Acoustic waves in a poroelastic medium with periodic structure are studied with respect to permanent seepage flow which modifies the wave propagation. The effective medium model is obtained using the homogenization of the linearized fluid–structure interaction problem while respecting the advection phenomenon in the Navier–Stokes equations. For linearization of the micromodel, an acoustic approximation is introduced which yields a problem for the acoustic fluctuations of the solid displacements, the fluid velocity and pressure. An extended Darcy law of the macromodel involves the permeability and advection tensors which both depend on an assumed stationary perfusion of the porous structure. The monochromatic plane wave propagation is described in terms of two quasi-compressional and two quasi-shear modes. Two alternative problem formulations in the frequency domain are discussed. The one defined in terms of displacement and velocity fields leads to generalized eigenvalue problems involving non-Hermitean matrices whose entries are constituted by the homogenized coefficients depending on the incident wave frequencies, whereby degenerate permeabilities can be accounted for. The homogenization procedure and the wave dispersion analysis have been implemented to explore the influence of the advection flow and the microstructure geometry on the wave propagation properties, namely the phase velocity and attenuation. Numerical examples are reported.

针对具有周期性结构的多孔弹性介质中的声波，研究了永久性渗流会改变波的传播。使用线性化的流固耦合问题的均质化，同时考虑Navier–Stokes方程中的对流现象，可以获得有效的介质模型。为了使微模型线性化，引入了声学近似，这产生了固体位移，流体速度和压力的声学波动的问题。宏观模型的扩展达西定律涉及渗透率和对流张量，两者均取决于多孔结构的假定静态灌注。用两种准压缩模式和两种准剪切模式描述了单色平面波的传播。讨论了频域中的两个替代问题公式。用位移场和速度场定义的一个导致了广义特征值问题，涉及非赫米特矩阵，其项由入射波频率的均化系数构成，从而可以解决退化磁导率的问题。已经进行了均质化程序和波频散分析，以探索平流和微结构几何形状对波传播特性（即相速度和衰减）的影响。报告了数值示例。根据位移场和速度场定义的一个导致了广义特征值问题，涉及非赫米特矩阵，其项由入射波频率的均化系数构成，从而可以解决退化磁导率的问题。已经进行了均质化程序和波频散分析，以探索平流和微结构几何形状对波传播特性（即相速度和衰减）的影响。报告了数值示例。用位移场和速度场定义的一个导致了广义特征值问题，涉及非赫米特矩阵，其项由入射波频率的均化系数构成，从而可以解决退化磁导率的问题。已经进行了均质化程序和波频散分析，以探索平流和微结构几何形状对波传播特性（即相速度和衰减）的影响。报告了数值示例。已经进行了均质化程序和波频散分析，以探索平流和微结构几何形状对波传播特性（即相速度和衰减）的影响。报告了数值示例。已经进行了均质化程序和波频散分析，以探索平流和微结构几何形状对波传播特性（即相速度和衰减）的影响。报告了数值示例。