Hopf bifurcation control for some nonlinear torsional vibration system with delayed feedbacks

Torsional vibration generally causes serious instability and great damage in many rotating machinery. Hopf bifurcation control for some nonlinear torsional vibration system with delayed feedbacks is investigated. On the basis of the generalized dissipation Lagrange´s equation, the dynamics equation of nonlinear torsional vibration system is established, and a nonlinear time-delayed feedback controller is proposed. Under the condition of primary resonance, perturbation analysis of the controlled system is carried out with the method of multiple scales. The influence of time delays on Hopf bifurcation and limit cycle in torsional vibration system is studied. The stability conditions and amplitude formula of limit cycle are given. Finally, numerical simulations are performed to verify the analytical results. The conclusion can provide theoretical reference for further research on more complexed mechanical drive system.