Analysis on stability and bifurcation of cracked Jeffcott rotor

The stability and bifurcation of the responses of cracked rotor are studied. For the crack in shaft, the cosine switch function is applied to describe the opening and closing of the crack in rotation, and the cross stiffness originated from crack is considered. The motion equations are derived. To solve differential motion equations, Newmark-β method is applied. A method of computing Floquet Matrix by disturbing response is presented. Based on the Floquet theory, the Floquet Multiplier is computed by numerical method to analyze bifurcations. From simulation results, the jump from one periodic to another periodic motion corresponds to Saddle-node bifurcation, and the evolution from period to quasi-period corresponds to Hopf bifurcation. There exists period doubling bifurcation.