Rayleigh waves bandgap tuning via inertial amplified metasurfaces

Elastic metasurfaces are thin interfaces composed of locally resonant structures placed at the free surface or across the boundaries of elastic waveguides. The units which form this interface have sub-wavelength feature size and exploit their resonances to manipulate the dispersive properties of the hosting medium. When metasurfaces are constructed over an elastic half-space, they can be used to control the propagation of Surface Acoustic Waves. In particular, the collective resonant modes of the metasurface can open narrow bandgaps in the spectrum of Rayleigh Waves, which are filtered out as shear modes propagating in the medium bulk. One of the current limitations in the exploitation of such resonant band gaps is the need for large masses to widen their bandwidth. To overcome this drawback, we here investigate the possibility of designing an inertial amplified mechanism able to tune the natural frequency of the metasurface resonators. Our resonant unit exploits two lateral inerters, i.e., kinematical devices made by two inclined rigid links connected to an additional mass to modify the inertia of the resonator. After discussing the dynamic of the proposed resonator, here named as the Inertial Amplification Resonator (IAR), we unveil the properties of a metasurface composed by an array of IARs. By employing an effective medium approach, we investigate the interaction between Rayleigh waves and the metasurface deriving its closed-form analytical dispersion law. We show that the dynamic response of inertially amplified metasurfaces can be controlled by the added mass and geometrical configuration of the IARs and highlight the possibility of shifting the bandgap spectrum of the metasurfaces by modifying their design parameters without changing the mass and stiffness of the oscillators. We take advantage of the tunability feature of inertially amplified metasurfaces for designing multi-frequency (metawedges) metasurfaces to achieve broadband attenuation of Rayleigh waves. We analyze the transmission performance of the metasurface using 2D FE simulations and confirm the analytical predictions.