Closed‐Form Design and Understanding of Vertical Inerter–Based Dampers for Wind Turbines

Wind turbines with larger capacities face bending deformation due to taller towers and longer blades, necessitating mitigation against extreme seismic loads. A vertically installed inerter‐based damper, referred to as the tuned viscous mass damper (TVMD), is proposed alongside a closed‐form design approach. First, the mechanical model and simulation approach for the TVMD and wind turbines are introduced, followed by the derivation of governing equations and frequency response solutions, considering the parked state. Second, a nacelle‐hub assembly displacement–oriented design principle is formulated, providing mathematical design expressions and closed‐form solutions based on the generalized fixed‐point principle. Finally, the effectiveness of the proposed framework is validated through design cases and comparative investigation of theoretical approaches, under parked conditions with negligible aerodynamics and thus low effective damping, highlighting the advantages of the closed‐form design formulas. The results indicate that the vertically installed TVMD offers superior performance compared to traditional damping design approaches in wind turbines, enabling the simultaneous control of multiple seismic responses. Furthermore, the nacelle‐hub assembly displacement–oriented design principle and closed‐form design formulas provide a quantitative framework for optimizing key design parameters of vertical TVMDs, facilitating rapid design implementation and deeper theoretical understanding. In addition, the proposed closed‐form design formulas ensure enhanced energy dissipation and specific modal tuning capacity, offering robustness against parameter variations.