A study on coupled edgewise and flapwise vibration modes of wind turbine blade

The coupled flapwise and edgewise vibrations of a horizontal axis wind turbine blade (HAWT) are discussed in this paper. Kinetic and potential energies of the blade are evaluated with consideration of the effects of gravity and aerodynamic forces. Hamilton’s principle is employed to develop the nonlinear coupled modal equations of the blade. The coupling between the first order edgewise and the first two order of flapwise modes is considered. This leads to three equations with nonlinear terms. Multiple-scales perturbation method is employed to solve these equations. Furthermore, the numerical values of structural specifications of National Renewable Energy Laboratory (NREL) 5-MW reference wind turbine blade are used, for example. It is shown that first edgewise and first flapwise vibrations are dominant, while second flapwise mode of vibration is less significant in the case of transient responses. Energy transfer between resonant modes is observed in both internal and combination resonances. The amplitude–frequency curves and phase diagrams during primary and combination resonances are obtained for the steady-state responses. Combination and primary resonances are further examined by considering various factors such as geometric nonlinearity and aerodynamic force.