On bifurcation trees of period-1 to period-2 motions in a nonlinear Jeffcott rotor system

Abstract

In this paper, periodic motions in a nonlinear rotor system are predicted through an implicit mapping method. The bifurcation trees of different period-1 to period-2 motion are presented, and there are many segments for different period-1 and period-2 motions. Harmonic frequency-amplitude characteristics of periodic motions are discussed for analysis and design of nonlinear rotor systems. Numerical simulations of periodic motions are completed for comparison of predicted and numerical results. The predictions of periodic motions in the nonlinear rotor system can provide guides for practical measurements of rotor systems, and one can have a better understanding of nonlinear rotor dynamics compared to the traditional perturbation analysis. Such studies presented in this paper just throw out some guides and ideas to predict complex motions in nonlinear rotor systems. The authors hope one can follow what presented in this paper to do further studies in nonlinear rotor dynamical systems and to improve design and control of nonlinear rotor systems.