Elastic Waves in Homogeneous and Layered Transversely-Isotropic Media: Gaussian Wave Packets and Green Functions

Abstract

The increasing use of composites and composite laminates requires extensive efforts in developing NDE methods for these sophisticated materials. The main problem, especially with respect to algorithmic imaging, arises from their anisotropic nature which causes the splitting of phase-and group velocity directions. Therefore the inverse scattering theory established for acoustic [1] or isotropic materials [2] does not sufficiently describe wave propagation and imaging in composites. In layered structures additional difficulties are associated with multiple reflection and transmission. Hence, for transversely-isotropic materials such as fiber-reinforced composites, we first discuss plane wave solutions of the elastodynamic equation of motion yielding slowness-and group velocity diagrams, using a coordinate-free approach as given in [3] for the electromagnetic case and in [4] for the isotropic case. The propagation of Gaussian wave packets in unidirectional homogeneous and layered structures is then calculated for arbitrary layer orientations; the results are shown as time domain wavefront snapshots. Finally, an integral representation of Green’s functions for the transversely-isotropic medium is given via spatial Fourier-transforms, being particularly convenient to provide the basis for imaging in terms of Diffraction Tomography [1]. All results are given for arbitrary fiber direction.