Wave-based analysis on cut-on frequency of curvilinear acoustic black holes

Recently, the curvilinear acoustic black hole (ABH), a structure whose thickness is tapered according to the power-law while the baseline is curved, was proposed and shown to be a compact solution to absorb elastic waves in thin structures by numerical and experimental studies. To design a curvilinear ABH applicable to various industries, systematic investigations on the fundamentals such as the effect of curvature on the reflection coefficient and the cut-on frequency are required. In this study, we use the impedance method for curvilinear ABHs to investigate the effects of the baseline curvature on the reflection coefficient and the cut-on frequency of arc ABHs. We show that the cut-on frequency of an arc ABH increases linearly proportional to the baseline curvature.