Sound attenuation in rectangular and circular cross-section ducts with flow and bulk-reacting liner

Abstract A generalized theory is presented for sound propagation in lined ducts of arbitrary cross-section where acoustic wave propagation in the lining is also taken into account. The effects of a mean fluid flow in the duct airway, an anisotropic bulk reacting liner and a limp, impervious membrane covering the liner are all taken into account. Simple extension of the formalism to include the effect of a perforated facing is also provided. Bulk reacting and locally reacting liners are treated as limiting cases. The general analysis is pplied to ducts of both rectangular and circular cross-section, taking into account higher order modes as well as plane wave sound propagation. Design charts for duct attenuation in octave frequency band averages and in terms of dimensionless parameters are presented.