Coupling sonic black holes to a resonant cavity using patch transfer functions

Sonic black holes (SBHs) typically consist of a waveguide with concentric rings of decreasing radius separated by cavities that slow down incident sound waves, dissipate their energy, and cause minimal reflection. Although there are many works on SBH simulation methods, performance analysis, and design optimization, no one has considered the interaction of SBHs with other systems. The purpose of this paper is to begin to explore this point by considering the connection of an SBH to a resonant cavity and determining the effects the SBH has on the internal acoustic pressure field of the cavity. Since this is a complex problem, it is first proposed to resort to the patch transfer function (PTF) substructuring method to simulate the behavior of the coupled system. After validating the PTF with finite element simulations (FEM) of the entire coupled system, the PTF is used to perform parametric analyses to evaluate the influence of the position and the number of SBHs on the cavity mean quadratic pressure. Although SBHs are typically intended for medium and high frequency pressure reduction in ducts, it is shown that with proper design they can be very effective in dissipating low frequency pressure peaks within the cavity, with potential for room acoustics applications, among others.