A non-linear fluid force model for vortex-induced vibration of an elastic cylinder

Even under the assumption of a sinusoidal lift and drag force at a single frequency for a stationary cylinder in a cross flow, higher harmonics that represent non-linearity in the fluid–structure interaction process are present. This fact is considered in the formulation of a non-linear fluid force model for a freely vibrating cylinder in a cross flow. The force model is developed based on an iterative process and the modal analysis approach. The fluid force components in the model can be evaluated from measured vibration data with the help of the auto-regressive moving averaging (ARMA) technique. An example is used to illustrate that non-linear (higher order) force components are present at resonance, even for a case with relatively weak fluid–structure interaction. Further analysis reveals that the fluid force components are dependent on structural damping and mass ratio. The non-linear fluid force model is further modified by taking these considerations into account and is used to predict the dynamic characteristics of a freely vibrating cylinder over a range of Reynolds numbers, mass and structural damping ratios. On comparison with measurements obtained from four different experiments and predictions made by previous single-degree-of-freedom model, good agreement is found over a wide range of these parameters.