The spectral functions method for acoustic wave diffraction by a stress-free wedge: Theory and validation

Abstract

Non Destructive Examination (NDE) of industrial structures requires the modeling of specimen geometry echoes generated by the surfaces (entry, backwall …) of inspected blocks. For that purpose, the study of plane wave diffraction by a wedge is of great interest. The work presented here is preliminary research to model the case of an elastic wave diffracted by a wedge in the future, for which there exist various modeling approaches but the numerical aspects have only been developed for wedge angles lower than π. The spectral functions method has previously been introduced to solve the 2D diffraction problem of an immersed elastic wedge for angles lower than π. As a first step, the spectral functions method has been developed here for the diffraction on an acoustic wave by a stress-free wedge, in 2D and for any wedge angle, before studying the elastic wave diffraction from a wedge. In this method, the solution to the diffraction problem is expressed in terms of two unknown functions called the spectral functions. These functions are computed semi-analytically, meaning that they are the sum of two terms. One of them is determined exactly and the other is approached numerically, using a collocation method. A successful numerical validation of the method for all wedge angles is proposed, by comparison with the GTD (Geometrical Theory of Diffraction) solution derived from the exact Sommerfeld integral.