Dimensionally Consistent Torsional-Stiffness Modeling for Long Flexible Wind-Turbine Blades Using the Variational Asymptotic Method

With the increasing size of wind turbines and the trend toward longer and more flexible blades, the aeroelastic response of blades has become significant. To achieve efficient and high-fidelity modeling, a new approach is required. In this study, a parametric two-dimensional cross-sectional model is developed based on the Variational Asymptotic Method, retaining Saint-Venant free warping. Vlasov theory is incorporated to add the warping-rigidity term associated with longitudinal variation in the torsion rate to the energy functional, thereby representing non-uniform-warping energy. To address the taper effect in variable-section blade structures, dimensionally consistent offset- and gradient-dependent correction terms are introduced through Tapered Beam Modification (TBM) to establish an expression for tapered torsional stiffness. Numerical results are presented for a tapered beam, a uniform composite beam, and the NH1500 blade; the method is then applied to the IEA 15-MW blade. The results show that, for the tapered beam, TBM reduces the deviation in the global frequency-equivalent stiffness from 4.2% to 2.1%, while for the IEA 15-MW application the peak sectional correction is 3.88% at x=0.320 and the first torsional frequency differs by 5.21% between the two reduced-order models. The reported time-domain and AEP differences quantify sensitivity to the structural model.