Parametric resonances of floating wind turbine blades under vertical wave excitation

The parametric resonances of the blades in floating offshore wind turbines are theoretically and experimentally investigated. In the theoretical analysis, each blade is pinned to a horizontal, rotating shaft and has a spring with rotational stiffness at the end. The blade is subjected to horizontal excitation which represents winds; the rotating shaft to vertical excitation which represents waves. The equation of motion for the blade inclination angle includes parametric excitation terms with three different frequencies, i.e., the rotational speed of the blade, and the sum of and difference between the rotational speed and wave excitation frequency. Numerical simulations are conducted for the corresponding linearized system, and it is found that unstable vibrations appear at several rotational speed ranges. An empirical approach is used to determine the regions where the unstable vibrations appear. Swept-sine tests are conducted to determine the frequency response curves for the nonlinear system and demonstrate that the parametric resonances appear at similar rotational speeds as those of the unstable regions. In experiments, parametric resonances were observed at the rotational speeds and wave excitation frequencies predicted by the theoretical analysis.