Annular acoustic black holes to reduce propagative Bloch-Floquet flexural waves in periodically supported cylindrical shells

Current designs of acoustic black holes are mainly intended for straight beams and flat plates. However, many structures of interest in naval and aeronautical applications essentially consist in a periodically stiffened cylindrical shell, which could benefit from the acoustic black hole (ABH) effect to reduce vibrations and noise radiation. In this work, we suggest the design of annular ABHs to that purpose. To test the feasibility of such annular ABHs we consider the idealized case of a periodically simply supported cylindrical shell of infinite length. Such a structure allows for the propagation of Bloch-Floquet flexural waves at some passbands, which can play an important role in the radiation of noise at the far field. By means of wave finite element models, we show that the proposed annular ABHs constitute an effective way of reducing the shell flexural motion.