Low-frequency broadband characteristics of stepwise radial acoustical black holes

Abstract

In this paper, a stepped radial acoustic black hole (SR-ABH) structure formed by the stepwise arrangement of two-dimensional radial acoustic black holes is proposed. The finite element method is used to calculate the energy band and frequency response curve of SR-ABH, and it was found that the low-frequency bandgap at 0~2000Hz accounted for 83.4%, which is 7.6 times wider than the ABH arranged radially horizontally(HR-ABH). On the basis of modal analysis at special points, the introduction of gradient arrays into radial acoustic black holes is determined, which reduces the cut-off frequency of acoustic black holes and forms a low-frequency broadband coupling of local resonance effect and acoustic black hole effect. In addition, the mechanism of the influence of geometric parameters on the bandgap was explored. The results indicate that as the step height increases, the coupling relationship between local resonance effect and acoustic black hole effect shows a trend of first strengthening and then weakening, thereby affecting the movement of low-frequency bandgap. The proposal of this structure provides ideas for reducing the high cut-off frequency expansion of acoustic black holes.