Abstract This paper presents a theoretical examination of wave propagation in a cylindrical duct loaded with an array of closely spaced flush-mounted annular resonators forming a simple reactive silencer. A semi-analytical mathematical model is proposed considering higher evanescent modes in the duct and plane-wave- and first transverse mode in annular resonators. Viscothermal losses in annular resonators are considered by employing the equivalent-fluid model. A heuristic optimization algorithm based on the proposed mathematical model is used to maximize the minimum transmission loss in a given frequency range. The numerical results show that multiple resonances of the individual resonators can be effectively utilized to design compact (thin) silencers with a wide frequency range and a relatively small number of resonators. The numerical results are validated by comparison with finite element simulations.

中文翻译：

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带环形谐振器的优化紧凑型宽带反应消音器

摘要 本文介绍了在圆柱形管道中波传播的理论研究，该管道装有一组紧密间隔的嵌装环形谐振器，形成一个简单的反应式消音器。提出了一种半解析数学模型，该模型考虑了导管中较高的倏逝模以及环形谐振器中的平面波和第一横模。采用等效流体模型考虑环形谐振器中的粘热损耗。基于所提出的数学模型的启发式优化算法用于在给定频率范围内最大化最小传输损耗。数值结果表明，可以有效地利用单个谐振器的多重谐振来设计具有宽频率范围和相对较少谐振器数量的紧凑（薄）消音器。