Wave properties in poroelastic media using a Wave Finite Element Method

The application of the bidirectional Wave Finite Element Method (WFE) to Biot-Allard׳s theory of poroelasticity is investigated. This method has been successfully used in previous elastodynamics studies. In the case of porous media, the rigidity of the layer is very low, leading to very small wavelengths, and a high dissipation rate occurs within the pores. These differences with the elastic case justify a study of their consequences on numerical results. In this paper, it is shown that despite these difficulties, the WFE provides an efficient tool to compute the waves propagating through poroelastic media. The influence of boundary conditions on wave propagation is discussed, as well as the convergence of the numerical results, depending on the spatial discretization, the order of shape functions, and the choice of the formulation. Finally, the wavenumbers predicted with this method are compared with some simplified models such as equivalent fluid models or equivalent plate models. It is shown that the WFE can be used to validate the assumptions made by the simplified models.