Sound radiation and non-negative intensity of a metaplate consisting of an acoustic black hole plus local resonators

While acoustic black holes (ABHs) are well-known inefficient at low frequencies. However, attaching periodic local resonators to form a metamaterial ABH (MMABH) plate could be effective in suppressing low- to high-frequency sound radiation. To that goal, we first briefly review how to compute the vibration field of the MMABH using the Gaussian expansion component mode synthesis (GECMS) method. Then we characterize the far-field acoustic radiation of the MMABH and analyze its sound power level and radiation efficiency using a discrete radiation model. The non-negative intensity (NNI) on the MMABH surface is also computed to determine which regions of the plate are responsible for the far-field, and avoid the recirculation problem associated with standard intensity calculations. It is observed that the MMABH can substantially reduce sound radiation at all frequencies thanks to the combination of several mechanisms. In the low-frequency range, the formation of bandgaps induces a low-frequency coincidence effect with air that becomes beneficial, while at mid-high frequencies supersonic bending waves entering the ABH slow down and become subsonic once passed the transonic boundary. Their radiation efficiency experiences a big drop, resulting in poor outwards radiation. Simulations of all these phenomena are presented and detailed physical background explanations are provided.