Low-Frequency Surface Wave Attenuation of Multi Point Mass Resonance Metamaterials

Metamaterial isolated barriers can attenuate seismic waves and absorb the earthquake energy through the characteristic of the band gap. However, the traditional Bragg scatter foundation or local resonate barrier generally has shortcomings of narrow frequency band gap or large size. The purpose of this study is to investigate the attenuation effect of a new type of seismic metamaterial on low-frequency surface waves.

The paper proposes a multi-point mass resonance metamaterial (MRM) enclosed externally by steel plates and internally composed of four resonators. Each resonator consists of rubber columns embedded with four steel blocks. Firstly, theoretical derivation and frequency dispersion of the MRM were employed to obtain the band gap and frequency response. Subsequently, the influence of material parameters on the bandgap of the unit cell and the impact of structural arrangement on the filtering characteristics of metamaterial barriers were parametrically analyzed. Finally, a time-history analysis of metamaterial barriers was conducted using artificial waves and seismic waves.

The results indicate that MRM, owing to the local resonance effect, can produce a broader low-frequency bandgap, corresponding to the attenuation range of the frequency response. The elastic modulus of rubber, the density of steel blocks, and the number of filling layers on the bandgap have little effects on the attenuation of the seismic wave when the frequency falls outside of the bandgap. However, the number of columns, layers of the structure, and configuration of the barrier can significantly influence the attenuation effect of the MRM at high-frequency excitation. The proposed metamaterial structure exhibits an attenuation ratio of over 60% for both artificial and seismic waves within the bandgap and will not amplify seismic waves outside the bandgap. The research presented in this paper can provide valuable insights and references for designing seismic metamaterial structures with low-frequency wide bandgaps.