This article presents a dispersion analysis of flexural trifurcated dominants acoustic wave mode propagating out of the mouth of a semi-rigid waveguide. The problem mainly concerns the study of the scattering characteristics of the structure subject to different material properties. The governing non Sturm-Liouville problem is approached through eigenfunction expansions while equating the orthogonal and non-orthogonal duct modes across the interface. Due to the multiple non-planar surfaces, the essential difficulty of root findings versus the respective scattering relationships is accomplished by proper justification. The uniqueness of the solution is assured while considering connections clamped and pinned on bending surfaces. In addition, the energy fluxes for each region of the duct are formulated in terms of scattered fields to analyze the energy distribution subject to different properties of the waveguide material. The results are well supported for different mathematical and physical reasons.

本文介绍了从半刚性波导口传播的弯曲三叉主声波模式的色散分析。该问题主要涉及研究结构在不同材料特性下的散射特性。控制非 Sturm-Liouville 问题是通过特征函数展开来解决的，同时使界面上的正交和非正交管道模式相等。由于多个非平面表面，根部发现与各自散射关系的基本困难是通过适当的证明来完成的。在考虑夹紧和固定在弯曲表面上的连接时，可以确保解决方案的唯一性。此外，管道每个区域的能量通量根据散射场进行公式化，以分析受波导材料不同特性影响的能量分布。由于不同的数学和物理原因，结果得到了很好的支持。