Analytical study of mode filtering in a duct with resistive layers

This paper presents an analytical mode-matching framework to examine acoustic wave propagation in a cylindrical waveguide structure featuring a central porous cavity bounded by flexible membrane discs. Unlike conventional models that consider rigid or purely absorptive boundaries, the proposed approach accounts for the dynamic response of membranes and the coupled behavior of air and porous media, enabling accurate representation of fluid-structure interactions. The acoustic field is decomposed into symmetric and anti-symmetric modal components to capture key physical phenomena such as mode conversion, energy dissipation, and complex reflection-transmission mechanisms. Continuity conditions at the interfaces are applied to determine the interaction of wave modes between subdomains, allowing the calculation of reflected, transmitted, and absorbed acoustic powers. Numerical results demonstrate strong reflection and efficient low-frequency absorption, with negligible transmission. Parametric analysis reveals that increasing the length of the porous cavity enhances sound attenuation by intensifying dissipative effects. These findings highlight the effectiveness of the multilayered configuration as a frequency-selective acoustic filter, offering a tunable and practical solution for silencers and noise control in engineering structures.