Abstract
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.
Highlights
$EVWUDFW The parametric resonances of the blades in floating offshore wind turbines are theoretically and experimentally investigated
Numerical simulations are conducted for the corresponding linearized system, and it is found that unstable vibrations appear at several rotational speed ranges
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
Summary
Equation (4), includes parametric excitation terms with different three frequencies, i.e., Z, Z+:, and Z:. By conducting numerical simulations of Eq (4), it is found that the following unstable vibrations, each of which includes a predominant frequency, appear as follows:. Because periodic vibrations of predominant frequencies may appear, the following empirical approach, based on the simulation results, is used to determine the boundaries of the unstable regions. A final substitution of the third-order approximate solution, including all the generated frequency components, into Eq (4), results in the equation. The boundaries for the unstable regions of other periodic vibrations of predominant frequencies such as (:2Z)/2 and (:3Z)/2 can be determined using the same empirical approach which resulted in Eq (9)
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