Surface wave attenuation by periodic hollow steel trenches with Bragg band gap and local resonance band gap

The use of phononic crystals and elastic metamaterials has been a significant concern as an efficient approach to attenuate the surface waves of ambient vibration and seismic vibration. In previous research, elastic metamaterials with periodic array of pillars or other forms of standing structures (such as H-fractal steel or built-up structural steel) erected on soil substrate can achieve a low frequency surface wave band gap (BG). However, such metamaterials with standing structures occupy land and affect the esthetics of cities, and buried metamaterials such as cross-like-cavity or hollow-cylinder structures with large size in soils necessitate continual maintenance for the stability of cavity soil structure. Thus, this study proposes two types of periodic hollow steel trenches exhibiting both a Bragg BG and a local resonance BG, the steel plates are used to support the soil on both sides of the trench to meet the stability requirements of cavity soil structure and avoid toppling or landslide of soils. The dispersion relations of periodic hollow steel trenches are calculated by using finite element method and the mechanism of generation for two kinds of BGs are interpreted by the eigenmodes. Furthermore, the effectiveness of periodic hollow steel trenches on isolating surface waves within the BGs is demonstrated in both frequency domain and time domain analysis. Several significant geometrical and material parameters on BGs that can affect the BG are studied as well. This study provides a new approach using the coupling effects of Bragg BG and local resonance BG to simultaneously attenuate the surface waves induced by the ambient and seismic vibration in a more practical way.