Nonlinear stochastic stability analysis of wind turbine wings by Monte Carlo simulations

Abstract

Wind turbines are increasing in magnitude without a proportional increase of stiffness, for which reason geometrical nonlinearities become increasingly important. In this paper the nonlinear equations of motion are analysed of a rotating Bernoulli–Euler beam including nonlinear geometrical and inertial contributions. A reduced two-degrees-of-freedom modal expansion is used specifying the modal coordinate of the fundamental blade and edgewise fixed base eigenmodes of the beam. The rotating beam is subjected to harmonic and narrow-banded support point motion from the nacelle displacement. It is shown that under harmonic excitation at certain combinations of eigenfrequencies, rotational frequency, amplitude and frequency of the support point motion, the nonlinear system may produce almost periodic response or even chaotic response. The strange attractor of this unstable behaviour is analysed under narrow-banded excitation, and it is shown that the qualitative behaviour of the strange attractor is very similar for the periodic and almost periodic responses, whereas the strange attractor for the chaotic case loses structure as the excitation becomes narrow-banded. Furthermore, the characteristic behaviour of the strange attractor is shown to be identifiable by the so-called information dimension. Due to the complexity of the coupled nonlinear structural system all analyses are carried out via Monte Carlo simulations.