Low frequency broadband bandgaps in elastic metamaterials with two-stage inertial amplification and elastic foundations

Abstract This paper proposes two improved elastic metamaterials (EMs) by separately introducing the two-stage inertial amplification structures and introducing the structures and elastic foundations simultaneously based on the existing EMs. Firstly, the dynamic analysis of the unit cells and the calculation of band structures are carried out, the bandgap characteristics of proposed systems are taken a comparative analysis with those of existing EMs, and the bandgap formation mechanism is clarified by the effective parameter singularity. Then, the effects of structural parameters on bandgap characteristics are discussed. Finally, the vibration attenuation characteristics of finite lattice structures based on the equivalent models are calculated, and the transmittance testing experiments are conducted on prototypes of four-unit structures. Theoretical and experimental results show that, compared with the existing EMs, the two proposed systems have lower bandgap starting frequencies and larger bandwidths. This research could provide certain guidance for the control and utilization of low and ultra-low frequency vibration in engineering applications and the regulation of low and ultra-low frequency broadband elastic waves in scientific research related functional devices.