Sonic black hole (SBH) is capable of the concentration for the sound energy by the shrinking duct and appropriate wall admittance. However, the concentrated energy cannot be dissipated due to the weak air damping. Meanwhile, when the inserted rings are insufficient, the accuracy of the conventional transfer matrix method (TMM) is less than satisfactory for the simulation of the original SBH. In this study we commit to modify this simulation method and broaden the effective absorption band by using porous materials. First, we derived the acoustic transfer relationship of the conical cavity and the acoustic admittance of the toroidal cavity, via formulating the basic equation. After combining with the two method, the modified TMM (MTMM) results show excellent agreement with the finite element results. The applicability of the derived wall admittance is analyzed in detail. The MTMM has also been applied to obtain the sound absorption of a SBH configuration with embedded porous materials (PMSBH). The proposed PMSBH can effectively dissipate the concentrated sound energy, leading to the ultra-low cut-on frequency of near-perfect absorption. Specifically, the cut-on frequency of the PMSBH is 387 Hz, with the corresponding wavelength being 8.8 times than the structural length. In addition, the parametric analysis shows the near independence of the absorption performance of the PMSBH on the damping loss, so that the PMSBH can achieve excellent absorption without adding other acoustic materials. These appealing characteristic could promote the application of the PMSBH in noise control.

中文翻译：

---

声速黑洞传递矩阵法的改进及展宽有效吸收带


声波黑洞（SBH）能够通过收缩的管道和适当的壁导纳来集中声能。但由于空气阻尼较弱，集中的能量无法消散。同时，当插入的环不足时，传统的转移矩阵法（TMM）对于原始SBH的模拟精度不能令人满意。在这项研究中，我们致力于修改这种模拟方法，并通过使用多孔材料来拓宽有效吸收带。首先，通过建立基本方程，推导了锥形腔的声学传递关系和环形腔的声导纳。将两种方法结合后，修正的TMM（MTMM）结果与有限元结果表现出极好的一致性。详细分析了推导的壁导纳的适用性。 MTMM 还被应用于获得嵌入多孔材料的 SBH 配置 (PMSBH) 的吸声效果。所提出的 PMSBH 可以有效地消散集中的声能，从而实现近乎完美吸收的超低截止频率。具体来说，PMSBH的截止频率为387 Hz，对应的波长是结构长度的8.8倍。此外，参数分析表明PMSBH的吸声性能对阻尼损失几乎独立，使得PMSBH无需添加其他声学材料即可实现优异的吸声效果。这些吸引人的特性可以促进PMSBH在噪声控制中的应用。