中国物理B ›› 2003, Vol. 12 ›› Issue (1): 17-21.doi: 10.1088/1009-1963/12/1/303

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Suppressing chaos by parametric perturbation at doubled frequency of periodic perturbation

彭解华1, 唐驾时1, 于德介1, 海文华2, 颜家壬2   

  1. (1)Department of Mechanics, Hunan University, Changsha 410082, China; (2)Department of Physics, Hunan Normal University, Changsha 410081, China
  • 收稿日期:2002-02-20 修回日期:2002-06-11 出版日期:2003-01-20 发布日期:2003-01-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 19874019), and the Natural Science Foundation of Hunan Province, China (Grant No 01JJY2007).

Suppressing chaos by parametric perturbation at doubled frequency of periodic perturbation

Peng Jie-Hua (彭解华)ac, Tang Jia-Shi (唐驾时)a, Yu De-Jie (于德介)a, Hai Wen-Hua (海文华)b, Yan Jia-Ren (颜家壬)b   

  1. a Department of Mechanics, Hunan University, Changsha 410082, China; b Department of Physics, Hunan Normal University, Changsha 410081, China; c Department of Physics, Shaoyang Teachers College, Shaoyang 422000, China
  • Received:2002-02-20 Revised:2002-06-11 Online:2003-01-20 Published:2003-01-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 19874019), and the Natural Science Foundation of Hunan Province, China (Grant No 01JJY2007).

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摘要： An analysis of the chaos suppression of a nonlinear elastic beam (NLEB) is presented. In terms of modal transformation the equation of NLEB is reduced to the Duffing equation. It is shown that the chaotic behaviour of the NLEB is sensitively dependent on the parameters of perturbations and initial conditions. By adjusting the frequency of parametric perturbation to twice that of the periodic one and the amplitude of parametric perturbation to the same as the periodic one, the chaotic region of the nonlinear elastic beam driven by periodic force can be greatly suppressed.

Abstract: An analysis of the chaos suppression of a nonlinear elastic beam (NLEB) is presented. In terms of modal transformation the equation of NLEB is reduced to the Duffing equation. It is shown that the chaotic behaviour of the NLEB is sensitively dependent on the parameters of perturbations and initial conditions. By adjusting the frequency of parametric perturbation to twice that of the periodic one and the amplitude of parametric perturbation to the same as the periodic one, the chaotic region of the nonlinear elastic beam driven by periodic force can be greatly suppressed.

Key words: suppression of chaos, threshold of chaos, nonlinear elastic beam, parametric perturbation

中图分类号:  (Beams, plates, and shells)

  • 46.70.De
46.25.Cc (Theoretical studies) 05.45.-a (Nonlinear dynamics and chaos)