A coupled SAFE-2.5D BEM approach for the dispersion analysis of damped leaky guided waves in embedded waveguides of arbitrary cross-section

The paper presents a Semi-Analytical Finite Element (SAFE) formulation coupled with a 2.5D Boundary Element Method (BEM) for the computation of the dispersion properties of viscoelastic waveguides with arbitrary cross-section and embedded in unbounded isotropic viscoelastic media. Attenuation of guided modes is described through the imaginary component of the axial wavenumbers, which accounts for material damping, introduced via linear viscoelastic constitutive relations, as well as energy loss due to radiation of bulk waves in the surrounding media. Energy radiation is accounted in the SAFE model by introducing an equivalent dynamic stiffness matrix for the surrounding medium, which is derived from a regularized 2.5D boundary element formulation. The resulting dispersive wave equation is configured as a nonlinear eigenvalue problem in the complex axial wavenumber. The eigenvalue problem is reduced to a linear one inside a chosen contour in the complex plane of the axial wavenumber by using a contour integral method. Leaky and evanescent poles are obtained by choosing appropriately the phase of the wavenumbers normal to the interface in compliance with the nature of the waves in the surrounding medium. Finally, the obtained eigensolutions are post-processed to compute the energy velocity and the radiated displacement wavefield in the surrounding domain. The reliability of the method is first validated on existing results for waveguides of circular cross section embedded in elastic and viscoelastic media. Next, the potential of the proposed numerical framework is shown by computing the dispersion properties for a square steel bar embedded in grout and for a H-shaped steel pile embedded in soil.