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Nonlinear vibration characteristics of a rub-impact Jeffcott rotor are investigated. The system is two dimensional, nonlinear, and periodic. Fourier series analysis and the Floquet theory are used to perform qualitative global analysis of the dynamical system The governing ordinary differential equations are also integrated using a numerical method to give the quantitative result. This preliminary study reveal ed the chaotic feature of the system. After the rub-impact, as the rotating speed is increased three kinds of routes to chaos are found, that is, from a stable periodic motion through period doubling bifurcation, grazing bifurcation, and quasi-periodic bifurcation to chaos.