Dependence of vibrational modes of a handbell on thickness and added mass

Abstract

The vibrational modes of a large tuned handbell (G2) are compared with those of an untuned bell casting having the same shape but with twice the thickness. Doubling the wall thickness is found to raise the frequencies of the various modes by factors ranging from 1.4 to 2.4 (flat plate theory predicts a factor of 2 for all modes). Unlike the tuned G2 handbell, whose pitch coincides with the frequency of the fundamental mode of vibration, the thick bell has two prominent strike notes, depending upon where it is struck. These subjective tones appear to be created by groups of three nearly harmonic partials radiated by the (m,l) and (m,l♯) families of modes, respectively. The acoustical effects of attacking up to twelve 35‐g brass cylinders have also been observed, both in a symmetrical pattern and in clusters similar to the clusters of mei found on ancient Chinese bells [Rossing et al., J. Acoust. Soc. Am. Suppl. 1 77, S102 (1985)]. The additional masses lower the frequencies of certain modes but have relatively little effect on modal decay rates.