In this paper, the analytical solutions of period-1 solutions are developed, and the corresponding stability and bifurcation are also analyzed by eigenvalue analysis. The Hopf bifurcations of periodic 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 nonlinear Jeffcott rotor systems are illustrated, and harmonic amplitude spectrums are presented for harmonic effects on periodic motions of the nonlinear rotor.

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