Analytical solutions of period-1 motions in a buckled, nonlinear Jeffcott rotor system

Abstract

In this paper, the analytical solutions of period-1 motions of a buckled nonlinear Jeffcott rotor are developed, and the corresponding stability and bifurcation of period-1 motion are also analyzed by eigenvalue analysis. The Hopf bifurcations of period-1 motions cause not only the bifurcation tree but quasi-periodic motions. The quasi-periodic motion can be stable or unstable. Displacement orbits of periodic motions in the buckled nonlinear Jeffcott rotor systems are illustrated, and harmonic amplitude spectrums are presented for harmonic effects on periodic motions of the buckled nonlinear Jeffcott rotor.