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Evolution Equations and Control Theory (EECT)
 

Stability analysis of non-linear plates coupled with Darcy flows

Pages: 193 - 232, Volume 2, Issue 2, June 2013      doi:10.3934/eect.2013.2.193

 
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Eugenio Aulisa - Department of Mathematics and Statistics, Texas Tech University, Lubbock TX, 79409-1042, United States (email)
Akif Ibragimov - Department of Mathematics and Statistics, Texas Tech University, Lubbock TX, 79409-1042, United States (email)
Emine Yasemen Kaya-Cekin - Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, United States (email)

Abstract: In this paper we study the dynamical response of a non-linear plate with viscous damping perturbed in both vertical and axial directions and interacting with Darcy flow. We first consider the problem for non-linear elastic body with damping coefficient; existence and uniqueness of the solution for the steady state problem is proven. The stability of the dynamical non-linear plate problem under certain conditions on the applied loads is investigated. Second, we explore the fluid structure interaction problem with Darcy flow in porous media. Energy functional for the displacement field of the plate and the gradient pressure of the fluid flow is built in an appropriate Sobolev type norm. We show that for a class of boundary conditions the energy functional is limited by the flux of mass through the inlet boundary.

Keywords:  Stability, non-linear plate, von Karman plate, Darcy flow.
Mathematics Subject Classification:  Primary: 58F15, 58F17; Secondary: 53C35.

Received: October 2012;      Revised: January 2013;      Published: March 2013.

 References