Wave scattering by plate array metacylinders of arbitrary cross-section

Metastructures composed of a closely spaced plate array have been widely used in bespoke manipulation of waves in contexts of acoustics, electromagnetics, elasticity and water waves. This paper focuses on wave scattering by discrete plate array metastructures of arbitrary cross-sections, including isolated vertical metacylinders, periodic arrays and horizontal surface-piercing metacylinders. A suitable transform-based method has been applied to each problem to reduce the influence of barriers in a two-dimensional problem to a set of points in a one-dimensional wave equation wherein the solution is constructed using a corresponding Green's function. A key difference from the existing work is the use of an exact description of the plate array rather than an effective medium approximation, enabling the exploration of wave frequencies above resonance where homogenisation models fail but where the most intriguing physical findings are unravelled. The new findings are particularly notable for graded plate array metastructures that produce a dense spectrum of resonant frequencies, leading to broadband 'rainbow reflection' effects. This study provides new ideas for the design of structures for the bespoke control of waves with the potential for innovative solutions to coastal protection schemes or wave energy converters.