Locally resonant metasurfaces for shear waves in granular media

In this paper, the physics of horizontally polarized shear waves traveling across a locally resonant metasurface in an unconsolidated granular medium is experimentally and numerically explored. The metasurface is comprised of an arrangement of subwavelength horizontal mechanical resonators embedded in a granular layer made of silica microbeads. The metasurface supports a frequency-tailorable attenuation zone induced by the translational mode of the resonators. The experimental and numerical findings reveal that the metasurface not only backscatters part of the energy but also redirects the wave front underneath the resonators, leading to a considerable amplitude attenuation at the surface level, when all the resonators have similar resonant frequency. A more complex picture emerges when using resonators arranged in a so-called graded design, e.g., with a resonant frequency increasing or decreasing throughout the metasurface. Unlike the mechanism observed in a bilayered medium, shear waves localized at the surface of the granular material are not converted into bulk waves. Although a detachment from the surface occurs, the depth-dependent velocity profile of the granular medium prevents the mode conversion and the horizontally polarized shear wave front returns to the surface. The outcomes of our experimental and numerical studies allow for understanding the dynamics of wave propagation in resonant metamaterials embedded in vertically inhomogeneous soils and, therefore, may be valuable for improving the design of engineered devices for ground-vibration and seismic wave containment.