A new direct boundary element method (DBEM) is developed for thin bodies whose surfaces are rigid or compliant. An imaginary interface surface is constructed initially to devide the acoustic domain into an interior and an exterior subdomain. Adding the Helmholtz integral equations and the normal derivative integral eqautions for each subdomain respectively, a combined Helmholtz integral equation and a combined normal derivative integral equation for the real surface are obtained. Unlike the usual assumption, the normal velocity is assumed to be discontinuous across the thin body. The primary variables in the integral equations are the velocity potential (or pressure) jump for the rigid surface, and the normal velocity jump across the thin-body surface of different materials (or normal vibrating velocities). The normal velocity on each surface is specified by general boundary conditions; the prescribed acoustic admittance and the prescribed vibrating velocity. Then the velocity potential values on each surface can be obtained by both the combined Helmholtz integral equation and the combined normal derivative integral equation simultaneously.
The hypersingular integral is regularized by using the Maue's less singular normal derivative integral equation. A standard Gaussian quadrature is used for the Maue's integral equation. Two different collocation points are used to confirm the condition at the corner and the vertex; at the nodal points for the combined Helmholtz integral equation and inside each element for the combined normal derivative integral equation. The knife-edge effect is treated by adopting a quarter-point element.
The method is validated by comparison with analytic and/or numerical results for acoustic scattering and radiation from several surface conditions of the thin body; the surfaces are rigid when stationary or vibrating, and part of the interior surface is lined with a sound-absorbing material. The effect of absorbing material is investigated for complicated geometries such as cylindrical shell with one side open, and anechoic wind tunnel.
