A multimodal framework for attenuation of piston and planar waves in impedance-lined ducts

This study presents a multimodal formulation to investigate the scattering of acoustic waves in duct systems lined with locally reacting liners. The primary objective is to analyze the attenuation of piston-driven and planar acoustic radiations by employing impedance-based boundary conditions that accurately model liner behavior. A multimodal framework is developed to solve the governing boundary value problems by projecting acoustic fields onto orthogonal basis functions, with eigenvalues and eigenvectors used to characterize the modal propagation. The proposed method is validated against benchmark configurations, including rigid-walled ducts and ducts with impedance boundaries, and cross-compared with traditional mode-matching techniques. Numerical results demonstrate the effectiveness of the liners in attenuating acoustic energy, particularly at low frequencies, and confirm the convergence of the multimodal approach across a range of excitation conditions. The formulation is further applied to a reactive silencer geometry containing impedance-lined cavities, highlighting the liner's influence on wave scattering and overall noise reduction performance. This work provides a comprehensive modeling framework for evaluating liner treatments in complex acoustic systems and contributes to the design of efficient noise-control devices in ducts and silencers.