Characteristic Frequencies of a Symmetrically Loaded Ring

Measurements of the natural frequencies of vibration of a uniform thin circular ring in the flexural radial and axial modes are reported. These vibrations occur in degenerate doublets whose behaviour under perturbations in the form of equal loads attached to the ring at the vertices of inscribed regular n-th order polygons is investigated experimentally, and compared with the predictions of “selection rules” previously obtained by group theoretical techniques. The results show a convincing correlation with the predictions of the rules.