A multiple scattering formulation for finite-size flexural metasurfaces

We provide an analytical formulation to model the propagation of elastic waves in a homogeneous half-space supporting an array of thin plates. The technique provides the displacement field obtained from the interaction between an incident wave generated by a harmonic source and the scattered fields induced by the flexural motion of the plates. The scattered field generated by each plate is calculated using an ad-hoc set of Green's functions. The interaction between the incident field and the scattered fields is modelled through a multiple scattering formulation. Owing to the introduction of the multiple scattering formalism, the proposed technique can handle a generic set of plates arbitrarily arranged on the half-space surface. The method is validated via comparison with finite element simulations considering Rayleigh waves interacting with a single and a collection of thin plates. Our framework can be used to investigate the interaction of vertically polarized surface waves and flexural resonators in different engineering contexts, from the design of novel surface acoustic wave devices to the interpretation of urban vibration problems.