This article deals with the analysis of planar trifurcated lined waveguide backed by a line walled cavity involving multiple step discontinuities. The duct configuration is placed symmetrically about x-axis. The main concern is to determine scattered fields behavior in different duct regions subject to different material properties of the walled duct. The governing problem reduces to that of a Sturm–Lioullie eigenvalue problem which is solved using the standard procedure of mode-matching. The scattering pattern is observed in the case of perforated and fibrous materials thereby analyzing noise effects for different settings of underlying structures. It is worth mentioning that underlying structures are closely related to silencer geometries in the practical context.

本文处理平面三叉线波导的分析，该波导由线壁腔支持，涉及多个台阶不连续性。管道配置关于x轴对称放置。主要关注的是确定不同管道区域中的散射场行为，这些区域受到壁管道的不同材料特性的影响。控制问题简化为 Sturm-Lioullie 特征值问题，该问题使用标准模式匹配程序解决。在穿孔和纤维材料的情况下观察到散射模式，从而分析底层结构不同设置的噪声影响。值得一提的是，在实际应用中，底层结构与消音器几何形状密切相关。