Sound radiation of a metaplate made of an acoustic black hole and local resonators

Acoustic black holes (ABHs) have not only proved very efficient in reducing vibrations in beams and plates at mid and high frequencies, but also in suppressing sound radiation. However, for lower frequencies with wavelengths larger than the ABH diameter waves cannot be trapped. It has been shown, though, that one can attach a periodic distribution of local resonators to the ABH plate and substantially diminish its vibration at low frequencies. Such design (local resonators plus ABH plate) can be viewed as a metaplate, referred to as the MMABH plate, with enhanced vibration properties as compared to a uniform plate or a standard ABH plate. In this work, we are interested in studying the radiation properties of the MMABH. Its sound power and radiation efficiency are characterized by means of a discretized radiation model and it is observed that broadband reduction in sound power level and far field radiated sound is attained. Non-negative intensity (NNI) also shows that sound reduction cannot be simply attributed to the damping effectivity of the ABH and resonators, but to the wave slowdown phenomenon inside the ABH that that breaks the coupling between bending and sound waves.