Abstract The curved acoustic black hole (ABH), a thin structure with a curved baseline and a thickness that tapers according to a power law, has been proposed and investigated numerically and experimentally as a candidate for an effective and compact absorber of flexural waves. To understand physically the wave motions within a curved ABH and to utilize a spiral ABH in practical applications, systematic investigations of the effects of geometrical parameters such as the curvature or the damping-layer thickness are needed, as well as a theoretical approach to facilitate fast and accurate calculations. In this paper, we propose a wave-based theoretical method and investigate the “cut-on frequency” of a curved ABH, the frequency from which waves start to propagate within the ABH, using this method. The governing equation of the wave motion is derived using Hamilton's principle, and the solution of the governing equation is obtained numerically by recasting the original equation into impedance-equation form. Using the proposed method, we calculate the reflection coefficients of arc ABHs and Archimedean spiral ABHs with various geometrical parameters and frequencies to investigate their cut-on frequencies. The cut-on frequency increases almost linearly in proportion to the curvature in arc ABHs, and decreases with increasing gap distance in spiral ABHs.

中文翻译：

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基于波的弯曲声学黑洞截止频率分析

摘要 弯曲声学黑洞 (ABH) 是一种具有弯曲基线和根据幂律逐渐变细的厚度的薄结构，已被提出并通过数值和实验进行研究，作为有效和紧凑的弯曲波吸收器的候选者。为了从物理上理解弯曲 ABH 内的波浪运动并在实际应用中利用螺旋 ABH，需要对曲率或阻尼层厚度等几何参数的影响进行系统研究，并需要一种理论方法来促进快速和准确的计算。在本文中，我们提出了一种基于波的理论方法，并使用这种方法研究了弯曲 ABH 的“截止频率”，即波开始在 ABH 内传播的频率。利用哈密顿原理推导出波浪运动的控制方程，将原方程改写为阻抗方程形式，数值求解得到控制方程的解。使用所提出的方法，我们计算了具有各种几何参数和频率的弧形 ABH 和阿基米德螺旋 ABH 的反射系数，以研究它们的截止频率。截止频率几乎与弧形 ABH 中的曲率成比例地增加，并随着螺旋 ABH 中间隙距离的增加而降低。我们计算了具有各种几何参数和频率的弧形 ABH 和阿基米德螺旋 ABH 的反射系数，以研究它们的截止频率。截止频率几乎与弧形 ABH 中的曲率成比例地增加，并随着螺旋 ABH 中间隙距离的增加而降低。我们计算了具有各种几何参数和频率的弧形 ABH 和阿基米德螺旋 ABH 的反射系数，以研究它们的截止频率。截止频率几乎与弧形 ABH 中的曲率成比例地增加，并随着螺旋 ABH 中间隙距离的增加而降低。