Coupled flap and edge wise blade motion due to a quadratic wind force definition

The wind force on turbine blades, consisting of a drag and lift component, depends nonlinearly on the relative wind velocity. This relative velocity comprises mean wind speed, wind speed fluctuations and the structural response velocity. The nonlinear wind excitation couples the flap wise and edge wise response of a turbine blade. To analyze this motion coupling, an isolated blade is modelled as a continuous cantilever beam and corresponding nonlinear expressions for the drag and lift force are defined. After reduction of the model on the basis of its principal modes, the nonlinear response up to the second order is derived with the help of a Volterra series expansion and the harmonic probing technique. This technique allows for response analysis in the frequency domain, via which the combined flap and edge wise responses can easily be visualized. As a specific case, the characteristics of the NREL5 turbine blades are adopted. For both non-operating and operating conditions, blade responses in a turbulent wave field, based on a Kaimal spectrum, are determined. The second-order responses are shown to cause additional motion coupling, and moreover, are proven not to be negligible straightforwardly