title: The Uniform geometrical Theory of Diffraction for elastodynamics: Plane wave scattering from a half-plane.
abstract: Diffraction phenomena studied in electromagnetism, acoustics, and elastodynamics are often modeled using integrals, such as the well-known Sommerfeld integral. The far field asymptotic evaluation of such integrals obtained using the method of steepest descent leads to the classical Geometrical Theory of Diffraction (GTD). It is well known that the method of steepest descent is inapplicable when the integrand's stationary phase point coalesces with its pole, explaining why GTD fails in zones where edge diffracted waves interfere with incident or reflected waves. To overcome this drawback, the Uniform geometrical Theory of Diffraction (UTD) has been developed previously in electromagnetism, based on a ray theory, which is particularly easy to implement. In this paper, UTD is developed for the canonical elastodynamic problem of the scattering of a plane wave by a half-plane. UTD is then compared to another uniform extension of GTD, the Uniform Asymptotic Theory (UAT) of diffraction, based on a more cumbersome ray theory. A good agreement between the two methods is obtained in the far field.
authors.affiliation: Department of Imaging and Simulation for Nondestructive Testing, CEA, LIST, 91191 Gif-sur-Yvette, France.
authors.forename: Audrey Kamta
authors.initials: AK
authors.lastname: Djakou
authors.affiliation: Department of Imaging and Simulation for Nondestructive Testing, CEA, LIST, 91191 Gif-sur-Yvette, France.
authors.forename: Michel
authors.initials: M
authors.lastname: Darmon
authors.affiliation: Sound Mathematics Ltd., Cambridge CB4 2AS, United Kingdom.
authors.forename: Larissa
authors.initials: L
authors.lastname: Fradkin
authors.affiliation: Laboratoire d'Acoustique de l'Université du Maine (LAUM), UMR CNRS 6613, 72085 Le Mans cedex 9, France.
authors.forename: Catherine
authors.initials: C
authors.lastname: Potel