Modeling and bending vibration of the blade of a horizontal-axis wind power turbine

The blade of a horizontal-axis wind power turbine is modeled as a rotating beam with pre-cone angles and setting angles. Based on the Bernoulli-Euler beam theory, without considering the axial extension deformation and the Coriolis forces effect, the governing differential equations for the bending vibration of the beam are derived. It is pointed out that if the geometric and the material properties of the beam are in polynomial forms, then the exact solution for the system can be obtained. Based on the frequency relations as revealed, without tedious numerical analysis, one can reach many general qualitative conclusions between the natural frequencies and the physical parameters of the beams. The validity of the conclusions is not limited in specialized domains. Finally, the influences of the pre-cone angle, the angular speed and the setting angle on the natural frequencies of the beam are studied by the proposed numerical method. The phenomenon of divergence instability is also discussed.