Modeling of wave number dependent absorptive characteristicswith the help of the theory of porous media

The modeling of sound fields in closed volumes is typically done with the help of the Statistical Energy Analysis. In the scope of this theory a diffuse sound field is assumed, resulting in random angles of incidence on the surfaces. If this assumption is violated, a realistic modelling of wave number dependent absorptive characteristics has to be considered. It is possible to describe the absorptive surfaces with their correct wave number depending impedances by modelling the fluid-structure-interaction with the help of the Finite Element Analysis, defining pressure and velocity as primary variables, which are evaluated with a phase-correct spatial resolution. The characteristics of wave number depending impedances for porous absorbers can e.g. be obtained from measurements of absorbers with varying angles of the incident waves. In order to consider this physical characteristics in the scope of a Finite Element approach, investigations based on the Theory of Porous Media are carried out. The system of coupled partial differential equations is transformed in the wave number-frequency domain and thus provides directly the impedances depending on the angle of the incident waves. The integration into a room acoustical simulation is presented.