Broadband and frequency dependent attenuation in reacting chamber with annular membrane resonators at junction planes

We study acoustic wave propagation and attenuation in a cylindrical waveguide in which a centrally located, impedance lined chamber is coupled to flexible membrane disks at its inlet and outlet junctions. The configuration comprises rigid upstream and downstream ducts connected through the lined section, while the membranes span the inner disk and outer annulus, introducing strong fluid–structure interaction and thereby modifying the reflection and transmission characteristics relative to rigid-walled geometries. A semi-analytical formulation is developed using a mode-matching framework for the acoustic field, combined with a Galerkin projection for the membrane dynamics, which yields a coupled linear system for the modal amplitudes and membrane coefficients. The membrane termination rings induce local edge singularities in the coupled acoustic membrane field, requiring careful representation in the modal reconstruction. The liner is modeled as locally reacting, allowing circumferentially varying impedance while keeping the axial distribution uniform. The analysis indicates that combining lined chambers with compliant membranes can provide both broadband and frequency dependent attenuation, supporting applications in HVAC ducts, exhaust silencers, and aero-engine intake systems.