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两自由度含间隙和预紧弹簧碰撞振动系统动力学分析 被引量：13

DYNAMICS OF A TWO-DEGREE-OF-FREEDOM IMPACT SYSRTEM WITH CLEARANCE AND PRE-COMPRESSED SPRING
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摘要 研究了一类两自由度含间隙和预紧弹簧的碰撞振动系统动力学模型,建立了系统的Poincaré映射,推导出了映射的Jacobian矩阵。研究了系统的周期和非周期运动,利用Lyapunov指数谱分析了系统的稳定性,用测试函数预测了系统发生"擦边"现象的参数范围;研究了系统的倍化序列和Hopf分岔过程因碰撞质块与约束"擦边"而中断或不连续的现象;分析了由边界碰撞引起的Jacobian矩阵在"擦边"点附近特征值、行列式、迹的变化情况。 A two-degree-of-freedom impact system with a clearance and pre-compressed spring is studied.The Poincaré map and its Jacobian matrix are constructed for analyzing the stability of the system.The periodic and aperiodic motions of the system are investigated,and verified by Lyapunov exponents.The parameter regions,where a boundary grazing phenomena may happen,are predicted by a test function.The phenomena of period-doubling and Hopf bifurcations intermitted due to boundary grazing motion are investigated.The changes of the eigenvalues,determinants and traces at the grazing points due to border collision are analyzed.
作者 张惠 丁旺才 李飞
机构地区 兰州交通大学机电工程学院
出处 《工程力学》 EI CSCD 北大核心 2011年第3期209-217,共9页 Engineering Mechanics
基金 国家自然科学基金项目(50675092) 甘肃省自然科学基金项目(0710RJZA052)
关键词 非光滑系统 弹性碰撞 POINCARÉ映射 LYAPUNOV指数谱 边界碰撞 non-smooth system soft impact Poincaré map Lyapunov exponents border collision
分类号 O322 [理学—一般力学与力学基础]
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参考文献12

  • 1de Souza S L T, Wiercigroch M. Suppressing grazing chaos in impacting system by structural nonlinearity [J]. Chaos, Solitons & Fractals, 2008, 38(3): 864-869.
  • 2Pavlovskaia E, Wiercigroch M, Grebogi C. Two dimensional map for impact oscillator with drift [J]. Physcies Review E, 2004, 70(3): 6201-6290.
  • 3Ma Yue, Agarwal Manish, Baneijee Soumitro. Border collision bifurcations in a soft impact system [J]. Physics Letters A, 2006, 354:281 -287.
  • 4Sharan R, Banerjee S. Character of the map for switched dynamical systems for observations on the switching manifold [J]. Physics Letters A, 2008, 372: 4234-4240.
  • 5Ma Yue. The nature of the normal form map for soft impacting systems [J]. International Journal of Non-Liner Mechanics, 2008, 43(6): 504- 513.
  • 6Shaw S W, Holmes P J. A periodically forced piecewise linear oscillator [J]. Journal Sound and Viberation, 1983, 90(1): 129- 155.
  • 7Hu Haiyan. Detection of grazing orbits and incident bifurcations of a forced continuous, piecewise-linear oscillator [J]. Journal Sound and Viberation, 1995, 187(3): 485-493.
  • 8Silvio L T de Souza, Ibere L Caldas. Calculation of Lyapunov exponents in systems with impacts [J]. Chaos, Solitons and Fractals, 2004, 19(3): 569-579.
  • 9Nordmark A B. Non-periodic motion caused by grazing incidence in an impact oscillator [J]. Journal Sound and Viberation, 1991, 145(2): 279-297.
  • 10Whiston G S. Singularities in vibro-impact dynamics [J]. Journal Sound and Viberation, 1992, 152(3): 427-460.

二级参考文献10

  • 1Oseledec Ⅵ. A multiplicative ergodic theorem: Lyapunov characteristic numbers for dynamical systems: Trans Moscow Math Soc, 1968, 19:197～231.
  • 2Parker TS. Practical Numerical Algorithms for Chaotic Systems. New York: Springer-Verlag, 1989.
  • 3Guckenheimer J, Holmes P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. New York: Springer-Verlag, 1983.
  • 4Stefanski A. Estimation of the largest Lyapunov exponent in systems with impacts. Chaos, Solitons & Fractals, 2000,11:2443～2451.
  • 5Stefanski A, Kapitaniak T. Estimation of the dominant Lyapunov exponent of non-smooth systems on the basis of maps synchronization. Chaos, Solitons & Fractals, 2003,15:233～244.
  • 6Galvanetto U. Numerical computation of Lyapunov exponents in discontinuous maps implicitly defined. Computer Physics Communications, 2000, 131:1～9.
  • 7Müller P. Calculation of Lyapunov exponents for dynamics systems with discontinuities. Chaos, Solitons & Fractals,1995, 5(9): 1671～1681.
  • 8de Souza SLT, Caldas IL. Calculation of Lyapunov exponents in systems with impacts. Chaos, Solitons & Fractals,2004, 19:569～579.
  • 9Nordmark AB. Non-periodic motion caused by grazing incidence in an impact oscillator. Journal of Sound and Vibration, 1991, 145(2): 279～297.
  • 10Shaw SW, Holmes PJ. A periodically forced piecewise linear oscillator. Journal of Sound and Vibration, 1983, 90(1):129～155.

共引文献29

同被引文献80

引证文献13

二级引证文献51

工程力学
2011年 第3期

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