The vibrations of flat circular plates have been studied for hundreds of years, and they are well understood by the scientific community. Unfortunately, when vibrating circular plates are discussed in textbooks, the relationship between pairs of spatially orthogonal vibrational patterns that occur at each of the normal-mode frequencies is often ignored. Usually these orthogonal solutions are presented to the student as being degenerate in frequency; however, in practice the degeneracy of the doublet is often broken and the two spatially orthogonal solutions are separated in frequency. We show theoretically and experimentally that the degeneracy can be broken by a small asymmetry 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 phenomena of doublet splitting and have confirmed the validity of the theory.
Deutsch, Bradley M., Richard J. Felce, and Thomas R. Moore. 2004. Nondegenerate normal-mode doublets in vibrating flat circular plates. American Journal of Physics 72 (2) (February 2004): 220-.
American Journal of Physics