UBC Theses and Dissertations
Mathematical modelling of the combined effects of vortex-induced vibration and galloping Corless, Robert Malcolm
In this thesis a mathematical model for the combined effects of vortex-induced oscillation and galloping of a square section cylinder in cross flow is examined. The model equations are obtained by simply combining Parkinson and Smith's Quasi-Steady Model for galloping with the Hartlen-Currie model for vortex-induced vibration, which is essentially the same model used by Bouclin in the hydrodynamic case. The semi-empirical model is solved using three popular approximate analytical methods, and the methods of solution are evaluated. The solution of the model is compared with recent experimental data. The methods of solution used are the Method of Van Der Pol, (also called the method of Harmonic Balance), the Method of Multiple Scales, and some results from the Hopf Bifurcation Theory. The Method of Multiple Scales provides the most useful solutions, getting good results even with just the ༠(1) terms, although the next-order terms are necessary for the solution in the resonance regions. The phenomenon of subharmonic resonance, observed in recent experiments, is also observed in the solution of the model equations.