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.

This article elucidates a non-planar trifurcated wave scattering problem by considering incident wave through multiple regions of the underlying waveguide. The scattered field potentials in respective duct regions are obtained via mode-matching technique (MMT) thereby dealing with the non-planar surfaces and step discontinuities positively. The scattering effects are determined by allowing the incident wave from each region explicitly and then simultaneously. The distribution of energies subject to different choices of regions for incidents are presented to analyze the effects of varying regions of incidents. It is mentioned that obtained solutions are thoroughly validated thereby displaying the scattering characteristics graphically.

The present communication addresses the reflection and transmission analysis of a two-dimensional waveguide structure with planar and non-planar surfaces. In the fields of physics, engineering and applied mathematics, research is being carried out to control or reduce unwanted and harmful noise to an acceptable level. Our aim is to solve the boundary value problem developed to simulate the transmission and reflection of a bifurcated waveguide structure in the channels or ducts that have abrupt changes in the height together with planar and non-planar surfaces. Furthermore, the eigenfunctions are linearly independent and non-orthogonal. To solve non-orthogonal eigenfunctions, a generalized orthogonality relation has been developed. Solution is obtained using mode matching technique (MMT) along with generalized orthogonal relations. In the last section, solution is viewed graphically in the inner and outer ducts or channels for different frequencies and height. The expressions for energy distribution in different duct regions are obtained and sketched subject to the various properties of the waveguide material. The results are well supported for a number of mathematical and physical reasons.