Reflection and transmission analysis of an acoustic trifurcated waveguide with wave-bearing structural discontinuity

The dilution of undesired and vandalize noise to a sustainable level is the subject of continuing research in the fields of applied mathematics, physics, and engineering. Therefore, the present study investigates the mechanism of an acoustic wave scattering, which includes the force propagation due to the incidence through region R1$$ {R}_1 $$ of elastic boundary condition. Both planar and nonplanar surfaces are allowed in this waveguide configuration. In this structure, the scattered fields in the regions of the inner surfaces are acoustically rigid and satisfy the standard orthogonality relation, while the fields on the upper outer surfaces are flexural nature that can be tackled using modified orthogonality relation. Thus, we intend to simultaneously take into account the behavior of the scattered field in both planar and nonplanar zones. Solving nonorthogonal eigenfunctions required the development of a modified orthogonality relation. Modified orthogonal relation and the mode-matching (MM) technique have combined to get the solution of proposed model. The last section graphically discusses the solution for various frequencies and heights to observe the scattering behavior in all regions of the duct. In accordance with different characteristics of the waveguide material, expressions for the distribution of powers in different parts of the channel are developed and schematically depicted. A variety of mathematical and physical justifications provide strong support to results.