This dissertation describes fundamental extensions to the hinge-spring model used to simulate the first mode of blade vibration in wind turbine dynamics. Complete equations of motion are developed while allowing for both bending of the blade perpendicular to its chord and overall motion of the rotor in azimuth and yaw. The model examines the relationship between the natural rotation frequency of the rotor ω and the fundamental natural bending frequency of the blades without including the bending frequency of the tower. In the case of no yaw motion, perturbation analysis and iteration lead to analytical solutions for the bending and azimuth equations of motion that involve as little simplification of these equations as possible. The natural bending frequency is "stiffened" by the rotor rotation and is expressed as a multiple of the rotor rotation, ω [low *] ω. While the bending frequency is used in models using the hinged blade, the solutions found in this work contain more detail than can be found in prior investigations. These analytical solutions reveal that the harmonics with frequencies N ω [low *] ω (ω [low *] + 1)ω and (ω [low *] - 1)ω are involved with the coupling between bending motion and azimuth motion with N = 1, 2, 3,.... Subsequent derivation of the power output for the condition of a relatively large amplitude of blade vibration predicts a noticeable contribution to power generation for the ω [low *] ω response, which is verified in the data.
Glauret's momentum transfer theory as extended by Wilson and Lissaman [1974] and de Vries [1979] is modified to allow for blade bending, variations of wind speed with time and position, and variations in wind direction with time. No vertical wind is considered. It is concluded that: (1) the bending frequency and linear combinations with the rotor rotation frequency provide an important contribution under at least some of the expected operating conditions of the turbine, (2) the dynamic mass imbalance produced by the effects of blade bending is not important for an otherwise balanced rotor, and (3) modest non-symmetric effects to the dynamics such as basic wind shear or changing wind speed and direction enhance the N ω frequencies much more readily than the N ω [low *] ω frequencies.
