The Uniform geometrical Theory of Diffraction for elastodynamics: Plane wave scattering from a half-plane
Résumé
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.
Mots clés
Stationary phase point
Method of steepest descent
Geometrical theory of diffraction
Elastodynamic problem
Diffraction phenomenon
Asymptotic evaluation
Wave propagation
Geometry
Electromagnetic wave scattering
Elastic waves
Diffraction
Asymptotic analysis
Steepest descent method
Uniform geometrical theory of diffraction
Uniform asymptotic theories
Approximation theory
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