Contributions to the theory of sound propagation in ducts with bulk-reacting lining lining

Abstract

A theoretical analysis of sound propagation in cylindrical ducts lined with porous material (bulk absorbers) is presented. Three configurations are discussed. (1) The porous material is homogeneous; then the sound field is built up of modes. (2) The properties of the liner vary slowly in an axial direction. A pure modal solution is, in general, not possible, but the field can be described by modes of the homogeneous liner, of which the amplitudes and wavenumbers vary in an axial direction slowly with the liner (multiple scale solution). (3) The porous material is embedded in an annular structure of partitions. For structural reasons this is a common situation. If the pitch of the partitions is small, the sound field in the liner is, per circumferential mode, decoupled from the duct field, and its effect can be described acoustically by an impedance (per circumferential mode). This ‘‘quasi-point-reacting’’ boundary condition may be easily incorporated in calculation procedures for ducts with locally reacting lining.