The dynamic analysis of random fibrous networks (RFNs) is a novel topic, which has many applications since these networks are very often subjected to dynamical loading conditions such as mechanical vibrations. In order to bypass the complexity of performing dynamic computations at the microscopic scale of RFN, we develop and identify couple-stress and second gradient models as effective continua at the mesoscopic level of windows of analysis. The static mechanical properties which are at the basis of the dynamical analysis are computed thanks to FE simulations performed over windows of analysis subjected to mixed boundary conditions allowing to capture the classical and non-classical effective moduli. The acoustic properties are captured by the dispersion diagrams and phase velocity plots; we analyze the influence on the dynamic properties of the fiber bending length, and the fiber network density. The impact of these parameters is successively assessed for the couple-stress and strain gradient substitution continua. A comparison of the acoustic properties of the two effective media is provided, showing that the couple-stress medium is essentially non-dispersive for the longitudinal mode and dispersive for the shear mode, whereas the strain gradient medium behaves in a dispersive manner for both modes.

随机纤维网络（RFN）的动态分析是一个新颖的话题，它具有许多应用，因为这些网络经常受到动态载荷条件（例如机械振动）的影响。为了绕过在RFN微观尺度上执行动态计算的复杂性，我们开发并确定了耦合应力和第二梯度模型作为分析窗口的介观水平的有效连续性。得益于在混合边界条件下对分析窗口进行的有限元模拟，可以计算出作为动力学分析基础的静态机械性能，从而可以捕获经典和非经典有效模量。声学特性由色散图和相速度图捕获。我们分析了对纤维弯曲长度的动态特性和纤维网络密度的影响。对于偶应力和应变梯度替换连续性，依次评估了这些参数的影响。比较了两种有效介质的声学特性，结果表明，耦合应力介质在纵向模式下基本上是非分散的，在剪切模式下是分散的，而应变梯度介质在两种模式下的行为都是分散的。