Diffraction of scalar waves by an impedance cone of arbitrary cross-section

✍ Scribed by J.M.L. Bernard; M.A. Lyalinov

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 262 KB
• Volume: 33
• Category: Article
• ISSN: 0165-2125
• DOI: 10.1016/s0165-2125(00)00055-x

✦ Synopsis

The diffraction of scalar waves by a cone of arbitrary cross-section, with constant impedance conditions on its surface, is studied for fields satisfying the Helmholtz equation. For this purpose, a particular use of integral transformations, with complex variables, is developed, which allows to consider boundary condition with radial dependence. The problem in question is reduced to that for a spectral function satisfying a Helmholtz type equation on the unit sphere with a hole cut out by the conical surface. This has to satisfy an impedance type boundary condition on the boundary of the hole, with a non-local term involving an integral operator on the spectral variable. Then the problem for the spectral function can be transformed to an integral equation of the second kind with non-oscillatory kernel. As an application, a closed form expression for the scattering diagram is deduced in the narrow cone approximation. Illuminations by a point source and by a plane wave are considered.