Rotational invariance in the design of structures with imbedded acoustic black hole vibration absorbers

Abstract

The acoustic black hole (ABH) effect, where the wavespeed of a structure is intentionally reduced to near zero by altering its thickness according to a power-law taper, has been utilized on plates and beams to achieve vibration reduction. Several ABH designs have been proposed for uniform beams including the inverted and the double leaf ABH. However, these designs are only applicable for reducing flexural vibration in a single dimension. A rotationally invariant concept is presented where the imbedded ABH is symmetric around the center line of the beam. Various damping configurations are then applied to the rotationally invariant ABH and their respective amounts of vibration reduction are compared. Finally, the challenges of manufacturing such an ABH design will be discussed in the context of three-dimensional printing and additive manufacturing.