Analytical periodic motions and bifurcations in a nonlinear rotor system

Abstract

In this paper, analytical solutions for period-\(m\) motions in a nonlinear rotor system are discussed. This rotor system with two-degrees of freedom is one of the simplest rotor dynamical systems, and periodic excitations are from the rotor eccentricity. The analytical expressions of periodic solutions are developed, and the corresponding stability and bifurcation analyses of period-m motions are carried out. Analytical bifurcation trees of period-1 motions to chaos are presented. The Hopf bifurcations of periodic motions cause not only the bifurcation tree but quasi-periodic motions. Displacement orbits of periodic motions in nonlinear rotor systems are used to illustrate motion complexity, and harmonic amplitude spectrums give harmonic effects on periodic motions of the nonlinear rotor. Coexisting periodic motions exist in the nonlinear rotor.