On the zero frequency bandgap of seismic metamaterials

Abstract

Seismic metamaterials are artificially designed materials within the sub-wavelength range, developed to attenuate low-frequency seismic surface waves. Previous studies revealed that through proper design, a zero-frequency bandgap (ZFBG) can be formed. However, the underlying mechanism for forming the ZFBG has not been well explained so far. Many existing studies attributed it to the collective behavior of the individual unit cells within the metamaterial. In this work, we clarify that the ZFBG is not exclusive to metamaterials. We investigate the mechanism of ZFBG by revisiting two typical designs: clamped barriers and resonant meta-barriers. Through analytical and numerical analyses, we claim that the ZFBG of the former design lies in the cut-off frequency originating from the rigid boundary condition, while the latter design is due to an intrinsic property of having a stiff upper layer atop a soft half-space, which cannot support low-order surface wave modes. This work corrects a misconception in this field and thus could facilitate the understanding, design, and implementation of seismic metamaterials.