A novel multi-frequency inerter-based resonant seismic metamaterials for attenuating vertical shear waves in nonlinear multi-layered soils

Seismic metamaterials effectively divert surface waves, but their use in attenuating vertically propagating shear waves is less explored. This study proposes a novel multi-frequency inerter-based resonant seismic metamaterial configuration to attenuate the waves in multi-layered soil. The seismic metamaterial designs incorporate inerters to create a broad attenuation zone at low frequencies. Both linear and nonlinear soil behaviours are investigated to compare the effectiveness of the proposed seismic metamaterial. Finite element analyses are conducted in the frequency and time domains, using the Christchurch Central Business District, New Zealand soil profile as an example. Results reveal that tuning inerterbased resonators to align with the characteristic frequencies of soils reduces the transmission of vertically propagating shear waves, protecting overlying buildings from seismic excitation. The proposed inerter-based resonant seismic metamaterial configuration demonstrates effective attenuation of acceleration amplitudes across a broad frequency range (1-5 Hz), with the peak ground acceleration reduced by about 40%. The proposed design, based on the natural frequencies of soils, advances the seismic metamaterials field and offers a practical approach for enhancing the seismic resilience of structures in earthquake-prone regions. Overall, this study introduces a novel multi-frequency inerter-based resonant seismic metamaterial, in which adjacent unit cells are tuned to distinct resonance frequencies to broaden attenuation band, and provides the numerical investigation under vertically propagating shear waves in a multi-layered profile, quantifying how soil nonlinearity and site frequency shifts influence resonator effectiveness.