Vibration Attenuation and Amplification of One-Dimensional Uncoupled and Coupled Systems with Optimal Metafoundations

Finite locally resonant metafoundations represent an innovative solution for structural seismic response mitigation based on their filtering capabilities at selected frequency ranges. They inherit the filtering properties of periodic foundations and bands in which response amplitudes are reduced, the so-called attenuation zones. Nonetheless, other bands of vibration-induced resonances amplify the components of superstructure response and are generally named nonattenuation zones. Both frequency bandwidths and amplification depend on the dynamic properties of metafoundations and superstructures as well as their coupling. Thus, in order to shed light on the mechanisms of seismic mitigation of coupled systems endowed with optimal metafoundations, this paper explores both elastic uncoupled and coupled unit-cell chains in the frequency domain based on the analysis of various transfer functions. Moreover, to address uncertainty at the excitation level, time history analyses are performed with a set of natural accelerograms that characterize operating basis earthquakes; thus, response contributions from both attenuation zones and nonattenuation zones can be distinguished by relating response variances to peak responses. Eventually, the attenuation effects of optimal metafoundations, frequency shift of superstructures due to unit cells of metafoundations, and coupling of both attenuation zones and nonattenuation zones are analyzed in depth.