Analysis of dynamic stress in an acoustic black hole taper

Acoustic Black Holes (ABHs) provide a lightweight and high-performance alternative to traditional methods for the attenuation of structural vibration. Usually implemented through a gradual reduction in the structural thickness, ABHs introduce a reduction in the local wavespeed within the ABH taper region. This results in a corresponding reduction in the wavelength of vibration, and thus increases the effectiveness of passive damping treatment applied to the ABH taper. However, the ABH effect inherently focuses vibrational energy into the ABH taper, resulting in high amplitude deflection of the ABH tip. This raises concerns about the level of dynamic stress within the ABH taper, which could result in a significant reduction in the useful life of the structure due to fatigue. This paper presents an investigation into the dynamic stress induced in an ABH taper used to terminate a uniform beam. A numerical analysis of dynamic stress is carried out and this links the maxima in the stress response to the modes of the structure, providing insight into the stress localisation mechanism. Following this, a parametric study explores the effect of varying three key ABH geometrical design parameters on both the vibration attenuation performance, quantified via the reflection coefficient, and the level of dynamic stress, highlighting the trade-off between these two performance metrics. Finally, experimental measurements of both the reflection coefficient and the dynamic stress within a representative ABH taper are presented to validate the results of the numerical study.