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Lyapunov exponent calculation of a two-degree-of-freedom vibro-impact system with symmetrical rigid stops
作者姓名:李群宏  谭洁燕
作者单位:College of Mathematics and Information Science,Guangxi University
基金项目: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.
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 exposents 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  ex-  ponent
收稿时间:2010-08-14

Lyapunov exponent calculation of a two-degree-of-freedom vibro-impact system with symmetrical rigid stops
Li Qun-Hong and Tan Jie-Yan.Lyapunov exponent calculation of a two-degree-of-freedom vibro-impact system with symmetrical rigid stops[J].Chinese Physics B,2011,20(4):40505-040505.
Authors:Li Qun-Hong and Tan Jie-Yan
Institution:College of Mathematics and Information Science, Guangxi University, Nanning 530004, China;College of Mathematics and Information Science, Guangxi University, Nanning 530004, China
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 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.
Keywords:vibro-impact system  Poincar'e map  Gram--Schmidt orthonormalization  Lyapunov exponent
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