Radial Seismic Metamaterials Based on Layering Theory: Broadband Shielding of Ultra-Low Frequency Seismic Surface Waves

Abstract

In this paper, a novel radial seismic metamaterial (LRSM) based on layering theory is proposed. Compared with traditional seismic metamaterials, the structure of LRSM is a periodic array of multi-layer rings distributed along the radial direction. By using the finite element method, the dispersion relationship and displacement vector field of LRSM with different layers are studied, and the influence of structural geometric parameters and circumferential continuity on the band gap characteristics of LRSM is discussed. The frequency domain analysis of finite periodic structure and the three-dimensional transient wave propagation analysis are carried out. The results show that the LRSM has ultra-low frequency broadband characteristics, which is produced by the coupling between the local resonance of the LRSM and the surface wave mode. Comparing three LRSMs with different layers, the initial frequency and bandwidth do not change monotonically with the increase of the number of layers. There is an optimal bandgap characteristic in two layers, and the relative bandwidth can reach 83.9%. The increase of the number causes the change of the structural stiffness, which is caused by the change of the local resonance strength. The position and width of the band gap in the LRSM are very sensitive to the height of the structure. The increase of the height of the LRSM can move the first band gap to the low frequency, and the total bandwidth increases, which is mainly caused by the increase of the equivalent mass of the system with the increase of the height of the structure. Further, it is verified that LRSM can effectively attenuate seismic surface waves of 0.1–20 Hz, and its maximum amplitude attenuation can exceed 85%. The novel periodic structure proposed in this paper can provide new options for the fields of earthquake and low-frequency vibration reduction.