MATHEMATICAL-MODELING OF THE COMBINED EFFECTS OF VORTEX-INDUCED VIBRATION AND GALLOPING .2.

A semi-empirical mathematical model based on the Hartlen-Currie model of vortex-induced vibration and the quasi-steady model of Parkinson and Smith has been shown elsewhere to be in good agreement with experimental observations under two-dimensional nonresonant and subharmonically resonant conditions. The present work gives an improved solution of the model for the primary resonance case. The method of multiple scales is used with an appropriate asymptotic embedding. We give an approximate analytical solution exhibiting 180° phase jumps in time. Numerical solution of the slow-flow equations shows that phase entrainment and phase drift can also occur. In addition to steady-state amplitudes, we exhibit libration oscillations where the limiting body amplitude and wake amplitude vary periodically, while the phase difference does not. We also present some bifurcation studies of the model equations. We also give an explicit analytical solution for the equilibria of the Hartlen-Currie model, calculated using Gröbner bases, which is more compact and useful than previous solutions. This solution exhibits phase jumps as the wind speed is changed. © 1993 by Academic Press, Inc.