Modeling and Bending Vibration of the Blade of a Horizontal-Axis Wind

Abstract: 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 Corio-lis forces effect, the governing differential equa-tions 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 poly-nomial forms, then the exact solution for the sys-tem can be obtained. Based on the frequency rela-tions as revealed, without tedious numerical anal-ysis, one can reach many general qualitative con-clusions between the natural frequencies and the physical parameters of the beams. The validity of the conclusions is not limited in specialized do-mains. Finally, the influences of the pre-cone an-gle, 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