Comprehensive analysis of the mechanism of sensitivity to initial conditions and fractal safe basins for wind turbine blade dynamics

The aim of this work is to enhance the understanding of the nonlinear dynamics of wind turbine blade oscillators. A novel in-plane and out-of-plane dynamic model of wind turbine blade oscillators (featuring Mathieu-Duffing oscillators) is proposed to investigate their global dynamic behavior. Firstly, the method of multiple scales (MMS), stability theorems, and basins of attraction are employed separately as quantitative and qualitative approaches to determine the existence of multistability and frequency jumps in this model. Subsequently, the new variable method and Melnikov method are applied to investigate the complex dynamic behavior such as chaos of global bifurcations. Finally, the evolution of the safe basin is utilized to characterize its fractal features. Both qualitative and quantitative results consistently confirm that the mechanism of sensitivity to initial conditions of this oscillator is attributed to the global instability dynamics of heteroclinic bifurcations. This study provides valuable insights into the global dynamic behavior and engineering applications of wind turbine blade oscillators.