LAUM, CNRS, Universite du Maine, Avenue Olivier Messiaen, 72085 Le Mans, France.
J Acoust Soc Am. 2010 Feb;127(2):692-702. doi: 10.1121/1.3277190.
The nonlinear propagation through porous media is investigated in the framework of Biot theory. For illustration, and considering the current interest for the determination of the elastic properties of granular media, the case of nonlinear propagation in "model" granular media (disordered packings of noncohesive elastic beads of the same size embedded in a visco-thermal fluid) is considered. The solutions of linear Biot waves are first obtained, considering the appropriate geometrical and physical parameters of the medium. Then, making use of the method of successive approximations of nonlinear acoustics, the solutions for the second harmonic Biot waves are derived by considering a quadratic nonlinearity in the solid frame constitutive law (which takes its origin from the high nonlinearity of contacts between grains). The propagation in a semi-infinite medium with velocity dispersion, frequency dependent dissipation, and nonlinearity is first analyzed. The case of a granular medium slab with rigid boundaries, often considered in experiments, is then presented. Finally, the importance of mode coupling between solid and fluid waves is evaluated, depending on the actual fluid, the bead diameter, or the applied static stress on the beads. The application of these results to other media supporting Biot waves (porous ceramics, polymer foams, etc.) is straightforward.
本文在 Biot 理论的框架下研究了非线性在多孔介质中的传播。为了说明问题，同时考虑到当前人们对确定颗粒介质弹性性质的兴趣，我们考虑了在“模型”颗粒介质（由相同尺寸的无粘性弹性珠粒无序堆积在粘弹性流体中组成）中非线性传播的情况。首先考虑介质的适当几何和物理参数，得到线性 Biot 波的解。然后，利用非线性声学的逐次逼近法，通过考虑固体框架本构律中的二次非线性（其起源于颗粒间接触的高度非线性），推导出二次谐波 Biot 波的解。首先分析了具有速度频散、频率相关耗散和非线性的半无限介质中的传播。然后介绍了在实验中经常考虑的刚性边界颗粒介质板的情况。最后，根据实际流体、珠粒直径或施加在珠粒上的静态应力，评估了固体波和流体波之间的模式耦合的重要性。这些结果可直接应用于支持 Biot 波的其他介质（多孔陶瓷、聚合物泡沫等）。
