Locally resonant metamaterials for controlling seismic Love waves

In this work, we discuss the possibility of designing a resonant layer to effectively attenuate the propagation of seismic Love waves. To do so, we consider a medium comprising a resonant layer of arbitrary thickness made of locally resonant metamaterials placed over an isotropic and homogeneous half-space. The resonant layer is made of several rows of mechanical resonators embedded within the soil medium. Each row includes an array of periodically distributed resonators with dimensions much smaller than the wavelength of Love waves in the frequency range of interest. We exploit a homogenization technique to estimate the effective parameters of the resonant layer, which are valid in the long-wavelength regime. We then derive the dispersion law of Love waves traveling within the homogenized equivalent resonant layer. The dynamic interaction between the Love waves and the resonant layer yields a low-frequency bandgap stemming from the local resonance mechanism of the embedded resonators. Within this specific frequency range, the propagation of Love waves is prevented. Furthermore, we design meter-size resonators based on the derived dispersion relation to attenuate the propagation of Love waves in the frequency range relevant to ground-borne vibration isolation applications. Finally, we perform a parametric study to investigate the effect of the design parameters of the resonators on the extension of the bandgap frequency range.