A radial seismic metamaterial filled with auxetic foam for filtering low-frequency Lamb waves and surface waves

This study presents a novel radial seismic metamaterial (RSM) based on auxetic foam, which can achieve omnidirectional ultra-low-frequency suppression of Lamb waves in the range of 0.97 to 21.04 Hz and effectively shield omnidirectional surface waves within 10 Hz. Firstly, the Finite Element method is utilized to investigate the bandgap (BG) characteristics and vibration modes, which shows that the BG can be significantly widened by utilizing the local resonance of the auxetic foam. Subsequently, a three-dimensional radial periodic structure is constructed and the displacement fields of Lamb waves are analyzed in the frequency and time domains. The simulation results demonstrate that the proposed RSM can effectively attenuate Lamb waves. Parametric analysis indicates that filling auxetic foam with a high elastic modulus, low Poisson’s ratio, and low mass density can further expand the BG. For surface waves, the band structure is first analyzed using the acoustic cone method. Furthermore, a radial periodic structure consisting of the RSM cells is analyzed in the frequency domain, and a significant attenuation is observed within the BG. The attenuation capability of the designed RSM is further tested against real seismic wave signals, and a satisfactory shielding effect for low-frequency signals is achieved within 10 Hz. The designed RSM provides new insights into the development of SMs, exhibiting the superior application potential of auxetic foam for seismic wave shielding.