中国物理B ›› 2011, Vol. 20 ›› Issue (4): 40505-040505.doi: 10.1088/1674-1056/20/4/040505

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Lyapunov exponent calculation of a two-degree-of-freedom vibro-impact system with symmetrical rigid stops

李群宏, 谭洁燕   

  1. College of Mathematics and Information Science, Guangxi University, Nanning 530004, China
  • 收稿日期:2010-08-14 修回日期:2010-11-16 出版日期:2011-04-15 发布日期:2011-04-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 10972059), the Natural Science Foundation of the Guangxi Zhuang Autonmous Region of China (Grant Nos. 0640002 and 2010GXNSFA013110), the Guangxi Youth Science Foundation of China (Grant No. 0832014) and the Project of Excellent Innovating Team of Guangxi University.

Lyapunov exponent calculation of a two-degree-of-freedom vibro-impact system with symmetrical rigid stops

Li Qun-Hong(李群宏)† and Tan Jie-Yan(谭洁燕)   

  1. College of Mathematics and Information Science, Guangxi University, Nanning 530004, China
  • Received:2010-08-14 Revised:2010-11-16 Online:2011-04-15 Published:2011-04-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 10972059), the Natural Science Foundation of the Guangxi Zhuang Autonmous Region of China (Grant Nos. 0640002 and 2010GXNSFA013110), the Guangxi Youth Science Foundation of China (Grant No. 0832014) and the Project of Excellent Innovating Team of Guangxi University.

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摘要： A two-degree-of-freedom vibro-impact system having symmetrical rigid stops and subjected to periodic excitation is investigated in this paper. By introducing local maps between different stages of motion in the whole impact process, the Poincar'e map of the system is constructed. Using the Poincar'e map and the Gram-Schmidt orthonormalization, a method of calculating the spectrum of Lyapunov exponents of the above vibro-impact system is presented. Then the phase portraits of periodic and chaotic attractors for the system and the corresponding convergence diagrams of the spectrum of Lyapunov exponents are given out through the numerical simulations. To further identify the validity of the aforementioned computation method, the bifurcation diagram of the system with respect to the bifurcation parameter and the corresponding largest Lyapunov exponents are shown.

关键词: vibro-impact system, Poincar'e map, Gram--Schmidt orthonormalization, Lyapunov exponent

Abstract: A two-degree-of-freedom vibro-impact system having symmetrical rigid stops and subjected to periodic excitation is investigated in this paper. By introducing local maps between different stages of motion in the whole impact process, the Poincaré map of the system is constructed. Using the Poincaré map and the Gram-Schmidt orthonormalization, a method of calculating the spectrum of Lyapunov exponents of the above vibro-impact system is presented. Then the phase portraits of periodic and chaotic attractors for the system and the corresponding convergence diagrams of the spectrum of Lyapunov exponents are given out through the numerical simulations. To further identify the validity of the aforementioned computation method, the bifurcation diagram of the system with respect to the bifurcation parameter and the corresponding largest Lyapunov exponents are shown.

Key words: vibro-impact system, Poincaré map, Gram--Schmidt orthonormalization, Lyapunov exponent

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
05.10.-a (Computational methods in statistical physics and nonlinear dynamics)