利用数值仿真方法，对一类两自由度含间隙弹性碰撞系统的动力学特性做了深入研究，分析了系统周期运动及其参数存在区域，并揭示了系统的颤碰运动特性。首先，详细分析了激振频率和系统间隙等关键参数对系统周期运动及存在区域的影响。其次，在小间隙低频工况下，数值计算了系统p/1周期运动序列及其存在区域。最后，得出随着激振频率的递减，p/1运动的碰撞次数p因擦边分岔而逐一增加，当p/1运动的碰撞次数p足够大时，系统呈现出颤碰特性，总结了系统由1/1周期运动到颤碰运动的转迁规律。
Abstract
A two-degree-of-freedom system with clearance and soft impacts is considered. The existence regions of periodic motions and chattering-impact characteristics of the system are analyzed by the numerical simulation method. Firstly, the influence of key parameters of the system, such as the exciting frequency and clearance value, on its existence regions of periodic-impact motions is studied in detail. Secondly, the sequence of p/1 motions and its existence regions in the small clearance and low exciting frequency case are investigated using numerical simulation. Finally, a series of grazing bifurcations occur with decreasing exciting frequency so that the impact number p of p/1 motions correspondingly increases one by one. When the impact number p of p/1 motions becomes big enough, the chattering-impact characteristics will be appearing. The transition law from 1/1 motion to chattering-impact motion via grazing bifurcation with decreasing exciting frequency is summarized explicitly.
关键词
振动 /
颤碰 /
周期运动 /
分岔 /
存在区域
{{custom_keyword}} /
Key words
vibration /
chattering-impact /
periodic motion /
bifurcation /
existence region
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[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] 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.
[3] 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 Sijin. Cell-Mapping computation method for non-smooth dynamical system[J]. Acta Mechanica Solida Sinica, 2007, 28(1): 93-96.
[4] Dankowicz H, Zhao Xiaopeng. Local analysis of co-dimension-one and co-dimension-two grazing bifurcations in impact microactuators[J]. Physica D, 2005, 202 (3-4): 238-257.
[5] Nordmark A B, Kowalczyk P. A codimension-two scenario of sliding solutions in grazing-sliding bifurcations[J]. Nonlinearity, 2006, 19(1): 1-26.
[6] Mason J F, Humphries N, Piiroinen P T. Numerical analysis of codimension-one, -two and -three bifurcations in a periodically-forced impact oscillator with two discontinuity surfaces[J]. Mathematics and Computers in Simulation, 2013, 95: 98-110.
[7] Wen Guilin, Xu Huidong, Xiao Lu. Experimental investigation of a two-degree-of-freedom vibro-impact system[J]. International Journal of Bifurcation and Chaos, 2012, 22(5):1250110(1-7).
[8] 吕小红, 罗冠炜. 小型振动冲击式打桩机的非线性动力学分析[J]. 工程力学, 2013, 30(11): 227-232.
LÜ Xiao-hong, LUO Guan-wei. Analysis of nonlinear dynamics of a small vibro-impact driver[J]. Engineering Mechanics, 2013, 30(11): 227-232.
[9] 俞翔,朱石坚,楼京俊.基于碰撞振动的隔振系统混沌化实验研究[J].振动与冲击,2014,33(18):59-64.
YU Xiang, ZHU Shi-jian, LOU Jing-jun. Tests for chaotification method of a vibration isolation system with a vibro-impact subsystem[J]. Journal of Vibration and Shock,2014,33(18):59-64.
[10] Peterka F, Tondl A. Phenomena of subharmonic motions of oscillator with soft impacts[J]. Chaos, Solitons and Fractals, 2004, 19(5): 1283-1290.
[11] G.W.Luo, X.H.Lv, Y.Q.Shi. 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.
[12] G.W.Luo, X.F.Zhu, Y.Q.Shi. 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.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
PDF(2852 KB)
