  We study the propagation of elastic waves in the time-harmonic regime in a
waveguide which is unbounded in one direction and bounded in the two other
(transverse) directions. We assume that the waveguide is thin in one of these
transverse directions, which leads us to consider a Kirchhoff-Love plate model
in a locally perturbed 2D strip. For time harmonic scattering problems in
unbounded domains, well-posedness does not hold in a classical setting and it
is necessary to prescribe the behaviour of the solution at infinity. This is
challenging for the model that we consider and constitutes our main
contribution. Two types of boundary conditions are considered: either the strip
is simply supported or the strip is clamped. The two boundary conditions are
treated with two different methods. For the simply supported problem, the
analysis is based on a result of Hilbert basis in the transverse section. For
the clamped problem, this property does not hold. Instead we adopt the
Kondratiev's approach, based on the use of the Fourier transform in the
unbounded direction, together with techniques of weighted Sobolev spaces with
detached asymptotics. After introducing radiation conditions, the corresponding
scattering problems are shown to be well-posed in the Fredholm sense. We also
show that the solutions are the physical (outgoing) solutions in the sense of
the limiting absorption principle.
