Space–time far-field representation of Green’s functions for cross-plane shear waves in general transversely isotropic media

For transversely isotropic materials like fiber composites, but also unidirectionally grain-structured austenitic steels, the elastodynamic dyadic and triadic Green’s functions for the pure shear (SH) wave mode are given in the space–time domain. The first stage of the derivation is performed in a way similar to the derivation of these functions in the form of their 2D space–time spectral representations [M. Spies, J. Acoust. Soc. Am. 96, 1144–1157 (1994)]. In the present study, the inverse Fourier integrations are performed using a far-field approximation. The resulting expressions appear in a coordinate-free form and contain the orientation of the material’s fiber axis as an additional parameter. Thus the results are particularly useful for extension to the case of layered material. Numerical evaluation is performed for a unidirectional composite material for several orientations. Since the application of the SH-wave type bears considerable potential in nondestructive testing, the results presented in this article may find some application within this framework.