An Efficient Finite Element Formulation for the Analysis of Acoustic and Elastic Waves Propagation in Sound Packages

A new mixed finite element formulation very well adapted to analyze the propagation of elastic and acoustic waves in porous absorbing media is presented. The proposed new formulation is based on modified Biot's equations [1,2,3] written in terms of the skeleton displacement and the acoustic pressure in the interstitial fluid. It generalizes the previous formulation proposed in reference [11], and has the great advantage over existing formulations [5, 6, 7, 8, 9, 10, 11, 12 and 13] of automatically satisfying interior and exterior boundary conditions without having to compute surface coupling integrals at porous sub-domain interfaces. When elastic forces in the skeleton are neglected, the formulation automatically degenerates to an equivalent fluid model taking into account inertial coupling with the skeleton. In addition it reduces to a minimum the number of degrees of freedom (dofs) and considerably simplify the modeling effort by allowing the computation of the generalized impedance matrix added by complex porous components to the vibro-acoustic impedance matrix of the bare vehicle body. Thus it simplifies the cooperative work between vehicle suppliers and manufacturers. This generalized mixed formulation and associated equivalent fluid model has been implemented by STRACO (France) in RAYON-PEM Solver. It is shown in this paper, that the numerical results predicted with RAYON-PEM agrees very well with experimental results using bazooka impedance tube and RTC tests.