A SYMMETRICAL GALERKIN FORMULATION OF THE BOUNDARY-ELEMENT METHOD FORACOUSTIC RADIATION AND SCATTERING

A symmetric Galerkin formulation of the Boundary Element Method for ac oustic radiation and scattering is presented. The basic integral equat ions for radiation and scattering of sound are derived for structures, which may consist of a combination of a three-dimensional closed part and thin-walled parts. For the numerical solution of these integral e quations a Galerkin-type numerical solution scheme is proposed. The ev aluation of the weakly-singular and the hypersingular integrals, occur ring in this formulation, is addressed briefly An improved CHIEF-metho d is employed in order to prevent the singularity of the coefficient m atrix of the algebraic system of equations at so-called irregular freq uencies. Subsequently, an algorithm for the automatic determination of the number of nodal unknowns at intersections of thin-walled parts of a structure, or of thin-walled parts and the three-dimensional dosed part of a structure, is described. The numerical study contains compar isons of analytical solutions for simple academic examples with the nu merical results. In addition, a comparison of measured and computed re sults is presented for a structure, consisting of both a three-dimensi onal closed part and a thin-walled part.