Sound propagation in acoustically lined elliptical ducts

• We study sound propagation in ducts of elliptical cross-section and lined walls.
• The acoustic pressure field is described in terms of Mathieu functions.
• The impedance boundary conditions lead to the coupling of modes of different orders.
• An approximation for small eccentricity, where modes are uncoupled, was derived.
• Mode attenuation for elliptical ducts is higher than for circular ducts.

Sound propagation in ducts with elliptical cross-sections can be described in terms of modes characterized by Mathieu functions of orders specified by the boundary conditions. For ducts with locally reacting liners there is coupling between modes because the admissible solutions are linear combinations of Mathieu functions of different orders and the eigenvalues are roots of an infinite determinant. The amount of mode coupling depends on the eccentricity of the duct. For the case of small eccentricity of the duct, approximate general solutions are derived and an example is discussed, where solutions are found.