MODE-LOCKING IN NONLINEAR ROTORDYNAMICS

We present a computer-assisted study of the dynamics of two nonlinearl y coupled driven oscillators with rotational symmetry which arise in r otordynamics (the nonlinearity coming from bearing clearance). The non linearity causes a splitting of the twofold degenerate natural frequen cy of the associated linear model, leading to three interacting freque ncies in the system. Partial mode-locking then yields a biinfinite ser ies of attracting invariant 2-tori carrying (quasi-) periodic motion. Due to the resonance nature, the (quasi-) periodic solutions become pe riodic in a corotating coordinate system. They can be viewed as entrai nments of periodic solutions of the associated linear problem. One pre sumably infinite family is generated by (scaled) driving frequencies o mega = 1+2/n, n = 1, 2, 3,...; another one is generated by frequencies omega = m, m = 4, 5, 6,.... Both integers n and m can be related to d iscrete symmetry properties of the particular periodic solutions. Unde r a perturbation that breaks the rotational symmetry, more complicated behavior is possible. In particular, a second rational relation betwe en the frequencies can be established, resulting in fully mode-locked periodic motion.