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Stability analysis of a relative rotation time-delay nonlinear dynamic system

Liu Hao-Ran Zhu Zhan-Long Shi Pei-Ming

Stability analysis of a relative rotation time-delay nonlinear dynamic system

Liu Hao-Ran, Zhu Zhan-Long, Shi Pei-Ming
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Publishing process
  • Received Date:  08 December 2009
  • Accepted Date:  29 January 2010
  • Published Online:  05 May 2010

Stability analysis of a relative rotation time-delay nonlinear dynamic system

  • 1. (1)Institute of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China; (2)Institute of Information Technology and Engineering, Yanshan University, Qinhuangdao 066004, China

Abstract: The dynamic equation of a relative rotation time-delay nonlinear dynamic system is established, which contains time-varying stiffness, nonlinear damping and harmonic excitation. The bifurcation equation of time-delay dynamic system is deduced by the method of multiple scales. The structure stability of the system is studied by singularity theory, the transfer concourse of primary resonance equation and topological structure of bifurcation function are obtained. The dynamic stability of the system is discussed by the Hopf bifurcation theory and the condition for the limit cycle occurrance is given. Moreover, it is indicated by numerical method that parameters of time delay affect the limit cycle amplitude.

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