A multibody dynamics approach on a tree-shaped acoustic black hole vibration absorber

Acoustic black hole (ABH) has shown great potential and aroused tremendous interest for vibration and sound control in the past two decades. However, efficient computational methods are still lacking for the design of ABH structures with practically required properties. Herein, a multibody system transfer matrix method is proposed to deal with a system comprising a host structure with an attached ABH cluster, exemplified by a novel tree-shaped ABH dynamic vibration absorber (ABH-DVA). Capitalizing on the flexibility offered by the method, the eigen-solutions and the steady-state vibration response of the combined system are derived and validated by finite element results. Observed vibration reduction and the underlying mechanisms are elucidated in terms of the vibrational energy ratio and vibration spatial distribution in the system. Owing to its rich modal dynamics and energy trapping capability, the proposed absorber demonstrates extraordinary and robust low-frequency and broadband vibration reduction performance from 25 Hz to 2500 Hz for different host structures. This can be ensured by designing its threshold frequency as the lower limit of the targeted frequency range. The proposed method and the vibration-reduction-effect are experimentally validated. This study offers a novel yet general approach for addressing complex ABH structures with various structural components and topologies.