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. (C) 2017 Elsevier Ltd. All rights reserved.