Eigenvalue Analysis of sound propagation characteristics in a circular duct lined with poroelastic foams

• We consider eigenvalue analysis of a coupled system of poroelastic foam and airway
• Complex dispersion relations in a cylindrical foam-lined duct are identified.
• The effect of thickness, boundary conditions, and viscosity of the foam is discussed.

An effective method for eigenvalue analysis of a circular duct lined with poroelastic foams is presented using axisymmetric finite element models based on Biot's theory and Helmholtz equation. Complex dispersion relations in a cylindrical foam-lined duct are successfully identified using an iterative Prony series method. It is shown that the numerical results obtained by the proposed method agree well with those obtained by measurements and direct forced response simulations. The influences of thickness and boundary conditions of the poroelastic foam on the sound propagation characteristics in a duct are also investigated. Furthermore, the damping effect due to viscosity of the foam on dispersion curves is discussed at a theoretical level.