Elastic wave radiation and diffraction of a piston source

Abstract

The radiation of an elastic field from a plane piston source is formulated using the representation theorem, in which the Green’s function for an elastic half-space is employed. On the basis of this formulation, the radiated elastic wave field for both compressional and shear cylindrical wave sources is derived. The diffraction of elastic waves incident on a receiver that has the same geometry as that of the source and is coaxially aligned with it is studied. The authors present a procedure in which both numerical and asymptotic techniques are employed to allow them to evaluate the diffraction effects in any frequency range of interest. The elastic diffraction is compared with the acoustic diffraction and it is discovered that they differ only in the nearfield of the piston source because of the coupling between shear and compressional components in the elastic case. In the farfield, however, the elastic diffraction approaches the acoustic diffraction. With the help of ultrasonic laboratory measurements, the authors test the theoretical results and find that the theory and experiments agree well for the elastic solution. An important application of the results of this study is in attenuation measurements using pulse propagation techniques, where spectral ratio of a sample relative to a standard sample, or ratio of samples of the same material but different length is used. In the former case, the attenuation can be overestimated. While in the latter case, the attenuation can be significantly underestimated, if corrections for diffraction effects are not made.