On the prediction of shell vibration and sound radiation by different thin-shell theories when a submerged empty cylindrical shell is driven by an axisymmetric force

When a cylindrical shell is excited by a steady axisymmetric force, axial and radial vibrations travel in the axial direction and undergo continued reflections at the two ends. The radial vibration radiates sound into the surrounding medium. To calculate the displacement of the radial vibration, four “thin shell theories” were examined: Membrane (M), Donnell-Mushtari (D), Flugge-Byrne-Lur’ye (F), and Epstein-Kennard (E). Of these, E makes the fewest approximations and is the most intricate of the twelve catalogued in Leissa’s monograph “Vibration of shells”. For a cylindrical shell of radius 3.25 m and wall thickness 40 mm (ratio 1.2%), spectra of radial displacement and far-field radiated sound were computed up to 10 kHz. The differences amongst the four theories are negligible over the whole band. When the wall thickness is increased to 200 mm (ratio 6.2%), the spectra are almost identical for frequencies up to around 2.5 kHz, but gradually diverge at higher frequencies. The results indicate that D and F require the wall thickness to not exceed around 10% of the vibration wavelength, whereas M and E allow that ratio to reach (and perhaps surpass) 30%.