A finite element scheme for acoustic propagation in flexible-walled ducts with bulk-reacting liners, and comparison with experiment

The effects of wall flexibility on the propagation of acoustical and structural waves in ducts lined with bulk-reacting sound-absorbing material is studied both theoretically and experimentally. The theoretical treatment involves the use of a coupled finite element model for the airway, liner and flexible wall. Coupled eigenmodes in the duct are determined and a composite solution is obtained, by the use of modal superposition, for the sound field in the vicinity of a transition from a rigid to a flexible-walled segment. Analogous experimental data are presented for the sound pressure level inside a simple test duct of rectangular cross-section with a flexible wall. The wall displacement is also measured, and good agreement is obtained between theoretical and measured results. Both indicate significant increases in sound absorption within the duct—compared with that in a rigid-walled duct—in the vicinity of “cut-on” frequencies for the axial structural modes in the duct wall. Some parametric studies of this effect are also presented.