An axisymmetric poroelastic finite element formulation

In the past, various two- and three-dimensional Cartesian, poroelastic fini te element formulations have been proposed and demonstrated. Here an axisym metric formulation of a poroelastic finite element is presented. The intent ion of this work was to develop a finite element formulation that could eas ily and efficiently model axisymmetric sound propagation in circular struct ures having arbitrary, axially dependent radii, and that are lined or fille d with elastic porous sound absorbing materials such as foams. The formulat ion starts from the Blot equations for an elastic porous material expressed explicitly in axisymmetric form.:By following a standard finite element de velopment, a u-U formulation results. Procedures for coupling the axisymmet ric elements to an adjacent acoustical domain are described, as are the bou ndary conditions appropriate for unfaced foams. Calculations described here show that the present formulation yields predictions as accurate as a Cart esian, three-dimensional model in much reduced time. Predictions made using the present model are also compared with measurements of sound transmissio n through cylindrical foam plugs, and the predicted results are shown to ag ree well with the measurements. Good agreement was also found in the case o f sound transmission through a conical foam plug. (C) 1999 Aconstical Socie ty of America. [S0001-4966(99)03308-1].