Scattering of plane waves from objects having surface impedance discontinuities

Abstract

The scattering of acoustic plane waves from partially coated submerged objects is investigated. On the boundary between the uncoated and coated portions of the surface, an impedance discontinuity exists giving rise to sharply varying surface pressures and normal velocities. In the limiting case in which the uncoated surface has infinite impedance and the coated surface has zero impedance, it can be shown that a singularity in surface normal velocity exists. When finite and nonzero impedances are considered for the hard and soft boundary conditions, respectively, the singularity in normal velocity apparently disappears, but the rapid variation in surface pressures and normal velocities still presents numerical difficulties. Two specific systems are investigated: an infinite cylinder and a finite cylinder. Both systems are coated over two unconnected regions on their surfaces. The infinite cylinder is analyzed using a spectral expansion with the series coefficients evaluated using an overdetermined collocation technique. The finite cylinder is analyzed using a boundary element approach based on the standard Helmholtz integral equation. CHIEF points are used to avoid ill‐conditioning at problem frequencies. [Work supported by ONR.]