Microstructure based estimation of the dynamic drag impedance of lightweight fibrous materials

This paper focusses on the prediction of one of the main mechanisms of acoustic attenuation, the dynamic drag impedance, of a bundle of fibres typical of lightweight fibrous porous materials. The methodology uses geometrical properties derived from microscopy, and is based on the assumption that the interaction between the shear stress fields of neighbouring fibres may be neglected in the predicted drag force of an individual fibre. An analytical procedure is discussed which provides an estimate of the drag forces acting on infinite longitudinal and transversely orientated cylinders oscillating sinusoidally in a viscous incompressible fluid of infinite extent, at rest. The frequency-dependent viscous drag forces are estimated from the shear stresses on the surface of the cylinders, and may be scaled in terms of fibre diameter distributions and orientation angles in order to predict the dynamic drag impedance of a real material. The range of validity for this modelling approach is assessed through finite element solutions of three different fibre arrangements.