当前位置: X-MOL 学术Acta. Mech. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Geometric variational approach to the dynamics of porous medium, filled with incompressible fluid
Acta Mechanica ( IF 2.7 ) Pub Date : 2020-07-02 , DOI: 10.1007/s00707-020-02726-3
Tagir Farkhutdinov , François Gay-Balmaz , Vakhtang Putkaradze

We derive the equations of motion for the dynamics of porous medium, filled with incompressible fluid. We use a variational approach with a Lagrangian written as the sum of terms representing the kinetic and potential energy of the elastic matrix, and the kinetic energy of the fluid, coupled through the constraint of incompressibility. As an illustration of the method, the equations of motion for both the elastic matrix and the fluid are derived in the spatial (Eulerian) frame. Such an approach is of relevance e.g. for biological problems, such as sponges in water, where the elastic porous medium, is highly flexible and the motion of the fluid has a ‘primary’ role in the motion of the whole system. We then analyze the linearized equations of motion describing the propagation of waves through the medium,. In particular, we derive the propagation of S-waves and P-waves in an isotropic medium,. We also analyze the stability criteria for the wave equations and show that they are equivalent to the physicality conditions of the elastic matrix. Finally, we show that the celebrated Biot’s equations for waves in porous medium, are obtained for certain values of parameters in our models.

中文翻译:

充满不可压缩流体的多孔介质动力学的几何变分方法

我们推导出充满不可压缩流体的多孔介质动力学的运动方程。我们使用变分方法,将拉格朗日量写为代表弹性矩阵的动能和势能以及流体动能的项的总和,通过不可压缩性约束耦合。作为该方法的说明,弹性矩阵和流体的运动方程都是在空间(欧拉)坐标系中导出的。这种方法与生物问题相关,例如水中的海绵,其中弹性多孔介质高度灵活,并且流体的运动在整个系统的运动中具有“主要”作用。然后我们分析描述波在介质中传播的线性化运动方程。特别是,我们推导出 S 波和 P 波在各向同性介质中的传播。我们还分析了波动方程的稳定性标准,并表明它们等价于弹性矩阵的物理条件。最后,我们证明了多孔介质中波的著名 Biot 方程是针对我们模型中的某些参数值获得的。
更新日期:2020-07-02
down
wechat
bug