A Van Der Pol Absorber for Rotor Vibrations

Abstract A type of vibration damper applied to a rotor is described. The damping properties of the absorber are non-linear. The damper transforms the whirling motion of the rotor to a periodic one-line motion. An analytical procedure is developed for analyzing the motion of the non-linear rotor. It is based on the well known asymptotic method of Bogoliubov and Mitropolski. The mathematical model of the rotor is a system of two coupled second order non-linear differential equations. The steady state motion for such a system is always in one direction, which is proved by applying the Hopf bifurcation theorem. The angular position of the vibration motion is obtained analytically.