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

Abstract

A theoretical analysis is presented of sound propagation in cylindrical ducts lined with porous material (bulk absorbers). Various configurations are discussed: (i) The porous material is homogeneous; then the sound field is built up of modes, (ii) The properties of the liner vary slowly in 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 wave numbers vary in axial direction slowly with the liner (multiple scale solution), (iii) 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 acoustically can be described 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.