Resonant metasurfaces for the mitigation of elastic wave propagation

The guided propagation of planar shear-horizontal (SH) waves in a linear elastic plate coated on the external surfaces with identical resonant layers is investigated. The plate is modeled as a finite-thickness nondissipative homogeneous Cauchy solid, while the resonant layers are represented by continuous distributions of spring–mass oscillators. The field equations governing the plate dynamics are complemented with time-dependent boundary conditions coupling the resonant layer oscillations with the superficial plate displacements. By applying the partial wave technique, the dispersion relation governing the harmonic wave propagation is achieved. The symmetry of the dynamic problem separates the spectrum into symmetric and antisymmetric solutions for the propagating waveforms. The resonant layers generate extra low-frequency branches, and complete bandgaps for suitable resonator parameters. Time-domain finite-element simulations of a finite coated region validate the dispersion predictions, confirming strong attenuation of transmitted SH waves for propagating signals whose frequency falls within the bandgap, as well as redistribution of motion between the plate and resonant layers.