Bifurcation and chaos in a rub-impact Jeffcott rotor system

Non-linear vibration characteristics of a rub-impact Jeffcott rotor are investigated. The system is two-dimensional, non-linear and periodic. Fourier series analysis and the Floquet theory are used to perform qualitative global analysis on bifurcation and stability. The governing ordinary differential equations are also integrated using a numerical method to give the quantitative result. This preliminary study reveals 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 a sudden transition from periodic motion to chaos. Quasi-periodic motions are also found. (C) 1998 Academic Press Limited.