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A new twist on an old model for predicting the vortex-excited vibrations of flexible cylindrical structures is developed. A van der Pol equation, driven by the local transverse motion of the cylinder, is taken as the governing equation for one component of the fluctuating lift force on the cylinder. The second component of the lift force is represented by a stall term which is linearly proportional to the local transverse velocity of the cylinder. In previous models, the van der Pol equation has been employed as the governing equation for the entire fluctuating lift force on the cylinder. The new model preserves the modal scaling principle for the structural response, as initially predicted by the previous models and since verified experimentally. The empirical parameters in the model are related to the physical mass and damping parameters that define the structural properties so that the maximum structural response and the reduced velocity at which it occurs agree with experimental observations. Because of the stall term, the new model provides for an asymptotic, self-limiting structural response at zero structural damping. This asymptotic, self-limiting behavior was not captured by the previous models.
Skop et al. (Thu,) studied this question.