Along-wind and cross-wind coupled nonlinear oscillations of wind turbine towers close to 1:1 internal resonance

An approximate analytical solution is obtained to detect the along-wind and cross-wind coupled oscillations of wind turbine towers, in the neighbourhood of a 1:1 internal resonance. The obtained formulas are general, and they are applied to the NREL 5-MW reference wind turbine. It is shown that the coupled solution is branched (by a pitchfork bifurcation) from the main uncoupled along-wind oscillation. The coupled motion is initially stable, but for increasing excitation amplitudes it becomes unstable in favour of quasi-periodic solutions, a fact that is particularly dangerous from a practical point of view and so must be avoided. The critical threshold is determined for varying excitation amplitude, and the analytical solution is checked by means of numerical simulations.