Topology optimization of wave-focusing waveguide acoustic black holes

Abstract

The acoustic black hole, as first proposed by Mironov for beams and plates, provides broadband wave focusing, exploitable for energy harvesting, for weak signal sensing, and as a strategy to minimize the amount of damping material needed for efficient, broadband damping. There have been a few suggestions aimed at providing an analogous device for acoustics in air. However, although these waveguide devices may work fine as broadband absorbers, their operational mechanism is decidedly different from their structural counterparts. Instead of providing wave focusing, all published devices seem to rely on the creation of resonances occurring increasingly closer to the waveguide entrance for increasing frequency. To explore a much larger class of possible designs than previously examined, we here apply a gradient-based material distribution topology optimization method. The optimization objective is a broadband maximization of power in a small region towards the end of the waveguide. We demonstrate that with this tool, it is indeed possible to design broadband true wave-focusing waveguides. These are geometrically much more complex than the previously proposed ones, a complexity that nevertheless efficiently can be handled by a recently developed gradient-based optimization method, able to accommodate also visco-thermal boundary-layer losses.