Elastic metasurfaces for surface SH waves control

Elastic metasurfaces composed of arrays of subwavelength mechanical oscillators located at the free surface of an elastic medium have been proposed to manipulate the propagation of surface waves at diverse length scales. In particular, metasurfaces of vertical resonators embedded in homogeneous elastic substrates can forbid the propagation of in-plane polarized waves, i.e., Rayleigh waves, generating band-gaps at specific frequencies. This ability has led to emergence of a new research area, which focuses on the design of meter-scale metasurfaces to shield buildings and infrastructures from undesired ground-borne vibrations. In this work, we investigate experimentally and numerically the interaction between a metasurface of horizontal resonators with polarized shear waves localized at the surface of a granular medium with an inhomogeneous depth-increasing elastic profile. A strong hybridization between the fundamental SH mode and the mechanical oscillators occurs and a frequency zone of quasi-zero displacements is found in proximity of the resonant frequency of the metasurface. Our outcomes reveal that SH waves, impinging the horizontal resonators, are steered downwards and channeled between the resonant boundary and the in-depth stiffer layers. Finally, we study the dynamic of these SH waves when traveling through a resonant metasurface of increasing frequency, shortly referred to as "inverse metawedge”. We numerically show how the stiffness gradient induced by gravity in granular substrates impedes the surface-to-shear wave-conversion phenomenon, preserving the wave localization at the surface