Attenuation mechanism of Rayleigh waves by elastic metasurfaces in various layered half-spaces

Abstract

To comprehensively investigate the wave attenuation mechanisms of elastic metasurfaces in top-soft bottom-hard and top-hard bottom-soft layered half-spaces, we propose a general analytical framework combining the thin-layer method and effective medium theory to describe the interaction between Rayleigh waves and elastic metasurfaces. The results show that elastic metasurfaces exhibit different attenuation and mitigation effects in the two types of half-spaces. Specifically, in top-soft bottom-hard scenario, the first-order Rayleigh wave mode dominates surface energy propagation, and the elastic metasurfaces couples with it to attenuate surface energy. However, at the resonant frequency, higher-order modes carrying part surface energy persist, preventing effective isolation of surface energy. The overlying layer thickness affects the number of higher-order modes involved in propagation, which exhibits different wavefield characteristics and influences the attenuation effect. In top-hard bottom-soft scenario, the higher-order leaky Rayleigh wave modes dominate the surface energy, accompanied by energy leakage into the bulk. The elastic metasurfaces amplify their leakage effects, causing significant Rayleigh-to-bulk wave conversion and vibration reduction, even in the absence of a bandgap. Notably, elastic metasurfaces may induce vibration amplification at frequencies below the resonant frequency, which requires careful consideration during design. This framework offers valuable insights for designing elastic metasurfaces to mitigate vibration in practical layered foundations.