J]. International Journal of Non- Linear Mechanics, 2005, 40(8):1076-1087.
[13] Nordmark A B, Piiroinen P T, Simulation and stability analysis of impacting systems with complete chattering[J]. Nonlinear Dynamics 2009, 58(): 85-106.
[14] Csaba Hős, Champneys A R. Grazing bifurcations and chatter in a pressure relief valve model[J]. Physica D: Nonlinear Phenomena, 2012, 241(22):0-0.
[15] 张艳龙, 唐斌斌, 王丽, et al. 动摩擦作用下含间隙碰撞振动系统的动力学分析[J]. 振动与冲击, 2017(24).
ZHANG Yanlong, TANG Binbin, WANG Li, et al. Dynamic analysis of impact vibration system with clearance under dynamic friction [J]. Journal of Vibration and Shock, 2017, 36(24): 58-63.
[16] 吕小红,罗冠炜. 碰撞-渐进振动系统的周期振动与分岔[J].振动与冲击, 2018, 37(06): 162-167.
LV Xiaohong, LUO Guanwei. Periodic Vibration and Bifurcation of Collision-Asymptotic Vibration System [J]. Journal of Vibration and Shock, 2018,37(06): 162-167.
[17] Luo G W, Shi Y Q, Zhu X F, Du S S. Hunting patterns and bifurcation characteristics of a three-axle locomotive bogie system in the presence of the flange contact nonlinearity [J]. International Journal of Mechanical Sciences, 2018, 136: 321–338.
[18] Byrtus M , Vladimír Z. On modeling and vibration of gear drives influenced by nonlinear couplings[J]. Mechanism & Machine Theory, 2011, 46(3): 375-397.
[19] Ma Y , Ing J , Banerjee S , et al. The nature of the normal form map for soft impacting systems[J]. International Journal of Non-Linear Mechanics, 2008, 43(6):504-513.
[20] Kundu S , Banerjee S , Ing J , et al. Singularities in soft-impacting systems[J]. Physica D Nonlinear Phenomena, 2012, 241(5):553-565.
[21] Blazejczyk-Okolewska B , Czolczynski K , Kapitaniak T . Hard versus soft impacts in oscillatory systems modeling[J]. Communications in Nonlinear Science and Numerical Simulation, 2010, 15(5):1358-1367.
[22] 金栋平, 胡海岩. 两柔性梁碰撞振动类型的实验研究. 实验力学, 1999, 14(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.
[23] Long X H, Liu J B, Meng G.. Nonlinear dynamics of two harmonically excited elastic structures with impact interaction[J]. Journal of Sound and Vibration, 2014, 333: 1430-1441.
|
|
|
|
