Differential geometry of ray surfaces in anisotropic solids and its contribution to NDE: modelling and experiment

Point-source/point-receiver techniques are one of the most widely used methods for nondestructive evaluation of anisotropic materials. The group velocities resulting from these techniques must be, for further inverse evaluation of elastic coefficients, geometrically converted into corresponding phase velocities. On the other hand, the phase velocities can be determined from a material's response to a line source. But, due to the anisotropy, the short line sources generated by cylindrical lenses are insufficient for reliable determination of the phase velocity. In this paper, a long line source is approximated by a set of linearly arranged point sources. As it follows from the differential geometry of ray surfaces, information obtained from such set of sources is sufficient for determination of phase velocities of both the quasi-transverse and the quasi-longitudinal modes of propagation. Moreover, this approach can be generalized for any arbitrary set of point sources only by employing a proper time-base transformation. The applicability of the presented approaches is illustrated on transversely isotropic and tetragonal fibrous composite materials.