Nonlinear frequency shifts in quasispherical-cap shells: Pitch glide in Chinese gongs

The large-amplitude vibrational behavior of a shallow spherical-cap shell is investigated theoretically using simple arguments. The results of this approximate analysis are expressed in the form of appealingly simple nondimensional quantities. It is shown that the frequency of the fundamental mode of such a shell falls by as much as 50% as the vibration amplitude is increased to approximately the shell depth. For even larger amplitudes the frequency rises, and it exceeds the small-amplitude frequency when the amplitude is more than about twice the shell depth. The influence of shell thickness is considered and increasing thickness is shown to decrease the frequency shift. This analysis is shown to account for the pitch glide behavior of certain Chinese opera gongs.