Imbalance-induced nonlinear vibrations in wind turbine towers

This paper investigates the nonlinear dynamic response of a wind turbine tower under rotor imbalances. A coupled analytical model for a three-bladed horizontal-axis turbine on a tapered monopole tower is developed, using a Lagrangian formulation, with the nonlinear equations of motion derived via Hamilton's principle. The model incorporates a nonlinear aerodynamic torque, enabling accurate dynamic representation under varying conditions. In contrast to prevalent uncoupled models, this novel formulation captures essential nonlinear interactions and energy transfer between the tower and rotor. The equations are solved using an explicit Runge-Kutta method, and a customized continuation scheme analyses system bifurcations, identifying instability via Floquet multipliers. Results demonstrate that even small blade mass imbalances significantly amplify the tower's dynamic response, with effects increasing with imbalance severity. Comparisons with uncoupled models highlight the critical role of nonlinear coupling. These findings support improved design and assessment of wind turbine towers under fault conditions to avoid resonant or damaging behavior. • A nonlinear rotor-tower model incorporating blade mass imbalance. • Coupled rotor-tower dynamics formulated with rotation as an unknown. • Custom continuation algorithm maps the system's stability landscape. • Analysis shows blade-tower interaction critically affects stability thresholds.