An independent period-3 motion to chaos in a nonlinear flexible rotor system

Abstract

In this paper, a bifurcation tree of an independent period-3 motion to chaos in a flexible nonlinear rotor system is developed semi-analytically. The period-3 motion was traditionally called the subharmonic periodic motion of order-1/3, but one did not achieve the corresponding solutions yet. Herein, stable and unstable periodic solutions on the bifurcation tree in the flexible rotor system are achieved and the corresponding stability is analyzed by eigenvalue analysis. Harmonic frequency-amplitude characteristics for periodic motions on the bifurcation tree are presented. For comparison of analytical and numerical results, numerical simulation of periodic motions is completed. Phase trajectories, displacement orbits and velocity planes are illustrated, and harmonic amplitude spectrums of period-3 and period-6 motions are presented to show harmonic terms effects. Such studies presented in this paper help one better understand the subharmonic periodic oscillation of order-1/3 in nonlinear rotor systems.