A Design Parameter for Acoustic Black Holes

摘要

In recent years the concept of the Acoustic Black Hole has been developed as an efficient passive, lightweight absorber of bending waves in plates and beams. By having the plate or beam thickness decrease to zero according to a power law, the bending wave speed theoretically goes to zero and the waves never reflect back from the thin edge, thus they are “absorbed.” It has been found that it is possible to create ABHs that violate fundamental smoothness assumptions wherein the theory does not accurately describe bending wave behavior in the ABH. The theory does not account for impedance mismatches between a uniform beam and an ABH or impedance mismatches within the ABH taper which would cause bending waves to reflect. In this study Finite Elements were used to investigate the reflection of bending waves from ABHs attached to uniform beams. It was shown that the reflection of bending waves trended similarly to the Normalized Wavenumber Variation, a parameter that determines whether or not the fundamental assumptions are valid. The results will be useful for the characterization, design, and optimization of vibration attenuation performance of Acoustic Black Holes.