Green’s Function for Lamb’s Problem and Rayleigh Wave Propagation in General Transversely Isotropic Materials1

Composite materials have gained considerable industrial importance, being widely applied e.g. in aerospace industries. The need for their proper testing in view of delaminations, inclusions and other defects has correspondingly stimulated the interest in describing wave propagation in such anisotropic media. In this study, Lamb’s problem of determining the disturbance resulting from a point source in a half-space [1] is investigated for the case of transversely isotropic (TI) symmetry, which is characteristic for unidirectional fiber composites and extruded metal-matrix composites, but also for fiber-textured columnar-grained steels. Using the dyadic and triadic full-space Green’s functions obtained previously in their 2d-space-time spectral representations [2], a corresponding representation of Green’s dyad for the half-space has been derived exploiting the boundary condition of the stress-free surface. The resulting dyadic function is the solution of the elastic wave equation with point forces applied at the surface or within the uniform half-space, the fiber orientation being variable. First numerical evaluations have been performed with respect to Rayleigh-surface wave propagation by determining the zeroes of the corresponding Rayleigh function, which is included in the analytical expressions. Resulting slowness and wave curves are presented for several materials. The work presented can be further applied, e.g., to determine Rayleigh wave directivity patterns for point sources on the half-space as well as to model laser-generated wave propagation in composites. Application in the field of seismic wave propagation is also possible.