The spectral functions method for ultrasonic plane wave diffraction by a soft wedge

Abstract

NDE examination of industrial structures requires the modelling of specimen geometry echoes generated by the surfaces (entry, backwall…) of inspected blocks. For that purpose, the study of plane elastic wave diffraction by a wedge is of great interest since surfaces of complex industrial specimen often include dihedral corners. There exist various approaches for modelling the plane elastic wave diffraction by a wedge but for the moment, the theoretical and numerical aspects of these methods have only been developed for wedge angles lower than π. Croisille and Lebeau [1] have introduced a resolution method called the Spectral Functions method in the case of an immersed elastic wedge of angle less than π. Kamotski and Lebeau [2] have then proven existence and uniqueness of the solution derived from this method to the diffraction problem of stress-free wedges embedded in an elastic medium. The advantages of this method are its validity for wedge angles greater than π and its adaptability to more complex cases. The methodology of Croisille and Lebeau [1] has been first extended by the authors of the current communication to the simpler case of an immersed soft wedge [3]. The outline of their methodology is presented here and an application to the case of longitudinal incident and scattered waves in the case of the acoustic limit of the elastic code is presented.