Analysis of a mimetic finite difference approximation of flows in fractured porous media

We consider the mixed formulation for Darcy’s flow in fractured media. We give a well-posedness result that does not rely on the imposition of pressure in part of the boundary of the fracture network, thus including a fully immersed fracture network. We present and analyze a mimetic finite difference formulation for the problem, providing convergence results and numerical tests.

Design of a passive electrical analogue for piezoelectric damping of a plate

Vibrations of a mechanical structure can be reduced through a piezoelectric coupling to a passive electrical network exhibiting similar modal properties. For the control of a plate, the design of a two-dimensional analogous electrical network is considered. Depending on the mechanical boundary conditions, a finite difference formulation of the Kirchhoff–Love equation of motion shows that we need to ensure specific electrical connections along the edges of the analogous network. A numerical model involving an assembly of element matrices validates the electrical topology. Then, the passive electrical circuit is implemented with capacitors, inductors, and transformers, whose practical design is closely described. Focusing on the analogue of a clamped plate, experiments prove the ability of the proposed electrical network to approximate the behavior of the mechanical structure.