cea-01820753
https://cea.hal.science/cea-01820753
doi:10.1088/1742-6596/498/1/012010
[CEA] CEA - Commissariat à l'énergie atomique
[DRT] Direction de la recherche technologique
[LIST] Laboratoire d'Intégration des Systèmes et des Technologies
[DIN] Département d'Instrumentation Numérique
Edge diffraction coefficients around critical rays
Fradkin, L.
Harmer, M.
Darmon, M.
[PHYS] Physics [physics]
ART
Elastic waves
Geometry
Numerical methods
Seismic waves
Ultrasonic transducers
Diffracted waves
Geometrical theory of diffraction
High-frequency asymptotics
Industrial materials
Shadow boundaries
Stationary points
Transition regions
Transition zones
Diffraction
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.
2014
en
Journal of Physics: Conference Series
IOP Science