Finite element computation of leaky modes in stratified waveguides

Using guided waves can greatly facilitate the inspection of large structures such as pipes or plates. One can wonder if it remains possible for waveguides which are embedded in an elastic matrix. For NDT, guided modes could be replaced by the so-called ”leaky modes”: these modes are attenuated in the axial direction while they increase exponentially in the transverse ones. We are interested here in the finite element computation of leaky modes. The difficulty comes precisely from this exponential behaviour, which prevents us from simply truncating the infinite medium. This is the reason why we use Perfectly Matched layers (PMLs) in order to bound the domain of calculation. We checked this approach in the simple case of SH waves in a stratified waveguide, where the analytic dispersion relation is available. Numerical experiments show that the main parameter is the distance between the PML and the guide. Finally, we illustrate in this simple case a numerical application using leaky modes: the Green function of the embedded waveguide is given by modal expansion.