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We address the problem of scattering and transmission of a plane flexuralwave through a semi-infinite array of point scatterers/resonators, which take avariety of physically interesting forms. The mathematical model accounts forseveral classes of point defects, including mass-spring resonators attached tothe top surface of the flexural plate and their limiting case of concentratedpoint masses. We also analyse the special case of resonators attached toopposite faces of the plate. The problem is reduced to a functional equation ofthe Wiener-Hopf type, whose kernel varies with the type of scattererconsidered. A novel approach, which stems from the direct connection betweenthe kernel function of the semi-infinite system and the quasi-periodic Green'sfunctions for corresponding infinite systems, is used to identify specialfrequency regimes. We thereby demonstrate dynamically anisotropic wave effectsin semi-infinite platonic crystals, with particular attention paid to designingsystems to exhibit dynamic neutrality (perfect transmission) and localisationclose to the structured interface.

Controlling flexural waves in semi-infinite platonic crystals