Near-threshold effects of the scattering of waves in a distorted elastic two-dimensional waveguide

Near-threshold effects of the almost total reflection or transmission of elastic waves in a two-dimensional strip-waveguide with a locally perturbed rigidly clamped surface are described using an asymptotic analysis. The quantitative characteristics of the scattering depend on a unitary and symmetric scattering matrix at the threshold and, in particular, are determined by the presence or absence of bounded solutions at the cutoff frequency.