Sound radiation and transonic boundaries of a plate with an acoustic black hole.

The acoustic black hole (ABH) phenomenon has shown promise for noise and vibration control applications. In this paper, a two-dimensional (2-D) Daubechies wavelet (DW) model is established for the sound radiation prediction of plates embedded with a circular ABH indentation. ABH plates are shown to exhibit a reduced sound radiation efficiency as compared with their flat counterpart. Below the critical frequency, this is caused by the weakening of the structural stiffness due to the ABH indentation. Above the critical frequency, a subsonic region inside the ABH cell may appear, containing acoustically slow structural waves. This region, confined within a transonic boundary, is due to the ABH-specific phase velocity reduction of the bending waves. Drawing energy away from the supersonic region of the plate, this subsonic region warrants a reduced sound radiation to the far field. Numerical results on the investigated configuration show an increase in the sound radiation efficiency due to the added stiffness effect of damping layers. Sound radiation efficiency alongside the transonic boundary changes is scrutinized and quantified. Visualization of the supersonic acoustic intensity and radiation allows identifying the effective sound radiation regions of ABH plates and their relationship with the transonic boundaries at different frequencies.