# American Institute of Mathematical Sciences

2011, 2011(Special): 813-823. doi: 10.3934/proc.2011.2011.813

## FLUID STRUCTURE INTERACTION PROBLEM WITH CHANGING THICKNESS NON-LINEAR BEAM Fluid structure interaction problem with changing thickness non-linear beam

 1 Department of Mathematics and Statistics, Texas Tech University, Lubbock TX, 79409-1042 2 Department of Mathematical Sciences, George Mason University, Fairfax VA, 22030

Received  July 2010 Revised  April 2011 Published  October 2011

In this work we consider the dynamical response of a non-linear beam interacting with potential flow. The beam part is modeled using a non-linear system of momentum equations for the axial and transverse displacements. Changing in the beam thickness has been modeled in the momentum of inertia. The fluid flow part is subjected to the Bernoulli potential law. In particular we show that for a class of boundary conditions and for a speci c constraint in the beam thickness rate of change, there exists an appropriate energy norm which is bounded by the incoming flow velocity in the liquid region.
Citation: Emine Kaya, Eugenio Aulisa, Akif Ibragimov, Padmanabhan Seshaiyer. FLUID STRUCTURE INTERACTION PROBLEM WITH CHANGING THICKNESS NON-LINEAR BEAM Fluid structure interaction problem with changing thickness non-linear beam. Conference Publications, 2011, 2011 (Special) : 813-823. doi: 10.3934/proc.2011.2011.813
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