Influence of acoustic dominant mode propagation in a trifurcated lined duct with different impedances

Abstract

In this study, we analyzed the diffraction of the acoustic dominant mode in a parallel-plate trifurcated waveguide with normal impedance boundary conditions in the case where surface impedances of the upper and lower infinite plates are different from each other. The acoustic dominant mode is incident in a soft/hard semi-infinite duct located symmetrically in the infinite lined duct. The solution of the boundary value problem using Fourier transform leads to two simultaneous modified Wiener–Hopf equations that are uncoupled using the pole removal technique. Two infinite sets of unknown coefficients are involved in the solution, which satisfy two infinite systems of linear algebraic equations. These systems are solved numerically. The new kernel functions are factorized. Some graphical results showing the influence of sundry parameters of interest on the reflection coefficient are presented.