Natural Modal Computation of Wind Turbine Blades Considering Structural Multi-Degree-of-Freedom Coupling
This study addresses the structural coupling mechanisms in large wind turbine blades by deriving a free vibration equation based on Euler-Bernoulli beam theory and Lagrange's equation, incorporating shear, bend-twist coupling, flap-lag coupling, and axial-bending coupling. The NREL 5 MW reference turbine serves as the case study. The formulation yields explicit mass and stiffness matrices, and the resulting eigenvalue problem is solved to quantify modal frequency shifts and mode shape variations. Results indicate that shear deformation reduces flapwise and edgewise frequencies, with second-order flapwise and edgewise modes decreasing by approximately 4.7% and 1.0%, respectively. Bend-twist coupling lowers bending frequencies while elevating torsional frequencies; the effect intensifies with mode order, as evidenced by a 3.1% reduction in third-order edgewise frequency and a 1.6% increase in second-order torsional frequency. Flap-lag coupling exerts a more pronounced influence on edgewise characteristics than on flapwise ones. Axial-bending coupling exhibits the least impact among the three coupling types. In terms of mode shapes, bend-twist and axial-bending couplings minimally affect low-order bending modes, whereas flap-lag coupling is the primary driver of pronounced coupling in bending mode shapes. These findings provide a reference for subsequent multi-degree-of-freedom coupled dynamic modeling.