A parametric study of an acoustic black hole on a beam

Abstract

Acoustic black holes (ABHs) are geometric structural features that provide a potential lightweight damping solution for flexural vibrations. In this article, a parametric study of an ABH on a beam has been carried out to assess how practical design constraints affect its behaviour, thus providing detailed insight into design trade-offs. The reflection coefficient of the ABH has been calculated for each taper profile, parameterised via the tip-height, taper-length, and power-law, and it has been shown to exhibit spectral bands of low reflection. These bands have been related to the modes of the ABH cell and become more closely spaced in frequency as the ABH parameters are suitably varied. This suggests that ABH design should maximise the modal density to minimise the broadband reflection coefficient; however, the minimum level of reflection is also dependent on the power-law and tip-height. Consequently, broadband reflection values have been used to show that optimum power-law and tip-height settings exist that achieve a balance between maximum modal density and minimum level of reflection. Additionally, at discrete frequencies, in cases where tip-height and taper-length are practically constrained, the power law can be tuned to maximise performance. Finally, an experimental study is used to validate the results.