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.