Abstract: Periodic solutions of nonlinear rotor-SFD supporting system are calculated by using Newton-Fox shooting method and pseudo-arc length continuation procedure.According to multi-variable Floquet theory,bifurcations and stability of the system are analyzed.Bifurcation diagrams of the system are obtained from on Poincaré map.The results show that the motion of the rotor system undergoes nonlinear dynamics phenomena,such as period doubling bifurcation,tangent bifurcation and so on.