Investigation of boundary-taper reflection for acoustic black hole design

In recent years the concept of the acoustic black hole (ABH) has been developed as an efficient, passive, lightweight absorber of bending waves in beams and plates. ABHs are implemented into structures by introducing a smoothly decreasing local change in the thickness of a beam or plate according to a power lawfunction. By having the beam or plate thickness decrease to zero the bending wave speed theoretically goes to zero and the waves never reflect back from the thin edge; thus they are "absorbed." ABH theory does not account for impedance mismatches between a uniform beam, and impedance mismatches within the ABH taper, which can cause bending waves to reflect off of an ABH, hindering performance. In this study numerical models were used to investigate the reflection of bending waves from ABHs attached to uniform beams with and without anechoic terminations. It was shown that the reflection of bending waves trended similarly to the normalized wavenumber variation, a parameter that determines whether or not fundamental theoretical assumptions are valid. The results will be useful for the design, characterization and optimization of vibration attenuation performance of acoustic black holes.