Nonlinear aeroelastic equations of motion of twisted, nonuniform, flexible horizontal-axis wind turbine blades
The second-degree nonlinear equations of motion for a flexible, twisted, nonuniform, horizontal-axis wind turbine blade are developed using Hamilton's principle. The derivation of the equations has its basis in the geometric nonlinear theory of elasticity, and the final equations are consistent with the small deformation approximation in which the elongations and shears are negligible compared to unity and the square of the derivative of the extensional deformation of the elastic axis is negligible compared to the squares of the bending slopes. A mathematical ordering scheme which is consistent with the assumption of a slender beam is used to discard some higher-order elastic and inertial terms in the second-degree nonlinear equations. The blade aerodynamic loading which is employed accounts for both wind shear and tower shadow and is obtained from strip theory based on a quasi-steady approximation of two-dimensional, incompressible, unsteady, airfoil theory. The resulting equations have periodic coefficients and are suitable for determining the aeroelastic stability and response of large horizontal-axis wind turbine blades.
- Research Organization:
- Toledo Univ., OH (USA)
- DOE Contract Number:
- AI01-76ET20320
- OSTI ID:
- 5414577
- Report Number(s):
- DOE/NASA/3139-1
- Country of Publication:
- United States
- Language:
- English
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