Numerical modeling of acoustic radiation and scattering from thin bodies using a Cauchy principal integral equation

In this paper, the Helmholtz integral equation and its normal derivative are used for the numerical solution of acoustic radiation and scattering from thin bodies. A regularized form of the normal derivative integral equation, originally derived by Maue, is adopted to calculate the pressure jump across the thin body. This regularized normal derivative integral equation converges in the Cauchy principal value sense rather than only in the finite-part sense. The Cauchy principal value integral can be further transformed into an integral that converges in the normal sense. The C⁰ continuous isoparametric elements are used in the formulation so that the numerical model is compatible with other analysis tools such as the finite element method. Collocation points are placed inside each element to insure a unique normal direction and the C¹ continuity condition. The pressure jump is forced to be zero at the knife edge where the 1/√r singularity of the tangential velocities is modeled by the quarter-point technique. Numerical examples on scattering from a circular disk and an open cylindrical shell are given to verify the formulation.