An analytical model for noise radiated from axial vibration of a simplified pressure hull of an underwater vehicle

An analytical model is presented for the hull vibration and sound pressure radiated when a large empty cylindrical hull submerged in water is excited by an axial thrust along a central propeller shaft. The model, which is based on the Donnell-Mushtari coupled equations of motion for axial and radial vibration of a cylindrical shell, yields frequency-dependent phase velocity and attenuation of those vibrations. The amplitudes of the vibrations that travel along a hull and reflected by both ends are described in terms of the incident thrust. A solution is obtained for the consequent radiated sound pressure. Both unstiffened and stiffened shells are considered, in which the analytical model for the stiffened shell is based on a smeared approach. Results from the analytical model presented here are compared with the analytical results from literature. The main contribution of this work is to consider phase velocities that vary with frequency and their effect on the radiated sound pressure.