On the unsymmetrical deformation and reverse snapping of a spinning non-flat disk

In this paper we study the steady state deflection and reverse snapping phenomenon of a spinning non-flat disk. Both the initial and the deformed shapes of the disk are allowed to have axisymmetrical and unsymmetrical components. For the analysis of a rotating axisymmetrical disk, we conclude that there is no need to include the unsymmetrical assumed modes in the solution because all the unsymmetrical steady state deformations are unstable. In addition, the stability of the axisymmetrical positions will not be affected by the inclusion of the unsymmetrical assumed modes. In the case when the initial shape of the disk contains a dominant axisymmetrical component and a smaller unsymmetrical component, attention is focused on the effect of this unsymmetrical component on the overall deformation and stability of the spinning disk. It is found that the unsymmetrical component with one nodal diameter tends to slightly defer the occurrence of the reverse snapping phenomenon. On the other hand, all other unsymmetrical components with more than one nodal diameter tend to reduce dramatically the reverse snapping speed. Experiment is conducted on a non-flat brass disk containing an axisymmetrical component and an unsymmetrical component with two nodal diameters. The experimental measurement confirms the theoretical prediction.