REGULAR AND CHAOTIC FORCED VIBRATION OF THIN ROTATING RINGS

Dynamics of thin rings rotating with constant spin speed is investigat ed. The rings rotate with respect to their axis of rotational symmetry and they are under the influence of external forcing which leads to c onditions of two-frequency or single-frequency primary resonance. Firs t, a two-degree-of-freedom weakly non-linear model is employed, govern ing the amplitude of two in-plane bending modes of the ring with the s ame wave number. Then, a perturbation procedure is applied and modulat ion equations are derived for the amplitudes and phases of approximate analytical solutions of this model. For two-frequency quasiperiodic f orcing, constant solutions of the modulation equations are shown to co rrespond to structural response involving combinations of forward and backward traveling waves, while for single-frequency resonant Forcing the ring response is dominated by a forward or backward traveling wave . Characteristic effects of system parameters on the ring dynamics are then illustrated by representative series of response diagrams. Final ly, direct integration of the modulation equations reveals rich dynami c behavior, involving coexistence and interaction of constant solution s with periodic and chaotic solutions. (C) 1998 Elsevier Science Ltd. All rights reserved.