An intermediate range solution to a diffraction problem with impedance conditions

Abstract

An intermediate range solution for the problem of plane wave diffraction by a finite plate with impedance boundaries is presented. Initially, the problem is expressed in terms of two Wiener–Hopf equations with the help of Fourier transform and the boundary conditions in the transformed domain. The consideration of the intermediate range approximation in terms of source position renders integrals that are generally elusive to tackle because of the presence of branch points. These integrals are evaluated by invoking a modified stationary phase method, thereby a field valid over an intermediate range is calculated. The graphical analysis is preformed for various parameters of physical interest for both intermediate and far-field solutions.

Keywords:

• diffraction
• impedance boundary condition
• Wiener–Hopf
• intermediate range solution