Seismic metamaterials for low-frequency mechanical wave attenuation

Abstract

In this study, a triangular array of cylindrical holes was shown to function as a local resonator to seismic metamaterials against the vibration generator loading in the geophysics concept. The field test showed that the seismic waves applied to one side of the proposed array interacted with the triangularly arranged holes, resulting in a strong attenuation in two narrow frequency bands. The numerical analysis was carried out using simulations based on the finite element method, which provides optimal dimensions and arrangement at a sub-wavelength scale to achieve maximum attenuation against incoming seismic wave at a very low frequency range. Different band gaps were observed due to interaction of the longitudinal resonance between the cylindrical holes and vertical components of soil response under the applied wave. Experimental analysis was carried out using optimum dimensions and hole arrangements, and a strong attenuation due to impedance matching between soil and seismic metamaterials was shown. It was also observed that, at very low frequencies, the soil response was due to the inverse proportionality between the resonator length and the seismic energy wavelength applied for longitudinal resonance. Two band gaps have been observed around 25–36 Hz as shown in band diagram. The proposed structure exactly prevents the seismic wave propagation at 25 Hz and 36 Hz in accordance with band diagram. Therefore, the proposed system can prevent the seismic waves from attaining the backside of the seismic array. The attenuation was obtained at a level of 0.00125, observed at a 0.0001 source point, measured by a speed sensor located at the back of the seismic metamaterials, with an attenuation rate of 12.5 at 8 Hz.