Theoretical prediction of sound attenuation in a liquid‐filled rectangular flow duct using a viscoelastic‐fluid composite liner

A theoretical investigation was made of the sound attenuation in a two‐dimensional, liquid‐filled duct treated with a composite liner consisting of a viscoelastic slab and a fluid layer, which is backed by a perfectly rigid plate. The viscoelastic material is a rubber‐like material that has a loss factor associated with the shear modulus, and is characterized by Lame constants and the material density. The fluid layer of the composite liner is assumed to be lossless and nondispersive medium, and is characterized by the fluid density and the speed of sound. The fluid contained in the lined duct is assumed to be inviscid and characterized by the fluid density and the speed of the sound. The eigenvalue equation was derived based on the theory of elasticity, the acoustic wave equation in the presence of the flow in the duct, the acoustic wave equation in the absence of the flow for the fluid layer of the composite liner, and pertinent boundary conditions. The eigenvalue equation was solved numerically for a given duct geometry, the liner configuration, the composite liner material properties, and the flow velocity. Then, the sound attenuation was obtained using the calculated eigenvalues.