A generalized internal source density method for the forward and backward projection of harmonic pressure fields from complex bodies

Abstract

A generalized internal source density (GISD) method is presented to address the forward and backward projection of harmonic pressure fields from complex three-dimensional bodies. The GISD approach is based on decomposing the field on a closed surface of revolution in the fluid into a summation of circumferential orders where the pressure field for each order is associated with an internal linear distribution of ring sources on the axis of revolution of the surface. Both Dirichlet and Neumann boundary value problems may be addressed using the approach in which the axial variation of each ring source distribution is formulated as the solution of a minimum mean square error problem which is subsequently solved using SVD methods. The resulting linear distributions of ring sources can be simply used to determine the entire pressure and velocity fields of a complex harmonically vibrating body. In particular, the pressure and/or normal velocity on a vibrating body can be readily obtained from the pressure field over a closed surface. Local intensity and radiated power can thus be simply obtained. Far field pressures are simply obtained from the axial Fourier transforms of the ring source distributions. Several examples are presented to illustrate the behaviour of the source distributions for spherical geometries. The analytical results obtained via the GISD method agree with those obtained via classical methods.