Practical tutorial on cylindrical structure vibro-acoustics Part 2 - Acoustics

In part 1 of this tutorial (proceedings of Inter-noise 2022) I explained vibrations in cylindrical shell structures. In that paper I limited the mathematics and focused on the key behavior of shells based on critical parameters like the ring frequency, helical wavenumbers, and mean mobilities over different frequency ranges. I compared measured data to the simple theories. In part 2, I focus on the acoustics of cylindrical shells, including sound within shells and the sound radiated outside them. Exterior sound radiation depends strongly on the circumferential order of the shell modes. Breathing modes near the ring frequency radiate sound extremely well, but have very high impedances, so can be difficult to excite. Beam-like modes, where the entire shell cross-section vibrates transversely, radiate less efficiently, but can be easily driven. Higher order, or 'lobar' modes radiate even less efficiently, but nevertheless are commonly observed in radiated sound spectra due to their low impedances. I also review statistical estimates of radiation efficiency of groups of shell modes, which show clear peaks at both the ring frequency as well as at the critical frequency of bending waves. The mathematics of sound inside cylindrical shells is some of the most challenging in vibro-acoustics. At low frequencies, however, the interior sound is dominated by simple one-dimensional planar acoustic waves. At higher frequencies, the sound depends on how well a shell vibration field matches the interior acoustic field based on proximity of resonance frequencies and the similarity of mode shape orders, as well as the 'cut on' frequencies of higher order internal acoustic modes. Finally, I review the well-known phenomenon of how a low shell wall impedance can reduce the effective acoustic sound speed of one-dimensional waves inside cylindrical shells.