Nonlinear motion cascade to chaos in a rotor system based on energy transfer

The nonlinear stiffness of a structure results in complex nonlinear dynamic behaviors and bifurcations of rotor systems. However, there still lacks of comprehensive studies on the bifurcation-induced motion to chaos of the nonlinear system. This study investigated the energy transfer during the motion evolution to chaos around bifurcations. In this paper, a flexible rotor system with nonlinear stiffness is established and the nonlinear responses under different parameter excitations are studied. We construct the energy trajectory in energy space and propose a bifurcation detection method based on generalized energy transfer for studying the evolution of motion cascades to chaos. The induction of period-doubling and period-halving bifurcation is revealed through the energy trajectory. The stability domains of the rotor system in different parameter planes are determined based on the Lyapunov stability criterion. A nonlinear rotor test platform is built and speed-up experiments are carried out to verify the proposed bifurcation detection method based on generalized energy transfer. These results indicate that the energy transfer is consistent with the switching of bifurcations. The sudden shift and fluctuation in the generalized energy amplitude correspond to period-doubling bifurcation and chaos, respectively. The generalized energy curves reveal the period-halving bifurcation, which cannot be observed in the speed-up test. This research and proposed method have potential for application in condition monitoring and bifurcation recognition during the operation of rotating machinery.