›› 2014, Vol. 23 ›› Issue (10): 104502-104502.doi: 10.1088/1674-1056/23/10/104502

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇    下一篇

Hopf bifurcation control for a coupled nonlinear relativerotation system with time-delay feedbacks

刘爽a b, 李雪a, 谈书贤a, 李海滨a   

  1. a Key Laboratory of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao 066004, China;
    b National Engineering Research Center for Equipment and Technology of Cold Strip Rolling, Yanshan University, Qinhuangdao 066004, China
  • 收稿日期:2014-03-15 修回日期:2014-04-11 出版日期:2014-10-15 发布日期:2014-10-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 61104040) and the Natural Science Foundation of Hebei Province, China (Grant No. E2012203090).

Hopf bifurcation control for a coupled nonlinear relativerotation system with time-delay feedbacks

Liu Shuang (刘爽)a b, Li Xue (李雪)a, Tan Shu-Xian (谈书贤)a, Li Hai-Bin (李海滨)a   

  1. a Key Laboratory of Industrial Computer Control Engineering of Hebei Province, Yanshan University, Qinhuangdao 066004, China;
    b National Engineering Research Center for Equipment and Technology of Cold Strip Rolling, Yanshan University, Qinhuangdao 066004, China
  • Received:2014-03-15 Revised:2014-04-11 Online:2014-10-15 Published:2014-10-15
  • Contact: Li Hai-Bin E-mail:hbli@ysu.edu.cn
  • About author:45.20.dc; 05.45.-a
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 61104040) and the Natural Science Foundation of Hebei Province, China (Grant No. E2012203090).

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摘要： This paper investigates the Hopf bifurcations resulting from time delay in a coupled relative-rotation system with time-delay feedbacks. Firstly, considering external excitation, the dynamical equation of relative rotation nonlinear dynamical system with primary resonance and 1:1 internal resonance under time-delay feedbacks is deduced. Secondly, the averaging equation is obtained by the multiple scales method. The periodic solution in a closed form is presented by a perturbation approach. At last, numerical simulations confirm that time-delay theoretical analyses have influence on the Hopf bifurcation point and the stability of periodic solution.

关键词: relative rotation, coupled nonlinear system, bifurcation, time delay

Abstract: This paper investigates the Hopf bifurcations resulting from time delay in a coupled relative-rotation system with time-delay feedbacks. Firstly, considering external excitation, the dynamical equation of relative rotation nonlinear dynamical system with primary resonance and 1:1 internal resonance under time-delay feedbacks is deduced. Secondly, the averaging equation is obtained by the multiple scales method. The periodic solution in a closed form is presented by a perturbation approach. At last, numerical simulations confirm that time-delay theoretical analyses have influence on the Hopf bifurcation point and the stability of periodic solution.

Key words: relative rotation, coupled nonlinear system, bifurcation, time delay

中图分类号:  (Rotational dynamics)

  • 45.20.dc
05.45.-a (Nonlinear dynamics and chaos)