Bandgap characteristics of a hybrid multi-resonator elastic metamaterial with negative stiffness mechanism and its application to mitigate seismic response of building structures

Seismic metamaterials have attracted extensive attention due to their unique ability to attenuate the transmission of elastic waves in their frequency bandgaps. However, generating a metamaterial with a low-frequency and wide bandgap remains challenging. Previous studies have shown that negative stiffness mechanisms can lower the frequency range of bandgaps while employing a multi-resonator technique can broaden the width of bandgaps. In this study, by combining these two techniques, a negative stiffness enhanced multi-resonator elastic metamaterial (NMEM) is first proposed. The feasibility of NMEM is validated by comparing the theoretical dispersion relation and the transmission spectra of a finite cell model. The results demonstrate that low-frequency and wide bandgaps can be realized by NMEM. To further widen the bandgap, a hybrid NMEM is proposed by connecting multiple types of cells in series. The proposed hybrid NMEM consists of two types of cells, one with a single resonator and another with two resonators, which merge individual bandgaps into a continuous and wider bandgap. The proposed hybrid NMEM is then adopted as a meta-basement for a case building to demonstrate its effectiveness in mitigating seismic responses. The results show that the seismic responses of the building with the hybrid meta-basement are considerably reduced than those of the building with the conventional basement. However, the hybrid meta-basement may lead to larger structural displacement response when the dominant frequency of ground motion is outside the designed bandgap.