Attenuation of ultra-low frequency surface waves by an embedded hollow hourglass-shaped seismic metamaterial

Abstract Seismic surface waves pose one of the primary threats to human life and property safety during earthquakes. In this work, we propose an embedded hollow hourglass-shaped seismic metamaterial (EHH-SM), comprising a core with symmetrically arranged hollow hourglass structures and a perforated substrate, as well as an outer shell composed of a thin concrete layer. By combining theoretical analysis and finite element simulations, the band structures and vibration modes of the proposed seismic metamaterial were first calculated, and its bandgap frequency range was discussed through geometric and material parameter analyses. The results demonstrate that the reasonable design can achieve ultra-low frequency locally resonant bandgaps below 10 Hz. Furthermore, from an engineering perspective, we conducted frequency-domain simulations on finite periodic configurations of the metamaterial and investigated the vibration isolation performance of gradient-designed seismic metamaterials under both positive and negative gradient propagation directions. Finally, the shielding performance of the metamaterial against real seismic waves was verified through time-domain analysis. This study aims to effectively block ultra-low frequency seismic surface waves from damaging large-scale infrastructure, offering theoretical support and innovative directions for seismic hazard mitigation.