A surface-wave seismic metamaterial filled with auxetic foam

Auxetic materials with negative Poisson's ratio (PR) exhibit superior mechanical properties with regard to energy absorption, while their potential for surface wave shielding is only in its beginnings. To attenuate surface waves in ultra-low frequencies (the starting frequency close to 0 Hz), which is the main scope of concern in seismic protection, this paper presents a novel type of seismic metamaterial (SM) with square pillars embedded as vibrators that is filled by auxetic foam. The designed SM is comprised of three commonly used construction materials, i.e., soil, concrete and auxetic foam. Combining the dispersive analysis and sound cone method, an ultra-low-frequency bandgap from 0 to 16.42 Hz is opened via the tensile resonance of the auxetic foam and the inverse dispersion effect. Furthermore, the parametric analysis further shows that filling material with a low Poisson ratio and low mass density is more favorable to widening the first complete bandgap (FCB), which means that foam is the ideal filling material for SM. The transmission spectra of the corresponding finite samples coincide well with the bandgap calculations. And the dynamic response of a scaled-down setup with a characteristic size of 1/10 of the original metamaterial is experimentally tested to validate the effectiveness of our study. We expect that this study prompts the engineering application of auxetic materials and ordinary building materials in seismic wave shielding at deep sub-wavelength frequencies.