An efficient finite element scheme for solving the three-dimensional poroelasticity problem in acoustics

Abstract

In this paper, the finite element method (FEM) is used to solve the three-dimensional poroelasticity problem in acoustics based on the isotropic Biot–Allard theory. A displacement finite element model is derived using the Lagrangian approach together with an analogy with solid elements. From this model, it is seen that the “damping” and “stiffness” matrices of the poroelastic media are complex and frequency dependent. This leads to cumbersome calculations for large finite element models and spectral analyses. To overcome this difficulty, an efficient algorithm is proposed. It is based on low-frequency approximations of the frequency-dependent dissipation mechanisms in poroelastic media. This efficient algorithm allows the poroelastic materials to be modeled with classical FEM codes. Also, the acoustic–poroelastic and the poroelastic–poroelastic coupling conditions are presented. The proposed model is compared to existing literature for both two-dimensional and three-dimensional problems. Excellent comparisons prove both the accuracy and effectiveness of the proposed model and its coupling with acoustic elements. Finally, to show the usefulness of the proposed model, the edge effect on the absorption coefficient of a multilayered poroelastic material is presented. Results show that both analytical models based on laterally infinite poroelastic layers, and standing wave tube measurements may be misleading at low frequencies.