Low-frequency broadband characteristics of stepwise radial acoustical black holes

Abstract

In this paper, a stepped radial acoustic black hole (SR-ABH) structure formed via a stepwise arrangement of two-dimensional radial acoustic black holes(ABH) is proposed. The finite element method is used to calculate the energy band and frequency response curve of the SR-ABH structure. It is found that the low-frequency bandgap accounts for 83.4% of the whole energy band region (0-2000 Hz) , which is 7.6 times broader than that of a horizontally arranged radial acoustic black hole (HR-ABH). On the basis of modal analysis at special points, the introduction of gradient arrays into radial ABH is confirmed, which reduces the cut-off frequency of ABH and leads to a low-frequency broadband coupling of local resonance and acoustic black hole effects. In addition, the influence of geometric parameters on the bandgap is explored. The results indicate that as the step height increases, the coupling relationship between local resonance and acoustic black hole effects shows a trend of first strengthening and then weakening, thereby affecting the movement of the low-frequency bandgap. In addition, the proposed structure provides a way to reduce the high cutoff frequency of ABH.