Seismic surface wave attenuation by resonant metasurfaces on stratified soil

Abstract

This study aims to theoretically and numerically investigate the dispersion relations of Rayleigh waves propagating through vertical oscillators periodically distributed on stratified media. The classical elastodynamics theory and an effective medium approximation method are adopted to describe the dynamic behavior of metasurfaces and hybridization between the local oscillators and the foundational surface wave modes. The Abo-zena algorithm and delta-matrix method are combined to simplify the Eigen equation to overcome the accuracy problem in solving the closed-form dispersion laws and improve the computational efficiency. Subsequently, plane-strain finite element (FE) models with three configurations are developed to confirm the analytical predictions and obtain further insight into the resonator-Rayleigh wave coupling mechanism. The numerical results are in good agreement with the analytical solutions, revealing that only the foundational mode is strongly coupled with the vertical resonators at resonance, while the surface wave band gap reported in homogeneous media is crossed by the remaining higher-order surface modes. The attenuation performance and mechanical behavior of a finite-length metasurface are investigated, and it is demonstrated that the output surface ground motion can be significantly reduced in a narrow frequency band near resonance. Moreover, a graded resonant metasurface with decreasing frequency is simulated to assess the feasibility of broadband attenuation. In summary, the aforementioned analytical framework and numerical simulation results show that the vertical oscillators placed atop a stratified soil system can be designed as resonant metasurfaces for shielding seismic surface waves to protect multiple large infrastructures or special structures from earthquake hazards.

Current developments in elastic and acoustic metamaterials science

“…Indeed, thanks to local resonance, elastic metasurfaces can be designed at the sub-wavelength scale, with applications encompassing sensing and energy harvesting [154], sound absorption [155,156], non-destructive evaluation [157]; spatial modulation of the resonant frequencies in elastic metasurfaces can induce wave focusing [158,159], rainbow trapping [160][161][162], mode conversion [163,164]. Moreover, elastic metasurfaces can be devised for seismic isolation and vibration mitigation [92,93,[165][166][167][168] at the geophysical scale. In this framework, two contributions are included in the theme issue regarding the design of periodic wave barriers (PWBs), which are large-scale phononic structures intended to mitigate ground vibrations from various sources.…”

Vibration mitigation using seismic metamaterials on layered soil

“…As a result, body waves are partially reflected at layer interfaces, propagating toward the surface of the soil. This hinders the surface-to-shear conversion evoked by inverse metawedges in a homogeneous medium [8]. Results considering 2D uniform and graded metasurfaces on layered soils were recently provided [9,10].…”

Elastic metasurfaces for Scholte–Stoneley wave control

“…These structures, often referred to as elastic metasurfaces, allow the control of surface waves at a very small sub-wavelength scale, thanks to the hybridization of propagating waves with local resonance [2,3]. Notable applications include seismic isolation [3][4][5][6][7], sound absorbing [8,9], radio-frequency signal processing [10,11], imaging [12], non-destructive evaluation [13], sensing and energy harvesting [14]. More recently, elastic metasurfaces have been investigated considering spatial or temporal modulations.…”