Sound attenuation in ducts lined with non-isotropic material

Abstract

This paper deals with the sound attenuation in rectangular ducts with non-isotropic lining. The non-isotropy may be due to the basic structure of the fibrous lining material or it may be deliberately created by rigid partitioning of the lining perpendicular to the duct axis. The propagation constant in the axial direction is obtained in the form of a transcendental equation which includes as special cases the locally reacting lining investigated by Morse [1] and Cremer [2] for infinite flow resistance in the direction of the duct axis, and the homogeneous lining as treated by Scott [4]. A simple approximate solution of the transcendental equation for low frequencies indicates that optimum attenuation of the fundamental mode is achieved by using a non-isotropic lining with a flow resistance in the direction of the duct axis that increases with increasing frequency. At middle and high frequencies, the propagation constant is evaluated numerically by using a Newton-Raphson scheme for several typical silencer geometries.