A Single-Phase Lightweight Double-Leaf Multi-Stage Acoustic Black Hole Model of Metamaterial

Abstract

In this paper, a novel single-phase double-leaf multi-stage acoustic black hole (SDM-ABH) is proposed. Compared with the traditional double-leaf ABH metamaterials, the unit cell consists of multiple sub-ABH structures arranged in a gradient periodically along the length direction. The energy band structure of the SDM-ABH metamaterial is calculated by the finite element method, and it is found that its weight decreases with the increase in the number of stages, but the bandgap ratio and attenuation both increase. By analysing the vibration modes at special points and the vibration displacement response of finite construction, it is revealed that strong attenuation at a low-frequency broadband is caused by the increase in the number of sub-ABHs that appear to have ABH effects due to the increase in the number of stages. In addition, the effect of structural parameters on the bandgap is investigated, and it is found that SDM-ABH metamaterials can be modulated at low frequencies by changing the truncation thickness and the power exponent of the sub-acoustic black hole, in which the increase in the truncation thickness t leads to the gradual weakening of the ABH effect of the sub-ABH until it disappears. The strong low-frequency attenuation properties of SDM-ABH metamaterials provide a method for a lightweight vibration damping design of metamaterials.