Sound propagation properties of a duct system with Helmholtz resonators (HRs) are affected by mean flow. Previous studies have tended to focus on the effects of mean flows on acoustic response of a duct system with a finite number of HRs. Employing an empirical impedance model, we present a modified transfer matrix method for studying the effect of mean flow on the complex band structure of an air duct system with an infinite periodic array of HRs. The efficiency of the modified transfer matrix is demonstrated by comparison between an example of transmission response calculation for a finite single HR loaded duct and the finite element simulation result calculated using the COMSOL software. Numerical results are presented to analyze the effect of mean flow on the band structure and transmission loss of the sound wave in the duct system. It is hoped that this study will provide theoretical guidance for acoustic wave propagation of HR silencer in the presence of mean flow. ...

中文翻译：

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平均流量对带有亥姆霍兹共振器周期阵列的管道中声波传播的影响

具有亥姆霍兹共振器（HRs）的管道系统的声传播特性受平均流量的影响。先前的研究倾向于集中于平均流量对有限数量HR的管道系统的声学响应的影响。利用经验阻抗模型，我们提出了一种改进的传递矩阵方法，用于研究平均流量对具有无限周期阵列的HRs的风道系统的复杂带结构的影响。通过比较有限的单个HR加载管道的传输响应计算示例与使用COMSOL软件计算的有限元模拟结果之间的比较，可以证明改进的传递矩阵的效率。给出数值结果，以分析平均流量对管道系统中声带的能带结构和传输损耗的影响。希望这项研究将为存在平均流量的HR消声器的声波传播提供理论指导。...