Fluid structure interaction problem with changing thickness beam and slightly compressible fluid

Eugenio Aulisa; Akif Ibragimov; Emine Yasemen Kaya-Cekin

doi:10.3934/dcdss.2014.7.1133

Article Contents

2014, Volume 7, Issue 6: 1133-1148. Doi: 10.3934/dcdss.2014.7.1133

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Fluid structure interaction problem with changing thickness beam and slightly compressible fluid

1.
Department of Mathematics and Statistics, Texas Tech University, Lubbock TX, 79409-1042
2.
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042

Received: January 2013

Revised: September 2013

Published: December 2014

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Abstract

In this work, we consider the dynamical response of a non-linear beam with changing thickness, perturbed in both vertical and axial directions, interacting with a Darcy flow. We explore this fluid-structure interaction problem where the fluid is assumed to be slightly compressible. In an appropriate Sobolev norm, we build an energy functional for the displacement field of the beam and the gradient pressure of the fluid flow. We show that for a class of boundary conditions the energy functional is bounded by the flux of mass through the inlet boundary.

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Mathematics Subject Classification: Primary: 74F10, 35Q35; Secondary: 58C35.

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