Wave properties in poroelastic media using a Wave Finite Element Method

• Published in: Journal of sound and vibration Vol. 335; pp. 125 - 146
• Main Authors: Serra, Q., Ichchou, M.N., Deü, J.-F.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 20.01.2015; Elsevier
• Subjects: Acoustics; Discretization; Equivalence; Finite element method; Mathematical analysis; Mathematical models; Mechanics; Media; Physics; Vibrations; Wave propagation; wave propagation 2000 MSC: 74J05; porous materials in vibroacoustics; Wave Finite Element Method; Biot-Allard's model
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2014.09.022

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. •Application of the Wave Finite Element Method to Biot–Allard theory for poroelastic media.•Linear elements can achieve same error than quadratic elements depending on the periodic substructure dimensions and mesh.•Using different formulations makes it possible to take into account for different lateral boundary conditions.•Analysis of influence of the solid phase and of the fluid phase.•Analytical models for flexural wave in poroelastic plates are limited to low-frequency range.