Dynamic properties investigation of an acoustic black hole beam with dynamic vibration absorber based on analytical method

Acoustic Black Holes (ABHs) have attracted much attention in recent years due to their characteristics of focusing vibration energy. Combining the focusing property of an ABH in a wide frequency band with the advantage of a dynamic vibration absorber (DVA), which could effectively suppress the vibration response at any tuning frequency, is expected to achieve excellent effective wide-band vibration reduction. However, the underlying mechanism and design method have not been provided by any existing open literature. In this work, the analytical dynamic model of a beam with an integrated one-dimensional ABH and a DVA (ABH+DVA) is established based on the transfer matrix method. The vibration attenuation of this ABH+DVA beam is investigated through this analytical model. Results demonstrate that, in comparison to a uniform-thickness beam with DVA and ABH beam with a damp layer in certain situations, the ABH+DVA beam provides superior vibration attenuation. Furthermore, the concept of region-specific vibration focusing ratio is proposed and defined to quantify the influence of ABH characteristic length on the focusing effect and focusing area of the ABH beam. Then based on the knowledge of focusing effect of the ABH beam, the influence of DVA placement on vibration reduction effect is studied and the mechanisms of the ABH beam attached with DVA are explained. Generally, the excellent vibration reduction effect of the ABH+DVA beam is closely related to the outstanding vibration focusing characteristic of an ABH beam.