Existence and uniqueness result for a fluid–structure–interaction evolution problem in an unbounded 2D channel

Abstract

AbstractIn an unbounded 2D channel, we consider the vertical displacement of a rectangular obstacle in a regime of small flux for the incoming flow field, modelling the interaction between the cross-section of the deck of a suspension bridge and the wind. We prove an existence and uniqueness result for a fluid–structure-interaction evolution problem set in this channel, where at infinity the velocity field of the fluid has aPoiseuille flowprofile. We introduce a suitable definition of weak solutions and we make use of a penalty method. In order to prevent the obstacle from going excessively far from the equilibrium position and colliding with the boundary of the channel, we introduce astrong forcein the differential equation governing the motion of the rigid body and we find a unique global-in-time solution.