A parametric study of dynamic stress in acoustic black holes

Acoustic Black Holes (ABHs) make modifications to a structure that act to reduce the speed of a wave travelling through the ABH region. The reduced wavespeed has a corresponding reduced wavelength which increases the effectiveness of damping treatment applied to the ABH. A common way in which the reduction of wavespeed can be achieved is by gradually reducing the thickness of a structure. This is commonly implemented as a beam termination, which results in a thin tip. In this case, the energy focusing effect of the ABH causes high amplitude vibrations to occur in the thin section of the structure, raising concerns about high levels of dynamic stress that could result in fatigue failure. This paper presents an investigation into the effect of changing the ABH taper length, tip height and power law on the dynamic stress in an ABH terminated beam. This is achieved via numerical model of the structure, which enables a full parametric analysis to be carried out. For each ABH parameterisation, the performance is also quantified in terms of reflection coefficient so that trade-offs between performance and stress can be observed.