A Rubber-Embedded Subwavelength Seismic Metamaterial with a Wide Low-Frequency Bandgap

This study introduces a novel underground subwavelength seismic metamaterial (SM) designed to attenuate ultra-low-frequency surface waves. The SM comprises a three-component column featuring rubber embedded within a steel resonator. Through calculations utilizing the Bloch theorem and the sound cone method, we investigate the dispersion relations and vibration modes of three distinct SM configurations. Our proposed rubber-embedded SM exhibits a wide bandgap (BG) and effectively attenuates surface Rayleigh waves within the frequency ranges of 1.19-1.31 Hz and 1.41-20 Hz, respectively. We elucidate the mechanism behind BG formation by analyzing vibration modes. Additionally, through numerical simulations in both frequency and time domains, we validate the attenuation capabilities of the SM system within the BG and observe the deflection phenomena of surface waves. We further simulate seismic wave propagation within the SMs. Comparative analysis of two-dimensional building frames, with and without SM protection, under realistic seismic waves demonstrates significant vibration attenuation and structural protection provided by SMs. We explore the impact of geometric and material parameters, as well as the number of SM layers, on BG frequency range, designing an optimal SM model with the widest BG. Finally, we calculate transmission spectra for two- and three-dimensional subwavelength SMs and evaluate their efficacy in Rayleigh wave attenuation.