Multiple modal resonances of thin cylindrical shells vibrating in an acoustic medium

Structural modes of a thin cylindrical shell can display as many as three natural frequencies when immersed in an acoustic medium, all lower than the corresponding in vacuo natural frequency. This phenomenon results from the marked peak displayed by the inertial radiation loading of a slender cylindrical shell when the structural wavenumber of a modal configuration lies close to the acoustic wavenumber. This is illustrated for the axisymmetric ‘‘breathing mode’’ in the limiting case of an infinitely periodic cylindrical shell. For the parameters of metal shells in water, three natural frequencies are anticipated for modes whose axial wavelength exceeds the radius by at least one order of magnitude. For submerged shells of less stiff material or smaller modal wavelength-to-radius ratio, one or two natural frequencies are predicted.