Tuned mass-damper-inerter (TMDI) for suppressing edgewise vibrations of wind turbine blades

This paper proposes the use of a tuned mass-damper-inerter (TMDI) for the mitigation of edgewise blade vibrations in wind turbines. The hollow nature of the wind turbine blades is utilized to install a TMDI at a location close to the tip of each blade. A flexible multi-modal offshore wind turbine model is developed in order to study the dynamics of wind turbine blade vibrations. Uncontrolled, TMD controlled and TMDI controlled models are derived. These models are developed using the Euler–Lagrangian approach and lead to time-varying systems with the possibility of negative damping. Closed-form expressions for the optimal tuning and damping ratios of blade-mounted TMDIs are derived. Numerical simulations are then presented to demonstrate the performance of the TMDI controlled blades. The results show that TMDIs can control edgewise vibrations in wind turbine blades while requiring significantly less damper stroke than classical TMDs. The inclusion of the inerter in the damper had a significant effect on the damper stroke with reductions of up to 55% demonstrated. These impressive reductions in damper stroke come at the cost of very slightly increased blade vibration as compared to the TMD controlled case. This is a trade-off that must be considered in the design of a wind turbine.