Topological optimization of damping layout for minimized sound radiation of an acoustic black hole plate

Damping material is one of the essential components to achieve effective Acoustic Black Hole (ABH) phenomena. Alongside the expected energy absorption by the viscoelastic coating, recent research revealed its adverse effect in increasing the sound radiation efficiency of ABH structures. The conflicting role that damping layers play calls for a balanced and meticulous design of their deployment to draw the best possible vibration or acoustic benefit. This paper proposes a general methodology for optimizing the layout of damping layers coated on the surface of an ABH plate through topological optimization. By combining a semi-analytical wavelet plate model with an optimizer, the sound radiation into a free space by the ABH plate is minimized at either a given frequency or within a frequency band. Results show that through optimization, a reduced sound power can be achieved, as compared with the intuitive coating at the central area of the ABH indentation. While the low frequency sound power reduction is due to the impaired structural vibration, the optimization-induced reduction in the radiation efficiency is shown to be the dominant factor that contributes to the minimization of the sound power at high frequencies. Changes in the topology of the coating, in relation to the optimization objective, are observed and interpreted. It is shown that the optimized coating area for acoustic optimization tends to be further away from the center of the indentation, in contrast to the case for structural vibration optimization. The optimized configuration warrants a systematic reduction of the sound radiation efficiency, as evidenced by a weakened vibration level of the supersonic components of the plate.