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### Leakage of Guided Waves in Embedded Waveguides of Arbitrary Cross Section

#### Abstract

A mathematical formulation is presented to compute the dispersion characteristics of waveguides with arbitrary shape and mechanical characteristics that are surrounded by infinite isotropic viscoelastic media. The propagation problem in the embedded waveguide is described via a Semi- Analytical Finite Element (SAFE) formulation, while a regularized 2.5D Boundary Element Method (BEM) is used to represent the radiation problem in the surrounding medium. The wave dispersive equation is obtained by imposing continuity and equilibrium conditions at the SAFE-BEM interface, resulting in a nonlinear eigenvalue problem. The generalized Snell-Descartes law is then enforced as additional constraint at the interface to determine the correct phase of the transverse wavenumbers. Complex poles relative to physical leaky and trapped guided modes are searched by means of a contour integral algorithm. Two cases are presented: a circular steel bar embedded in grout, for which results are available in literature, and a H-shaped steel beam embedded in soil.