Vortex-induced vibration of a single circular cylinder is a fundamental and significant case of flow-induced vibrations in both engineering practice and academic research. A force evolution model is developed for vortex-induced vibration of an elastic cylinder in a cross flow. In this model, the elastic cylinder is represented by the Euler-Bernoulli beam theory, and the vortex-induced force acting on the stationary cylinder is modeled by a bounded-noise process. Fluid-structure interaction is represented by an evolution process based on the concept of quasi-steady flow. A numerical iterative approach is used to simulate the evolution process and obtain time histories of cylinder vibration and vortex-induced force. The model is validated against available measurements. It is shown that the proposed model can reproduce the salient features observed in experiments. Furthermore, quantitative agreement with experimental measurements is obtained in general. However, when the vibration amplitude is very large due to intense fluid-structure interaction, the proposed model prediction is not quite satisfactory. This suggests that the concept of quasi-steady flow is only applicable for relatively weak fluid-structure interaction.

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