Vibrations of circular and noncircular cylindrical shells

Abstract

In order to better understand the vibrational modes of Chinese two-tone bells [Rossing et al., J. Acoust. Soc. Am. 83, 369–373 (1988)], the vibrational modes of capped and uncapped cylinders with circular and nearly elliptical cross sections have been studied. Mode doublets in the noncircular cylinders replace single modes in the circular cylinders. The higher frequency mode in each doublet, in both the capped and uncapped cylinders, generally belongs to the mode that has a node where the curvature is greatest. The frequency ratio of the doublet pair appears to decrease with increasing m (number of wavelengths around the circumference) but to increase with n (number of nodal circles). The splitting increases with eccentricity, as expected.