Stability prediction of vortex-induced vibrations of multiple freely oscillating bodies

The vortex-induced vibration of multiple spring-mounted bodies free to move in the orthogonal direction of the flow is investigated. In a first step, we derive a linear arbitrary Lagrangian–Eulerian method to solve the fluid–structure linear problem as well as a forced problem where a harmonic motion of the bodies is imposed. We then propose a low computational-cost impedance-based criterion to predict the instability thresholds. A global stability analysis of the fluid–structure system is then performed for a tandem of cylinders and the instability thresholds obtained are found to be in perfect agreement with the predictions of the impedance-based criterion. An extensive parametric study is then performed for a tandem of cylinders and the effects of mass, damping and spacing between the bodies are investigated. Finally we also apply the impedance-based method to a three-body system to show its validity to a higher number of bodies.