Stability and non-linear responses of a rotor-bearing system with pedestallooseness

Vibration characteristics of a rotor-bearing system with pedestal looseness are investigated. A non-linear mathematical model containing stiffness and damping forces with tri-linear forms is considered. The shooting method is used to obtain the periodic solutions of the system. Stability of these pe riodic solutions is analyzed by using the Floquet theory. Period-doubling b ifurcation and Naimark-Sacker bifurcation are found. Finally, the: governin g equations are integrated using the fourth order Runge-Kutta method. Diffe rent forms of periodic, quasi-periodic and chaotic vibrations are observed by taking the rotating speed and imbalance as the control parameter. Three kinds of routes to or out of chaos. that is, period-to-chaos. quasi-periodi c route and intermittence, are found. (C) 2001 Academic Press.