Abstract The numerical simulation of beams and plates with embedded acoustic black holes (ABHs) is computationally demanding because of the very thin thickness attained at the ABH central area. Semi-analytical approaches relying on the Rayleigh-Ritz method with wavelet or Gaussian basis functions have thus revealed as an accurate and fast alternative to determine the ABH vibration field in parametric studies. To date however, the vast majority of works on ABHs have only dealt with ABH indentations on straight beams and flat plates. It would be also worth exploring the feasibility of ABHs to control the vibrations of curved shells, typically found in aerospace and naval structures. In this work, we address this issue and extend the Gaussian expansion method (GEM) to characterize annular ABHs embedded on cylindrical shells. First, we show how the GEM can be modified to make Gaussian shape functions satisfy periodic boundary conditions in the circumferential direction of the cylinder. The GEM is then used to determine the vibration field of the ABH cylindrical shell and gets validated by comparison with finite element simulations. A thorough analysis of the performance of the annular ABH follows, which stresses the differences with the behavior of ABHs on flat surfaces. In particular, we show the influence that waves propagating in the circumferential direction have on the operational frequency range of the ABH. The effects of the viscoelastic layer and the inclusion of longitudinal stiffeners to strengthen the cylinder rigidity are also analyzed by means of the proposed GEM approach. This work broadens previous semi-analytical methods to start investigating the ABH effect on curved structures.

中文翻译：

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使用具有高斯基函数的 Rayleigh-Ritz 方法对嵌入环形声学黑洞的圆柱壳进行振动

摘要 嵌入声学黑洞 (ABH) 的梁和板的数值模拟在计算上要求很高，因为在 ABH 中心区域获得的厚度非常薄。因此，依赖于具有小波或高斯基函数的 Rayleigh-Ritz 方法的半解析方法已被揭示为在参数研究中确定 ABH 振动场的准确且快速的替代方法。然而，迄今为止，绝大多数关于 ABH 的工作仅涉及直梁和平板上的 ABH 压痕。探索 ABH 控制弯曲壳振动的可行性也是值得的，这通常存在于航空航天和海军结构中。在这项工作中，我们解决了这个问题并扩展了高斯扩展方法 (GEM) 来表征嵌入在圆柱壳上的环形 ABH。第一的，我们展示了如何修改 GEM 以使高斯形状函数满足圆柱圆周方向上的周期性边界条件。然后使用 GEM 来确定 ABH 圆柱壳的振动场，并通过与有限元模拟的比较进行验证。随后对环形 ABH 的性能进行了全面分析，重点分析了 ABH 在平面上的行为差异。特别是，我们展示了沿圆周方向传播的波对 ABH 的工作频率范围的影响。还通过所提出的 GEM 方法分析了粘弹性层和包含纵向加强筋以增强圆柱刚度的影响。