A normalized wave number variation parameter for acoustic black hole design

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. Theory predicts greater absorption for a higher thickness taper power. However, a higher taper power also increases the violation of an underlying theory smoothness assumption. This paper explores the effects of high taper power on the reflection coefficient and spatial change in wave number and discusses the normalized wave number variation as a spatial design parameter for performance, assessment, and optimization.