A resonant metasurface for Love waves

Elastic metamaterials comprise a broad class of artificially engineered media designed to control the propagation of elastic waves at sub-wavelength scales. This unique ability stems from the presence of resonant inclusions embedded in an elastic matrix which affect the wave propagation at specific frequency ranges. Elastic metasurfaces are a special class of metamaterials, realized by arranging an array of resonant structures at the free surface of the medium or at an interface between two media. Metasurfaces of vertical resonators over an elastic half-space have been successfully utilized to control the propagation of in-plane surface waves, i.e., Rayleigh waves, for various applications across different length scales, as waveguiding or wave filtering. In this talk, we present an extension of the metasurface concept to Love waves, anti-plane surface waves existing in semi-infinite layered media. We investigate the interaction between Love waves and a metasurface of horizontal oscillators deriving an original analytical solution for its dispersion relation. By tuning the mass and the frequency of the resonators we achieve full control of the Love wave phase velocity, and thus on the related metasurface refractive index. We exploit the ability to manipulate the metasurface refractive index to design gradient index lenses (i,e. Luneburg and Maxwell lenses) for Love waves redirection. We analyse the performance of the designed lenses using full 3D FE simulations confirming the analytical predictions. Our work can serve as a guide for advanced Love wave-based devices and sensors as well as for the design of meter-scale barriers for low-frequency vibrations attenuation.