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

The dynamic equation of a relative rotation time-delay nonlinear dynamic system is established, which contains time-varying stiffness, nonlinear clamping 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.