Design of a multi-material acoustic black hole using geometric profile mapping

Since their inception, acoustic black holes (ABHs) have taken on many forms. A wide range of profiles has been investigated for beam termination applications, including power laws and cosine profiles. However, all of these configurations have a common issue - the profiles have an inherent thin section at the end of the beam. This makes the profile susceptible to damage towards the tip, particularly through fatigue. Multi-material ABHs have been proposed as an alternative solution, maintaining a constant external geometry whilst varying the material properties along the length of the ABH termination. Previous work on multi-material ABHs has focused on optimising section lengths of each material based on a cost function, namely kinetic energy in the host beam. This work investigates the performance of multi-material ABH designs with section lengths chosen to approximate the effective impedance change of a range of geometric ABH terminations. The relative performance of each discretised gradient is compared through simulation in addition to comparison to an equivalent continuous gradient.