Added damping of a wind turbine rotor: Two-dimensional discretization expressing the nonlinear wind-force dependency

In determining wind forces on wind turbine blades, and subsequently on the tower and the foundation, the blade response velocity cannot be neglected. This velocity alters the wind force, which depends on the wind velocity relative to that of the blades This blade response velocity component of the wind force is commonly referred to as added damping. The relation between the relative wind velocity and the actual wind forcing is nonlinear. Moreover, the wind excitation couples the flap and edge wise blade motion. This work analyzes both the nonlinear excitation and the coupling of the lateral blade motions. To this end, a single blade is modelled as a cantilever beam, which is exposed to the nonlinear wind excitation. Flap and edge wise blade motions are coupled via the wind forcing. Thereupon, the continuous model, described by a system of partial differential equations, is reduced to a two-degree-of-freedom system, accounting for the principal flap and edge wise modes only. The dynamic response is determined in the frequency domain for a blade of the academic NREL5 turbine. The response to the quadratic terms in the force formulation is determined with the help of the Volterra series expansion, in combination with the harmonic balance technique. Results are presented for a blade of both a non-operating and an operating turbine, where a bandlimited white noise input signal was applied. The quadratic terms in the forcing equations do not contribute much to the total responses. For some second order responses, however, negative added damping due to the structural motion is observed.