Abstract This study proposes a new solution to control low-frequency noise in acoustic duct. The control device is in the shape of a Helmholtz resonator combined with a tensioned membrane in the air cavity, referred to as a membrane resonator. The membrane resonator is connected to the main waveguide through two necks. A theoretical model is developed to evaluate its acoustic performance when attached to a U-shaped duct as the host structure. Numerical simulation shows that the proposed resonator generates effective transmission loss in the very low-frequency region, as a result of the vibro-acoustic coupling between the integrated membrane and the two-end Helmholtz resonator. Since the attenuation band is deep sub-wavelength, a lumped-mass model is developed to capture the main physics involved in the acoustical-mechanical coupling. With the developed models, the tuning range of the proposed system is further investigated. Several tuning mechanisms are demonstrated by changing the membrane tension, thickness, material type and combining multiple resonators. The transmission loss has fairly large variation range and the desired frequency band is fully controllable. The proposed resonator has simple geometry and mechanical design, whilst the deep sub-wavelength characteristics and the offered tunability are promising. It has the potential to be used solely or as the basic building block in a wide range of noise control applications.

中文翻译：

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带膜耦合声谐振器的 U 形管道中低频声音的衰减：建模与分析

摘要 本研究提出了一种新的声管低频噪声控制解决方案。控制装置呈亥姆霍兹谐振器的形状，在气腔中与张紧的膜片组合在一起，称为膜片谐振器。膜谐振器通过两个颈部连接到主波导。开发了一个理论模型来评估其作为主体结构连接到 U 形管道时的声学性能。数值模拟表明，由于集成膜和两端亥姆霍兹谐振器之间的振动声耦合，所提出的谐振器在极低频区域会产生有效的传输损耗。由于衰减带是深亚波长，因此开发了集中质量模型来捕捉声学-机械耦合中涉及的主要物理场。使用开发的模型，进一步研究了所提出系统的调谐范围。通过改变膜张力、厚度、材料类型和组合多个谐振器，展示了几种调谐机制。传输损耗变化范围较大，所需频段完全可控。所提出的谐振器具有简单的几何形状和机械设计，而深亚波长特性和提供的可调性很有希望。它有可能在广泛的噪声控制应用中单独使用或作为基本构建块使用。传输损耗变化范围较大，所需频段完全可控。所提出的谐振器具有简单的几何形状和机械设计，而深亚波长特性和提供的可调性很有希望。它有可能在广泛的噪声控制应用中单独使用或作为基本构建块使用。传输损耗变化范围较大，所需频段完全可控。所提出的谐振器具有简单的几何形状和机械设计，而深亚波长特性和提供的可调性很有希望。它有可能在广泛的噪声控制应用中单独使用或作为基本构建块使用。