Attenuation of higher-order acoustic modes in a cylindrical waveguide using lined panel-cavity coupling

This work presents a mode-matching framework for analyzing acoustic attenuation in a waveguide that incorporates a centrally lined chamber, membrane discs at the interfaces, and extended inlet-outlet sections. The formulation also covers configurations with a lined cavity backed by rigid or soft discs, coupled to a single membrane disc at an interface adjoining an extended radiating region. The acoustic field within the waveguide is expressed through eigenfunction expansions, while the membrane response is modeled using a Galerkin procedure. The membrane displacement is projected onto orthogonal modal solutions constructed via Fourier series expansion. Applying interface continuity and orthogonality relations leads to truncated linear algebraic systems, which are solved numerically. These truncated solutions are then used to reconstruct matching conditions and confirm power conservation, thereby ensuring consistency of the formulation and convergence of modal amplitudes. The analysis reveals strong coupling between incident duct modes and localized cavity resonances, producing a panel-cavity interaction mechanism that drives selective attenuation. Numerical results highlight the efficiency of the proposed configuration in improving sound suppression over targeted frequency ranges under various lining conditions. The study offers practical insights for computational design and optimization of advanced noise-control solutions in ducted systems.