  We address the problem of scattering and transmission of a plane flexural
wave through a semi-infinite array of point scatterers/resonators, which take a
variety of physically interesting forms. The mathematical model accounts for
several classes of point defects, including mass-spring resonators attached to
the top surface of the flexural plate and their limiting case of concentrated
point masses. We also analyse the special case of resonators attached to
opposite faces of the plate. The problem is reduced to a functional equation of
the Wiener-Hopf type, whose kernel varies with the type of scatterer
considered. A novel approach, which stems from the direct connection between
the kernel function of the semi-infinite system and the quasi-periodic Green's
functions for corresponding infinite systems, is used to identify special
frequency regimes. We thereby demonstrate dynamically anisotropic wave effects
in semi-infinite platonic crystals, with particular attention paid to designing
systems to exhibit dynamic neutrality (perfect transmission) and localisation
close to the structured interface.

Classical Physics;Analysis of PDEs