A parametric study and modal analysis of an acoustic black hole on a beam

Acoustic black holes are structural features that have a varying thickness profile, and provide a potential lightweight damping solution for flexural vibrations. In practical applications, the length of an acoustic black hole will be constrained by the available space and the minimum tip height will be limited by both the manufacturing capabilities and strength requirements. Therefore, the power law of the taper is often the critical design parameter. In this paper, a parametric study of an acoustic black hole termination on a beam is presented with practical constraints on the length and tip height. The reflection coefficient of the acoustic black hole has been calculated for a range of power laws and it has been shown that, for a fixed power law, the reflection coefficient varies over frequency and exhibits bands of high and low reflection. These bands can be related to modes of the acoustic black hole. In addition, it has been found that an optimum power law exists for minimising the broadband average reflection coefficient for each acoustic black hole configuration.