Radial Gradient Seismic Metamaterials with Ultra-Low Frequency and Ultra-Wide Band Gap

Abstract

In this paper, a radial gradient seismic metamaterial (RGSM) is proposed. The structural unit cell is composed of an external square soil embedded with a triangular-cross-sectioned steel ring, which is filled at different angles of multiple steel rings to form a supercell. The dispersion curve and attenuation spectrum of the unit cell are calculated by the finite element method, and the opening mechanism of the band gap is explained by analyzing the modes at the band gap boundary. The influence of geometric parameters and material parameters on the band gap is further studied, and the optimized supercell radial gradient seismic metamaterial (OS-RGSM) structure is designed through structure and parameter optimization. The ultra-low broadband excellent band gap in the range of 2.35–20 Hz for seismic Lamb waves is realized, and its three-dimensional frequency response and displacement field diagram are calculated. In addition, the attenuation characteristics of the optimized supercell seismic metamaterial on the seismic surface wave are calculated and analyzed. It is found that the attenuation can reach more than 50% in the ultra-low frequency range of 3.5–9 Hz. The seismic wave barrier is verified by the vibration transmission characteristics of RGSM under finite period and dynamic time history analysis. The results show that RGSM can effectively shield from seismic Lamb waves in the ultra-wideband with the starting frequency of 2.35 Hz and can also effectively attenuate the seismic surface wave in semi-infinite space.