Propagation and attenuation of Rayleigh and pseudo surface waves in viscoelastic metamaterials

The development of seismic metamaterials has attracted much research interest in the past decade. Efforts have been made by using experimental and theoretical approaches to isolate buildings and structures susceptible to elastic surface wave damage. However, most seismic metamaterials were designed without considering the viscoelastic effect that widely exists in nature. In this work, we investigate the propagation and attenuation of the Rayleigh and pseudo surface waves (PSWs) in two types of viscoelastic seismic metamaterials, namely, pillared and inclusion-embedded metamaterials, by analyzing the complex band structures and transmission spectra. The complex band structure developed in this work reveals for the first time the existence of PSWs and their propagation properties in inclusion-embedded metamaterials at the surface. These PSW modes are hidden in the traditional omega (k) technique, therefore showing the usefulness of the complex band structure approach. Introducing viscosity to the substrate of both types of seismic metamaterials will enhance the attenuation of both the Rayleigh wave and PSW. For inclusion-embedded metamaterials, the viscoelastic effect in the soft coating layer can have a specific influence only on the PSW. PSWs show advantages to minimize the relative attenuating effect in general. The results in this work will open up great possibilities for designing and optimizing seismic metamaterials in practice.