Edge Diffraction Coefficients around Critical Rays

12th Anglo-French Physical Acoustics Conference

Fradkin, L.^1 ; Harmer, M.^1 ; Darmon, M.^2

Sound Mathematics Ltd., 11 Mulberry Close, Cambridge CB4 2AS, United Kingdom^1

CEA, LIST, Department of Imaging and Simulation for NDT, F-91191 Gif-sur-Yvette, France^2

关键词: Diffracted waves;    Geometrical theory of diffraction;    High-frequency asymptotics;    Industrial materials;    Shadow boundaries;    Stationary points;    Transition regions;    Transition zones;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/498/1/012010/pdf
DOI  :  10.1088/1742-6596/498/1/012010

来源: IOP

【 摘 要 】

The classical GTD (Geometrical Theory of Diffraction) gives a recipe, based on high-frequency asymptotics, for calculating edge diffraction coefficients in the geometrical regions where only diffracted waves propagate. The Uniform GTD extends this recipe to transition zones between irradiated and silent regions, known as penumbra. For many industrial materials, e.g. steels, and frequencies utlized in industrial ultrasonic transducers, that is, around 5 MHz, asymptotics suggested for description of geometrical regions supporting the head waves or transition regions surrounding their boundaries, known as critical rays, prove unsatisfactory. We present a numerical extension of GTD, which is based on a regularized, variable step Simpson's method for evaluating the edge diffraction coefficients in the regions of interference between head waves, diffracted waves and/or reflected waves. In mathematical terms, these are the regions of coalescence of three critical points - a branch point, stationary point and/or pole, respectively. We show that away from the shadow boundaries, near the critical rays the GTD still produces correct values of the edge diffraction coefficients.