Surface pressure and harmonic loading on shells of revolution using an internal source density method

An internal source density method is presented to evaluate the surface pressures and hence the fluid loading on a harmonically vibrating shell of revolution. The normal velocity of the shell is specified to be axisymmetric and harmonic. After expressing the normal velocity of the shell in terms of a modal vector expansion, the radial component of the modal vectors is used to define acoustic modal radiation impedances. In order to evaluate the surface pressures and acoustic radiation impedances, an unknown linear monopole source density is positioned along the axis of the shell. The normal components of the specified modal velocities are subsequently used to determine the monopole source distribution via a set of coupled linear algebraic equations. Extensive numerical results are presented to illustrate the spatial and frequency characteristics of the source density for both spherical and spheroidal shells. Numerical results for the modal acoustic radiation impedances for spherical and spheroidal shells are also presented and discussed.