This article explores the waveguide phenomenon that possesses trifurcated rigid inlet/outlet and muffler conditions. Additionally, this waveguide is linked to a finite, thin, and flexible shell with the aid of partitioning discs located at the interfaces. The inside of the discs is coated with sound absorbent material, which can be fibrous or perforated, depending on the impedance conditions of the surface. To demonstrate the use of absorbent material at the interfaces, impedance formulation is used. The mode matching procedure is then utilized to find solution, it relies on the orthogonality conditions accompanying the material characteristics of the bounding surface and within the fluid. The study includes modeling the utilization of absorbent material at interfaces, and numerical experiments to analyze the acoustic attenuation. The analysis focuses on a specific configuration with duct region radii and a half length of the chamber at a frequency of 700 Hz. The results demonstrate that the absorption of power and transmission loss versus frequency vary through the fibrous coating and the edge conditions, and changing the clamped ends to pin-jointed ends optimizes the dispersion powers and the loss due to transmission. The study yields useful information to the acoustic dispersion via flexural expansion chamber, highlighting the importance of material properties, edge conditions, and configuration settings in the acoustic attenuation. The mode matching method and numerical experiments presented in this study can be useful for designing acoustic devices with flexible shells, providing a better understanding of the underlying physics and optimizing their performance.

本文探讨了具有三叉刚性入口/出口和消声器条件的波导现象。此外，该波导借助位于接口处的分区盘连接到有限、薄且灵活的外壳。圆盘内部涂有吸声材料，根据表面的阻抗条件，该材料可以是纤维状的或穿孔的。为了演示在界面处吸收材料的使用，使用了阻抗公式。然后利用模式匹配程序来寻找解决方案，它依赖于伴随边界表面和流体内的材料特性的正交条件。该研究包括对界面处吸收材料的利用进行建模，以及分析声衰减的数值实验。该分析重点关注频率为 700 Hz 时具有管道区域半径和腔室一半长度的特定配置。结果表明，功率吸收和传输损耗随频率的变化随纤维涂层和边缘条件的变化而变化，并且将夹紧端改为销接端可以优化色散功率和传输损耗。该研究通过弯曲膨胀室提供了有关声学分散的有用信息，强调了材料特性、边缘条件和配置设置在声学衰减中的重要性。本研究中提出的模式匹配方法和数值实验可用于设计具有柔性外壳的声学设备，提供对底层物理的更好理解并优化其性能。