Nonlinear Oscillations of Spar-type Floating Offshore Wind Turbines under Parametric Sea Wave Excitation and External Wind Load

An approximate two-Degrees-Of-Freedom analytical model is developed to detect the nonlinear dynamic response of a Floating Offshore Wind Turbine, mounted on a spar platform, under parametric excitations induced by the periodic variation of the buoyancy force due to sea waves. The equations of motion are analytically studied through the Multiple Time Scales Method, up to the fifth order, under the main Parametric Resonance condition (that involves period-2 solutions) as well as through the Harmonic Balance Method (HBM) to detected the period-1 non resonant oscillations. The response amplitude-damping curve, obtained by the third order analyses, reveals that the rest position of the mechanical system loses its stability by a Hopf bifurcation in favor of an oscillatory solution, which is much more accurately described by the fifth order analyses. Furthermore, a new branch of solutions is detected through the HBM, which coexist with the resonant one but is detached from it. These results, all numerically verified also by means of basins of attraction, reveal a situation that could be particularly dangerous from an engineering point of view and, therefore, stress the necessity of accounting for such effects in the early stages of design and control strategies. Subsequently, a new more detailed 4-DOF analytical model is developed to study the nonlinear dynamic behavior of system, when it is subjected to both parametric sea wave excitation and external aerodynamic load.