A numerical method for the scattering by defects in axisymmetrical open elastic waveguides

Guided wave modes can provide precise physical analyses of scattering phenomena. When the structure is surrounded by an infinite medium (open waveguide), the unboundedness of the transverse direction greatly complicates the numerical resolution of the problem and its analysis. Theoretically, the wave field can be obtained through modal expansion on trapped modes and on two continua of radiation modes. The latter are sometimes approximated by a discrete sum over leaky modes. However, leaky modes grow at infinity in the transverse direction and hence can approximate the wave fields only in a spatially limited region. A perfectly matched layer (PML) enables to reveal leaky modes in the modal basis and defines two continua of PML modes, discretized by the truncation of the PML. In this paper, the scattering properties of the modes of an elastic axisymmetric open waveguide are investigated with a hybrid method. The semi-analytical finite element (SAFE) method is combined with a PML and then coupled to a FE-PML computation around the inhomogeneity. The hybrid method is validated against literature results for the scattering of a guided wave at the junction between a closed and an open waveguide. Then, the diffraction of a high-frequency leaky mode by a notch is presented