Abstract
In this work, we present three different formulations Viz. The pressure field integral equation formulation (PFIE), the velocity field integral equation formulation (VFIE), and the combined field integral equation formulation (CEDE) for solving acoustic scattering problems associated with two dimensional fluid-filled bodies of arbitrary cross section. In particular using the boundary conditions on the surface of the body, two equivalent problems, each valid for the outside and inside regions of the scatterer, are derived. By properly selecting the associated equations for these equivalent problems, the three different formulations are derived. The PFIE, VFIE, and CFIE are then solved by approximating the cylindrical cross section by linear segments and employing the method of moments. Further, it is shown that the moment matrices generated by the PFIE and VFIE are ill-conditioned at resonant frequencies of the cylinder, whereas the CFIE generates a well-conditioned matrix at all frequencies. The solution techniques presented in this work are simple, efficient and applicable to truly arbitrary geometries. Numerical results are presented for certain canonical shapes and compared with other available data.
Acoustic scattering by elastic cylinders of elliptical cross-section and splitting up of resonances