Modeling orchestral crotales as thin plates

Orchestral crotales are designed in such a way that the overtones become less harmonic as the fundamental pitch increases. Deutsch, et al. used Kirchhoff-Love theory to show that by eliminating the central mass and choosing the correct ratio of inner to outer radius the overtones can be harmonically related (J. Acoust. Soc. Am. 116, 2427 (2004)). However, when a crotale was constructed using this design, the overtones were not harmonically related. We show that this lack of agreement between theory and experiment is due to the fact that shear motion of the inner boundary, which is neglected in classical thin-plate theory and thought to be unimportant, can significantly affect the resonance frequencies of plates even when they are extremely thin.