Periodic in-filled pipes embedded in semi-infinite space as seismic metamaterials for filtering ultra-low-frequency surface waves

Abstract

The use of artificial periodic structures such as periodic wave barriers and seismic metamaterials has attracted attention as an effective approach to reduce the impact of ambient vibrations or earthquakes. In previous research, a large amount of steel was usually used in the design of seismic metamaterials to achieve ultra-low surface wave band gaps (BGs). However, the use of such large amounts of steel is inconvenient and expensive in practical engineering applications. To address this issue, this study considered the use of common building materials, namely, concrete, rubber, and soil, for the preparation of seismic metamaterials. Using these three materials, a one-dimensional (1D) seismic metamaterial composed of periodic in-filled pipes and a substrate was proposed. Ultra-low surface wave BGs (0–10 Hz) of the seismic metamaterial were identified using the sound cone method. Several important geometrical and material parameters that could influence the BGs were studied. Based on the 1D metamaterial, a 2D seismic metamaterial with a complete ultra-low BG was proposed to filter Rayleigh waves at any angle in the surface plane. The screening effectiveness of the 1D and 2D seismic metamaterials was evaluated using 2D and 3D numerical models, respectively. The results show that the ultra-low BG width decreases with an increase in the distance between two adjacent in-filled pipes. The small height of the in-filled pipe is beneficial for achieving a large ultra-low BG. A high elastic modulus and a low mass density of the soft filling material correspond to a large ultra-low BG width. The generation of ultra-low BGs in both 1D and 2D seismic metamaterials is attributed to the torsional resonance of the filling soft material. This study can serve as a reference for the design of new seismic metamaterials with practical value in engineering.