Complex dispersion analysis of true and pseudo surface waves propagating in two-dimensional viscoelastic seismic metamaterials

In this paper, the wave characteristics of true surface waves (TSWs) and pseudo surface waves (PSWs) in two-dimensional (2D) seismic metamaterials are explored. The 2D seismic metamaterial is formed by placing periodic concrete pillars on the surface of the soil substrate. The complex dispersion curves of the seismic metamaterial are numerically calculated by the ω–kapproach. The Kelvin–Voigt model is adopted to describe the material viscoelasticity. The results show that not only the TSW modes but also the PSW modes should be taken into account to evaluate the mitigation capacity of the seismic metamaterials. Due to the introduction of material viscoelasticity, the TSWs and PSWs convert from the propagative mode to the evanescent mode. When the PSW modes propagate along the substrate surface, their energy gradually leaks into the bulk of the substrate, leading to their transmission coefficient smaller than that of the TSW modes. Compared to the concrete pillars on the substrate surface, the viscoelasticity of the soil substrate plays a more important role in surface wave reduction. Moreover, the wave propagating length in the seismic metamaterials can be predicted by using complex dispersion relations.