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碰撞振动系统中周期轨擦边诱导的混沌激变

冯进钤 徐伟

冯进钤, 徐伟. 碰撞振动系统中周期轨擦边诱导的混沌激变[J]. 力学学报, 2013, 45(1): 30-36. doi: 10.6052/0459-1879-12-315
引用本文: 冯进钤, 徐伟. 碰撞振动系统中周期轨擦边诱导的混沌激变[J]. 力学学报, 2013, 45(1): 30-36. doi: 10.6052/0459-1879-12-315
Feng Jinqian, Xu Wei. GRAZING-INDUCED CHAOSTIC CRISIS FOR PERIODIC ORBITS IN VIBRO-IMPACT SYSTEMS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(1): 30-36. doi: 10.6052/0459-1879-12-315
Citation: Feng Jinqian, Xu Wei. GRAZING-INDUCED CHAOSTIC CRISIS FOR PERIODIC ORBITS IN VIBRO-IMPACT SYSTEMS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(1): 30-36. doi: 10.6052/0459-1879-12-315

碰撞振动系统中周期轨擦边诱导的混沌激变

doi: 10.6052/0459-1879-12-315
基金项目: 国家自然科学基金(11172233); 陕西省教育厅专项科研计划(12JK0854) 和西安工程大学博士科研基金(BS1003) 资助项目.
详细信息
    通讯作者:

    冯进钤

  • 中图分类号: O322

GRAZING-INDUCED CHAOSTIC CRISIS FOR PERIODIC ORBITS IN VIBRO-IMPACT SYSTEMS

Funds: The project was supported by the National Natural Science Foundation of China (11172233), the Scientific Research Program of the Education Bureau of Shanxi Province, China (12JK0854) and the Doctoral Program of Xi’an Polytechnic University, China (BS1003).
  • 摘要: 基于图胞映射理论, 提出了一种擦边流形的数值逼近方法, 研究了典型Du ng 碰撞振动系统中擦边诱导激变的全局动力学. 研究表明, 周期轨的擦边导致的奇异性使得系统同时产生1 个周期鞍和1 个混沌鞍. 当该周期鞍的稳定流形与不稳定流形发生相切时, 边界激变发生使得该混沌鞍演化为混沌吸引子. 噪声可以诱导周期吸引子发生擦边, 这种擦边导致了1 种内部激变的发生, 表现为该周期吸引子与其吸引盆内部的混沌鞍发生碰撞后演变为1 个混沌吸引子.

     

  • 1 罗冠炜,谢建华. 碰撞振动系统的周期运动和分岔. 北京:科学 出版社,2004 (Luo Guanwei, Xie Jianhua. Period Motion and Bifurcations of Vibro-impact Systems. Beijing: Science Press, 2004 (in Chinese))
    2 丁旺财,谢建华. 碰撞振动系统分岔和混沌的研究进展. 力学进 展,2005, 35(4):513-524 (Ding Wangcai, Xie Jianhua. Advances of research on bifurcations and chaos in vibro-impact system. Advances in Mechanics, 2005, 35(4):513-524 (in Chinese))
    3 金栋平,胡海岩. 碰撞振动与控制. 北京:科学出版社,2005 (Jin Dongping, Hu Haiyan. Vibration and Control of Collision. Beijing: Science Press, 2005 (in Chinese))
    4 Kunze M. Non-Smooth Dynamical Systems. Berlin: Springer- Verlag, 2000
    5 金俐,陆启韶. 非光滑动力系统Lyapunov 指数谱的计算方法. 力学学报,2005, 37(1):40-47 (Jin Li, Lu Qishao. A method for calculating the spectrum of Lyapunov exponents of non-smooth dynamical systems. Acta Mechanica Sinica, 2005, 37(1): 40-47 (in Chinese))
    6 Leine RI, Nijmeijer H. Dynamics and Bifurcations in Non-Smooth Mechanical Systems. Berlin: Springer-Verlag, 2004
    7 di Bernardo M, Budd C, Champneys AR, et al. Piecewise-smooth Dynamical Systems: Theory and Applications. London: Springer- Verlag, 2007
    8 秦志英. 非光滑动力系统的非光滑分岔研究.[博士论文]. 北京: 北京航空航天大学,2007 (Qin Zhiying. Research on nonsmooth bifurcations in nonsmooth dynamical systems. [PhD Thesis]. Beijing: Beihang University, 2007 (in Chinese))
    9 Piiroinen PT, Virgin LN, Champneys AR. Chaos and period-adding, experimental and numerical verification of the grazing bifurcation. Journal of Nonlinear Science, 2004, 14(4): 627-654
    10 Hsu CS. Global analysis of dynamical systems using posets and digraphs. International Journal of Bifurcation and Chaos, 1995, 5(4):1085-1118  
    11 Hong L, Xu JX. Crises and Chaotic transients studied by the generalized cell mapping digraph method. Phys Lett A, 1999, 262(4-5):361-375
    12 贺群,徐伟,李爽等. 基于复合胞花空间的图胞映射方法. 物理 学报,2008, 57(7):4021-4028 (He Qun, Xu Wei, Li Shuang, et al. The digraph cell mapping based on composite cell space. Acta Phys Sin, 2008, 57(7): 4021-4028 (in Chinese))
    13 van der Spek JAW, de Hoon CAL, de Kraker A, et al. Application of cell mapping methods to a discontinuous dynamic system. Nonlinear Dynamics, 1994, 6(1): 87-99
    14 李健,张思进. 非光滑动力系统胞映射计算方法. 固体力学学报,2007, 28(1): 93-96 (Li Jian, Zhang Sijin. Cell-mapping computation method for non-smooth dynamical systems. Chinese Journal of Solid Mechanics, 2007, 28(1): 93-96 (in Chinese))
    15 Mason JF, Piiroinen PT. Interactions between global and grazing bifurcation in an impacting system. Chaos, 2011, 21(013113): 1-9
    16 李爽,贺群. 非光滑动力系统的迭代图胞映射法. 力学学报,2011, 43(3):579-585 (Li Shuang, He Qun. The iterative digraph cell mapping method of non-smooth dynamical systems. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(3):579-585 (in Chinese))
    17 Gun CB, Lei H. Stochastic dynamical analysis of a kind of Vibroimpact system under multiple harmonic and random excitations. Journal of Sound and Vibration, 2011, 330: 2174-2184  
    18 Feng JQ, Xu W. Analysis of bifurcations for non-linear stochastic non-smooth vibro-impact system via top Lyapunov exponent. Applied Mathematics and Computation, 2009, 213: 577-586  
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出版历程
  • 收稿日期:  2012-11-09
  • 修回日期:  2012-12-18
  • 刊出日期:  2013-01-18

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