An acoustic black hole for the control of torsional vibration

Recent developments in vibration control have demonstrated the Acoustic Black Hole (ABH), whereby a gradual reduction in the wavespeed along the ABH structure enhances broadband energy dissipation due to the increase in efficacy of viscoelastic damping materials. Thus far, the ABH has only been realised for the control of flexural waves, with the reduction in wavespeed usually achieved with a graded reduction in stiffness, via a tapered thickness or graded material properties. Unlike flexural applications, the torsional wavespeed cannot be modified by a tapered cross-section alone. In this paper, a torsional ABH is achieved with a metastructure that grades the ratio between torsional stiffness and inertia along the length. The torsional ABH is shown to achieve a significant reduction in the vibration of a cylindrical shaft over a wide frequency range. The proposed torsional ABH design is also shown to exhibit a frequency-dependent localisation of wave energy, commonly known as “rainbow trapping”. A series of parametric studies is used to investigate the relationship between the geometry of the proposed ABH design and both the control performance and the rainbow trapping.