Analyzing the acoustic wave propagation characteristics in discontinuous bifurcated waveguide

This article examines the dispersion characteristics and energy distribution in different regions of the bifurcated waveguide with vertical step discontinuities. In this research study, we have considered mathematical model of noise reduction devices, specifically analyzing the acoustic wave propagation problem in a bifurcated waveguide with elastic membrane outer plates and rigid inner plates. Mode-matching (MM) technique is employed to match the eigenfunctions at the interface and analyzed the reflection and transmission amplitudes in all regions. Through MM scheme an infinite system of equations has been obtained for these boundary conditions by dividing the structure into three regions and finding dispersion relations and eigenfunctions using separation of variables and the corresponding orthogonality relations. Because of the flexible nature of the boundary surfaces, the acquired eigenfunctions and the dispersion relation do not satisfy the standard orthogonality relation. To resolve this difficulty, we have established a modified orthogonality relation to take into account the flexible nature of the boundary surfaces. With the implication of physical connections, the uniqueness of the problem has been ensured, and zero displacement and zero gradient edge conditions on bending surfaces have been considered to present results. Energy expressions are obtained showing how the energy is distributed in different sections of the waveguide, which is consistent with the energy conservation law. Finally, the numerical discussion illustrates the quantitative behavior of the physical parameters and summarizes the significant contribution of the study by presenting graphical data.