5.6 Wedge Diffraction

For wedges of non-zero included angle a solution technique analogous to the Wiener-Hopf method was developed by Maliuzhinets (1958c). The solution is carried out in cylindrical polar coordinates and, for a wedge subject to first order (possibly different) impedance boundary conditions on the two faces, the method is simple and elegant (see Chapter 4). Unfortunately, this is not true for second and higher order conditions, and the need to construct a particular solution of an inhomogeneous difference equation is a significant complication. Because of this, the problem has received little attention in the literature, and no correct solutions have yet appeared. Although Bernard (1987) tackled the most general problem of a wedge of arbitrary angle subject to GIBCs of arbitrary but finite order, he was unaware of the need for contact conditions, and sought to avoid the explicit evaluation of the particular solution of the difference equation. As a result his expression for the field is both incomplete and incorrect. The special case of a right-angled wedge with identical second order conditions on the two faces was treated by Senior (1989b) and, although the particular solution was obtained, his final result is still wrong. The correct solution is presented in Section 5.6.2.

To illustrate the method, it is convenient to start by considering a second order impedance half-plane, and this enables us to point out the similarities to the Wiener-Hopf approach.