New type of vibration dampers utilising the effect of acoustic 'black holes'

One of the well-known ways of damping resonant flexural vibrations of different engineering structures or their elements, e.g. finite plates or bars, is to reduce reflections of flexural waves from their free edges. In the present paper, a new efficient method of reducing edge reflections is described that utilises gradual change in thickness of a plate or a bar from the value corresponding to the thickness of the basic plate to almost zero. It is proposed to use specific power-law shapes of plates of variable thickness (wedges) that ideally provide zero reflection even for negligibly small material attenuation – the so-called ‘acoustic black hole effect’. In particular, for powers m ≥ 2 - in free wedges, and m ≥ 5/3 – in immersed wedges, incident flexural waves become trapped near the edge and do not reflect back. Since, because of ever-present edge truncations in real manufactured wedges, the corresponding reflection coefficients are always far from zero, to make up for real wedges and make the systems more efficient it is proposed to deposit absorbing thin layers on wedge surfaces. It is shown that the deposition of thin damping layers on the wedge surfaces can dramatically reduce the reflection coefficients. Thus, the combination of a wedge with power-law profile and of thin damping layers can utilise the acoustic ‘black hole’ effect resulting in very effective damping systems for flexural vibrations.