Abstract
Structural vibration induced by low frequency elastic waves presents a great threat to infrastructure such as buildings, bridges, and nuclear structures. In order to reduce the damage of low frequency structural vibration, researchers proposed the structure of seismic metamaterial, which can be used to block the propagation of low frequency elastic wave by adjusting the frequency range of elastic wave propagation. In this study, based on the concept of phononic crystal, a ternary seismic metamaterial is proposed to attenuate low frequency vibration by generating band gaps. The proposed metamaterial structure is periodically arranged by cube units, which consist of rubber coating, steel scatter, and soft matrix (like soil). The finite element analysis shows that the proposed metamaterial structure has a low frequency band gap with 8.5 Hz bandwidth in the range of 0–20 Hz, which demonstrates that the metamaterial can block the elastic waves propagation in a fairly wide frequency range within 0–20 Hz. The frequency response analysis demonstrates that the proposed metamaterial can effectively attenuate the low frequency vibration. A simplified equivalent mass–spring model is further proposed to analyze the band gap range which agrees well with the finite element results. This model provides a more convenient method to calculate the band gap range. Combining the proposed equivalent mass–spring model with finite element analysis, the effect of material parameters and geometric parameters on the band gap characteristic is investigated. This study can provide new insights for low frequency vibration attenuation.
Highlights
Transportation, construction, or earthquakes can induce the propagation of low frequency elastic waves near structures [1]
It is worth noting that the total width of the omnidirectional band gaps below 20 Hz reaches 8.524 Hz, accounting for 42.6% of the range of 0–20 Hz, which means that the proposed metamaterial structure can block the elastic waves propagation in a fairly wide frequency range within 0–20 Hz
We investigate the band gap characteristic based on finite element method (FEM)
Summary
Transportation, construction, or earthquakes can induce the propagation of low frequency elastic waves near structures [1]. The first large-scale outdoor experiment of seismic metamaterials is the low-frequency vibration attenuation experiment of the soil drilling array [30]. The finite element analysis methods are an important tool in obtaining the band gap and evaluating the vibration attenuation performance of seismic metamaterials. Based on the development of experiment methods and finite element analysis, many seismic metamaterials with lower band gap frequency were designed to attenuate the low-frequency vibration. Most of the above seismic metamaterials can block the low-frequency elastic waves below 20 Hz, the bandwidth of Materials 2022, 15, 1246 the band gap is not large enough. We proposed a ternary seismic metamaterial to attenuate low frequency vibration below 20 Hz. In Section 2, we present the structure model of the proposed metamaterial and the dispersion analysis for band gap calculation in finite element method (FEM).
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