Locally resonant metasurfaces for shear waves in granular media

TL;DR

This paper investigates how locally resonant metasurfaces embedded in granular media can control shear wave propagation, achieving attenuation and wavefront redirection, with potential applications in seismic wave mitigation.

Contribution

It introduces a novel metasurface design with sub-wavelength resonators that tailor shear wave behavior in granular media, including graded configurations that prevent mode conversion.

Findings

Metasurfaces induce frequency-dependent attenuation zones.

Resonator arrangements redirect wavefronts and reduce surface amplitudes.

Graded resonator designs prevent shear wave mode conversion.

Abstract

In this article the physics of horizontally polarized shear waves travelling across a locally resonant metasurface in an unconsolidated granular medium is experimentally and numerically explored. The metasurface is comprised of an arrangement of sub-wavelength horizontal mechanical resonators embedded in 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 wavefront 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/decreasing throughout the metasurface. Unlike Love waves propagating in a bi-layer medium, shear waves localized at the surface of our metasurface 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, steering again the horizontally polarized shear waves towards 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, are essential for improving the design of engineered devices for ground vibration and seismic wave containment.