Effects of annular acoustic black holes on sound radiated by cylindrical shells

While most acoustic black hole (ABH) designs are intended to reduce vibrations in beams and plates, annular ABHs have been recently proposed for cylindrical shells. The key to achieve the ABH effect in a structure consists in embedding an indentation on it such that it slows down incident waves and concentrates their energy at the center of the ABH. There, it can be typically dissipated by means of a viscoelastic layer. Many studies exist on the vibration of structures with ABH indentations but only a few address the topic of sound radiation. In this work, we evaluate the impact that an annular ABH has on the sound radiated by a baffled cylindrical shell. The vibration of the cylinder is computed using Gaussian basis functions in the Rayleigh-Ritz method. Once determined the surface velocity of the ABH cylinder, a Green's function approach is employed to obtain its surface acoustic pressure and then the sound power level and radiation efficiency. The dependency of the latter on the ranges determined by the ring and critical frequencies is analyzed for the case of a thick acoustic shell. Beyond the critical frequency, supersonic flexural waves entering the ABH become subsonic, substantially reducing the radiation efficiency and therefore, the emitted sound. Further reduction is achieved once passed the ring frequency.