An alternative and optimized thickness profile of an acoustic black hole plate

Owing to their unique wave retarding features, Acoustic Black Hole (ABH) structures with standard power-law thickness profiles have been extensively explored for various structural vibration and sound radiation control applications. In order to achieve even better ABH effects for a given minimum thickness that can be achieved or accepted in practice, this paper reports an alternative ABH thickness profile in a plate through an optimization procedure by using the fast and elitist nondominated sorting genetic algorithm II in conjunction with a 2D semi-analytical Daubechies wavelet model. The new thickness profile features a different geometry from the standard ones in that the position of the imposed minimum thickness is off-set from the ABH indentation center, thus forming a flexible ring-shaped area and creating bi-directional ABH effects, which is conducive to energy focusing and dissipation. Numerical results show that a plate embedded with the optimized ABH indentation exhibits better ABH effects than its standard ABH counterpart, as evidenced by an increase in the total system damping as well as an impairment of other vibration and sound radiation metrics. Mode shape analyses of the optimized ABH plate show that the observed damping increase is mainly attributed to these local (n¯, 1) and (n¯, 2) modes, as a result of the flexible ring-shaped area that is formed inside the optimized ABH indentation. Finally, the optimized ABH plate is shown to entail reductions in both the vibration response of the plate and its sound radiation into a free acoustic medium.