The in-plane free vibration of an elastically supported thin ring rotating at high speeds revisited

The in-plane free vibration of a rotating thin ring is revisited in this paper. A new model is proposed which accounts for the elastic foundation and the through-thickness variation of the radial stress. The emphasis is placed on a proper consideration of the geometrical nonlinearity, which is essential for the consistent modelling of the ring stiffening resulting from the radial expansion caused by rotation. The in-plane stability of a thin ring rotating at relatively high speeds is analysed thoroughly. It is shown that the ring can become unstable should the rotational speed exceed a critical value. This result is new as in most known to the authors previous studies the stability problem is either not considered or it is stated that the in-plane vibration of a rotating ring is stable. In the studies which did address the instability, the conclusions and the employed models are prone to criticism. A parametric study is conducted to illustrate the effects of the ring properties on the in-plane stability. Finally, modes, which appear as stationary displacement patterns of the ring to an observer in the space-fixed reference system, are investigated. It is shown that the stationary patterns can occur prior to the onset of the instability for certain ring parameters.