  We present a semi-analytical approach to compute quasi-guided elastic wave
modes in horizontally layered structures radiating into unbounded fluid or
solid media. This problem is of relevance, e.g., for the simulation of guided
ultrasound in embedded plate structures or seismic waves in soil layers over an
elastic half-space. We employ a semi-analytical formulation to describe the
layers, thus discretizing the thickness direction by means of finite elements.
For a free layer, this technique leads to a well-known quadratic eigenvalue
problem for the mode shapes and corresponding horizontal wavenumbers.
Rigorously incorporating the coupling conditions to account for the adjacent
half-spaces gives rise to additional terms that are nonlinear in the
wavenumber. We show that the resulting nonlinear eigenvalue problem can be cast
in the form of a multiparameter eigenvalue problem whose solutions represent
the wave numbers in the plate and in the half-spaces. The multiparameter
eigenvalue problem is solved numerically using recently developed algorithms.
