Reduced order modeling of fluid structure interaction and vortex induced vibration systems using an extension of Jourdain's principle
Abstract A first principles variational approach is proposed for reduced order modeling of fluid structure interaction (FSI) systems, specifically vortex induced vibration (VIV) FSI has to be taken into account in the design and analysis of many engineering applications, yet a comprehensive theoretical development where analytical equations are derived from first principles is nonexistent. An approach where Jourdain's principle is modified and extended for FSI is used to derive reduced order models from an extended variational formulation where assumptions are explicitly stated. Two VIV models are considered: an elastically supported, inverted pendulum and a translating cylinder, both immersed in a flow and allowed to move transversely to the flow direction. Their reduced order models are obtained in the form of (i) a single governing equation and (ii) two general coupled equations as well as the coupled lift oscillator model. Comparisons are made with three existing models. Based on our theoretical results, and especially the reduced order model, we conclude that the first principles development herein is a viable framework for the modeling of complex fluid structure interaction problems such as vortex induced oscillations.