Development of a reduced order model for nonlinear analysis of the wind turbine blade dynamics

In this paper, a reduced order model for the nonlinear dynamic analysis of the wind turbine blade under operational loading is presented. The accuracy and efficiency of the proposed model are investigated through various static and dynamic analyses. A comprehensive straightforward formulation for the nonlinear beam model is developed based on different large deformation strain theories. Also, the fluid-structure coupling effects due to quasi-steady aerodynamics and gravitational forces are included. The new matrix expressions are introduced for direct conversion of the developed formulation into the reduced order model (ROM). Thereafter, the ROM based on the Galerkin method is developed using all effective coupled modes of the blade (including the torsional modes which are neglected in the majority of previous works). The 5-MW National Renewable Energy Laboratory wind turbine blade is considered for the simulations. Presented results indicate the importance of torsional degrees of freedom; that neglecting them changes the trend of the system response apparently. Comparing with the results of full/complex finite element model, it is shown that the ROM with considering 11 coupled modes of the blade, guarantees the enough accuracy. The accordance of the proposed ROM for the Green-Lagrange and Jaummann-Biot-Cauchy strain theories is observed. However, for the case of ROM based on the Von Karman theory, the neglected large deformation kinematics leads to the inaccurate results. In addition to the coupled effect induced by the mass center offset, results show the importance of edgewise-torsional and edgewise-flapwise nonlinear coupled terms. These terms play a key role in transmission of harmonic excitation caused by gravitational loading from edgewise to the flapwise and torsional directions.