Scattering through a flexural trifurcated waveguide by varying the material properties

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.