Abstract Permeo-elastic media are permeable media whose pore fluid network is connected and their solid frame is made of a stiff skeleton onto which highly flexible thin films are fixed. In this work, we investigate acoustic wave propagation in permeo-elastic media accounting for pore-scale membrane and bending effects in the films. To this end, use is made of the two-scale asymptotic homogenisation method to derive upscaled models, of asymptotic analyses to disclose the different wave propagation regimes, and of the finite element method to solve the local fluid-structure interaction boundary-value problems arising from homogenisation. The study evidences the salient acoustic features of permeo-elastic media and shows that these may significantly depart from those of conventional porous media due to the interplay of the elastic and kinetic energies of the films with the viscous and kinetic energies of the fluid. It is concluded that the control of membrane and bending effects may lead to a useful way of tuning the atypical effective acoustical properties of permeo-elastic media.

中文翻译：

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渗透弹性介质中的孔隙尺度弯曲和膜效应

摘要 渗透弹性介质是一种渗透性介质，其孔隙流体网络相连，其实体框架由刚性骨架构成，其上固定有高柔性薄膜。在这项工作中，我们研究了渗透弹性介质中的声波传播，考虑了薄膜中的孔隙尺度膜和弯曲效应。为此，使用两尺度渐近均匀化方法来推导放大模型，使用渐近分析来揭示不同的波传播方式，并使用有限元方法来解决出现的局部流固耦合边界值问题来自同质化。该研究证明了渗透弹性介质的显着声学特征，并表明由于薄膜的弹性和动能与流体的粘性和动能的相互作用，这些可能显着不同于传统多孔介质的声学特征。得出的结论是，膜和弯曲效应的控制可能会导致一种有用的方法来调整渗透弹性介质的非典型有效声学特性。