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含双侧约束碰撞振动系统的OGY混沌控制

吕小红 朱喜锋 罗冠炜

吕小红, 朱喜锋, 罗冠炜. 含双侧约束碰撞振动系统的OGY混沌控制[J]. 机械科学与技术, 2016, 35(4): 531-534. doi: 10.13433/j.cnki.1003-8728.2016.0406
引用本文: 吕小红, 朱喜锋, 罗冠炜. 含双侧约束碰撞振动系统的OGY混沌控制[J]. 机械科学与技术, 2016, 35(4): 531-534. doi: 10.13433/j.cnki.1003-8728.2016.0406
Lü Xiaohong, Zhu Xifeng, Luo Guanwei. Chaos Control of a Vibro-impact System with Two-sided Constraints Based on OGY Method[J]. Mechanical Science and Technology for Aerospace Engineering, 2016, 35(4): 531-534. doi: 10.13433/j.cnki.1003-8728.2016.0406
Citation: Lü Xiaohong, Zhu Xifeng, Luo Guanwei. Chaos Control of a Vibro-impact System with Two-sided Constraints Based on OGY Method[J]. Mechanical Science and Technology for Aerospace Engineering, 2016, 35(4): 531-534. doi: 10.13433/j.cnki.1003-8728.2016.0406

含双侧约束碰撞振动系统的OGY混沌控制

doi: 10.13433/j.cnki.1003-8728.2016.0406
基金项目: 

国家自然科学基金项目(11462012,11362008)、甘肃省科技计划项目(148RJZA034)及甘肃省高等学校科研项目(2014A-046)资助

详细信息
    作者简介:

    吕小红(1977-),副教授,博士研究生,研究方向为机械动力学及其控制,lvxh@mail.lzjtu.cn

Chaos Control of a Vibro-impact System with Two-sided Constraints Based on OGY Method

  • 摘要: 以单自由度含双侧约束碰撞振动系统为研究对象,数值仿真了系统1-1-1周期运动经周期倍化分岔和Grazing分岔向混沌转迁的路径;给出了OGY控制方法的原理和步骤。利用混沌运动对参数微小扰动的敏感性和混沌轨道的遍历性质,选择嵌入混沌吸引子中的一个不稳定不动点作为控制目标,当系统状态访问目标不动点的微小邻域时,给系统参数施加微小扰动,把混沌控制到期望的目标轨道。仿真结果表明,在极短的时间内系统的混沌得到了抑制。
  • [1] Luo G W, Xie J H. Hopf bifurcation of a two-degree-of-freedom vibro-impact system[J]. Journal of Sound and Vibration, 1998,213(3):391-348
    [2] Yue Y, Xie J H. Lyapunov exponents and coexistence of attractors in vibro-impact systems with symmetric two-sided rigid constraints[J]. Physics Letters A, 2009,373(23-24):2041-2046
    [3] Xu J Q, Li Q H, Wang N. 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
    [4] Wagg D J. Rising phenomena and the multi-sliding bifurcation in a two-degree of freedom impact oscillator[J]. Chaos, Solitons & Fractals, 2004,22(3):541-548
    [5] 李群宏,陆启韶.一类双自由度碰振系统运动分析[J].力学学报,2001,33(6):776-786 Li Q H, Lu Q S. Analysis to motions of a two-degree-of-freedom vibro-impact system[J]. Acta Mechanica Sinica, 2001,33(6):776-786 (in Chinese)
    [6] 李万祥,边红丽,蒋湘云.含间隙弹性约束系统的Hopf分岔与混沌研究[J].机械科学与技术,2004,23(10):1212-1214 Li W X, Bian H L, Jiang X Y. Hopf bifurcation and chaos of a system with a pair of symmetric set-up Elastic Stops[J]. Mechanical Science and Technology, 2004,23(10):1212-1214 (in Chinese)
    [7] Dankowicz H, Svahn F. On the stabilizability of near-grazing dynamics in impact oscillators[J]. International Journal of Robust and Nonlinear Control, 2007,17(15):1405-1429
    [8] Misra S, Dankowicz H. Control of near-grazing dynamics and discontinuity-induced bifurcations in piecewise-smooth dynamical systems[J]. International Journal of Robust and Nonlinear Control, 2010,20(16):1836-1851
    [9] Wang L, Xu W, Zhao R, et al. Tracking desired trajectory in a vibro-impact system using backstepping design[J]. Chinese Physics Letters, 2009,26(10):100503
    [10] De Souza S L T, Caldas I L. Controlling chaotic orbits in mechanical systems with impacts[J]. Chaos, Solitons & Fractals, 2004,19(1):171-178
    [11] 马永靖,丁旺才,杨小刚.碰撞振动系统的参数自调节混沌控制[J].振动与冲击,2007,26(1):24-26 Ma Y J, Ding W C, Yang X G. Chaos control of a vibro-impact system with parameter adjustment[J]. Journal of Vibration and Shock, 2007,26(1):24-26 (in Chinese)
    [12] 徐慧东,谢建华.一类单自由度分段线性系统的分岔和混沌控制[J].振动与冲击,2008,27(6):20-24 Xu H D, Xie J H. Bifurcation and chaos control of a single-degree-of-freedom system with piecewise-linearity[J]. Journal of Vibration and Shock, 2008,27(6):20-24 (in Chinese)
    [13] De Souza S L T, Caldas I L, Viana R L. Damping control law for a chaotic impact oscillator[J]. Chaos, Solitons & Fractals, 2007,32(2):745-750
    [14] 苟向锋,罗冠炜,吕小红.含双侧刚性约束碰撞振动系统的混沌控制[J].机械科学与技术,2011,30(8):1262-1266 Gou X F, Luo G W, Lü X H. Chaos control of a two-degree-of-freedom vibrating system with two rigid constraints[J]. Mechanical Science and Technology for Aerospace Engineering, 2011,30(8):1262-1266 (in Chinese)
    [15] Luo G W, Lü X H. Controlling bifurcation and chaos of a plastic impact oscillator[J]. Nonlinear Analysis, Series B: Real World Applications, 2009,10(4):2047-2061
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出版历程
  • 收稿日期:  2014-04-15
  • 刊出日期:  2016-04-05

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