Rayleigh Wave Attenuation by a Nonlinear Metasurface with Both Vertical and Horizontal Resonators

Abstract

It is well known that earthquakes are one of the most catastrophic geological disasters. In recent years, the use of metasurfaces to suppress the propagation of seismic surface waves to protect surface buildings has received extensive attention. However, most of the previous research works are on linear metasurfaces and the effect of vertical resonators. In this work, we propose a nonlinear metasurface, which consists of a linear elastic semi-infinite space with vertical nonlinear and horizontal linear resonators attached to its top surface. Our study shows that the interaction between the dynamics of the resonators and the waves of the semi-infinite space creates a hybrid Rayleigh wave propagating along the surface. First, the dispersion of the hybrid Rayleigh wave is derived analytically. Then, numerical calculations are conducted and the effect of the coupling of the vertical and horizontal resonators on the dispersion is discussed. Afterward, a finite-element simulation is performed to verify the analytical predictions. The results demonstrate that an ultra-wide bandgap for the hybrid Rayleigh wave can be achieved by the designed nonlinear metasurface. This work may help promote the application of metasurfaces in the field of earthquake protection.