Bandgaps and topological interfaces of metabeams with periodic acoustic black holes

Abstract

Acoustic black hole (ABH) with extraordinary properties of wave manipulation and energy focalization has been drawing growing attention in mechanical metamaterial, and the development of topological phenomena provides a novel way for investigation of ABH characteristics. This paper explores the physical mechanism of dispersion curves of three metabeams with embedded periodic ABHs and studies the topological phenomena of the compound metabeam for energy localization. First, the mass-spring models are employed according to lattice dynamics method to clarify the formation mechanism of bandgaps and the effect of the parameters on dispersion relation. Meanwhile, the diatomic mass-spring model provides an analytical framework to investigate the band inversion and the displacement distribution of topological states. Furthermore, numerical analyses are carried out to investigate the band structures, eigenmodes, transmission, and the achievement of topological interface state by proposed compound metabeam. The adjustment of structural parameters, changing the mass and stiffness of the mass-spring model, can broaden the bandgap in low frequency for better vibration attenuation performance. Besides, the modal formation in low frequency is explained by masses vibration distribution. The correctness of the method is verified by comparing the transmission numerically with previous experiments. This work enriches the existing knowledge of ABH on wave manipulating and energy harvesting.