Acoustic black hole with functionally graded perforated rings

A new class of acoustic black hole (ABH) waveguides is presented, which relies in its operation on an array of optimally designed functionally graded perforated rings (FGPRs). In this manner, the developed ABH is provided with built-in energy dissipation characteristics generated by virtue of the flow through perforations, which enhances its acoustic absorption behavior and makes the speed of the propagating waves vanish faster when reaching the end of the waveguide. Furthermore, the particular design of the rings enables sandwiching of additional porous absorbing layers between the rings to further boost the absorption characteristics of the proposed ABH. Accordingly, the operating principle of the new class of ABH is radically different from that of the conventional ABH that employs sequential solid-flat rings of decreasing inner radii to create a virtual power law taper necessary for generating the black hole effect, but through reactive means rather than the effective dissipative means of the proposed ABH. Therefore, this paper develops a transfer matrix modeling (TMM) approach to model the absorption and reflection characteristics of the new class of ABH, in an attempt to predict its behavior, optimize the selection of its design parameters, and more importantly, demonstrate its merits as effective means for controlling sound propagation. Numerical examples are presented to highlight the merits and behavior of the proposed ABH. Predictions of the TMM are validated against experimental results that are available in the literature for one and two micro-perforated plates. Comparisons are also established between the ABH with FGPR and the conventional ABH in order to distinguish the behavior and underlying principles of their operations.