Nondegenerate normal-mode doublets in vibrating flat circular plates

Abstract

The vibrations of flat circular plates have been studied for hundreds of years and are well understood. However, when vibrating circular plates are discussed in textbooks, the relation between pairs of spatially orthogonal vibrational patterns that occur at each of the normal-mode frequencies often is ignored. Usually these orthogonal solutions are presented to the student as being degenerate in frequency. However, in practice the degeneracy of the doublet often is broken, and the two spatially orthogonal solutions are separated in frequency. We show theoretically and experimentally that the degeneracy can be broken by small density perturbations in the plate, and we derive a formula for predicting the magnitude of the frequency splitting. We have used electronic speckle pattern interferometry to investigate the phenomenon of doublet splitting and have confirmed the validity of the theory.