Selection Rules for the Splitting of the Degenerate Pairs of Natural Frequencies of Thin Circular Rings

The flexural radial and axial vibrations of thin uniform circular rings each occur in degenerate doublets. Group theoretical techniques are applied to obtain selection rules for the splitting of these doublets under the application of a perturbation in the form of equal masses attached to the ring at the vertices of an inscribed regular n-th order polygon. It is suggested that these selection rules may also be applicable to other modes of vibration of thin uniform circular rings.