A note on the acoustics of a duct with a wall treatment of axially partitioned porous material

Abstract

Considered is the problem of sound propagation through a cylindrical duct with a wall treatment consisting of a layer of porous material, usually fixed by a segmented structure. The mathematical problem is one of sound fields in the duet and in the layer coupled by conditions of continuity across the interface. So, in general, the layer is not locally reacting and cannot be represented by an impedance of the wall. As a result calculations tend to be quite complex. However, in the present paper it is shown that if the porous layer is segmented by an axial array of annular partitions with a small enough pitch, the coupling of the fields simplifies in such a way that the condition of continuity reduces to a boundary condition, per circumferential mode similar to that of a point reacting liner. So then the porous material is characterized by a circumferential mode number‐dependent impedance of the duct wall. Consequently, all the well‐established theory for sound propagation in ducts with uniform wall impedance is applicable from here on.