Dispersion Curves for Guided Elastic Waves in Multilayered Anisotropic Media Generated with the Spectral Method

Guided waves are now well established in NDE and there is ongoing research interest in guided waves for many applications so it is important to have reliable and accurate information about the waves and modes that can be propagated in a chosen waveguide structure. Valuable information is provided by the dispersion curves of different modes within various combinations of geometries and materials. However, the approach normally used to find them, root-finding methods, can suffer from certain limitations concerning geometry, type of material, ill-conditioning of the matrix used to derive the dispersion relation, the well-known "large-fd" problem and incomplete solutions (missing modes). In this paper we extend the Spectral Method, previously and successfully used in simple waveguide cases, to handle more complicated waveguide problems and show that all the above pitfalls and limitations are overcome by using this approach. All the cases presented deal with anisotropic homogeneous perfectly elastic materials in flat and cylindrical geometry. We also address the problem of multi-layered systems with both solid and fluid layers.