Abstract:

Hopf bifurcation type and Hopf bifurcation control of a relative rotation dynamical system with nonlinear damping force were mainly studied. Firstly, the original system was changed to a twodimensional system via center manifold theory, and the stability coefficient of the twodimensional system was calculated to determine the Hopf bifurcation type of the original system. Then, the cubic nonlinear controller based on Washout filter theory was designed to control Hopf bifurcation, and the effects of control parameter on Hopf bifurcation type and periodic solution’s amplitude were discussed. The results show that when the control parameter satisfies certain condition, the potential threat subcritical Hopf bifurcation of original will be changed to supercritical Hopf bifurcation, thus the normal vibration of original system is guaranteed, and the amplitude of vibration will decrease with the reduction of the control parameter.

Key words: relatively rotation, Hopf bifurcation, bifurcation control, center manifold theory, Washout filter