| In recent years,wind power is flourishing in the world.The wind turbine blade plays a crucial role in the normal operation of wind turbines since it is the key component in capturing wind energy.As blade damage affects the normal operation of wind turbines,reduces power generation efficiency and in some cases even causes the collapse of the entire turbine,it is particularly important to monitoring and identify damage of turbine blades during their service life.As the blade size increases,so does the blade flexibility;this in turn weakens the coupling between the blades and hub.Therefore,the rotor can be regarded as a weakly coupled periodic structure.As the same time,structural damage of wind turbine blades mean that different blades are generally slightly different from each other.Such blade variation is known as mistuning.With the presence of mistuning,significant changes in the dynamics of wind turbine blades will occur and resulting in detuned effects such as mode localization and modal jumping in the wind turbine structure.Therefore,it is great important to study the dynamic characteristics of mistuned wind turbine structure which could help us to understand the mechanism and process of blades damage malfunctioning the wind turbines.This paper investigates the phenomenon of mode localization and jumping of the mistuned wind turbine structures by modal analysis,finite element method,perturbation theory and modal parameter identification.In addition,a damage indicator for blades is proposed through this mistuned feature.The main contents are following:(1)The unique dynamic behavior of mode localization in linear time-varying wind turbine rotors is investigated.The rotating blades are approximated as cantilever Bernoulli–Euler beams,and the Lagrangian method is employed to derive the linear time-varying dynamic equations of the wind turbine rotor.Floquet analysis is employed for modal decomposition of a mistuned wind turbine rotor,and the effects of slight mistuning of the blade stiffness and rotor speed on different modes are examined systematically.Numerical simulation results indicate that slight mistuning of a single blade is sufficient for triggering mode localization.(2)The mechanism and influencing factors of mode localization in wind rotor due to the blade damage are investigated.The dynamic mechanism of mode localization is studied by the perspective of first-order perturbations of eigenvalues,and it is found that the essential cause of modal localization is the existence of closely spaced modes in periodic symmetric structures.The finite element model of NREL 5MW wind turbine rotor is established,and the effects of blade mistuning,modal order,and mistuning position on mode localization of the wind turbine rotor are analyzed.And the mode localization results indicate that the energy of the wind turbine rotor system is concentrated on the damaged blade in some modes which can further aggravate the blade damage and reduce the service life.(3)Two improved spatial Timoshenko beam elements are developed to improve the calculation accuracy of wind turbine blades.Analytical interpolation functions for bending deformation are constructed according to Timoshenko beam equilibrium equations.Shape functions for the translational deformation and transverse shear deformation are established based on the relationships between total deflection,bending slope and transverse shear.The eccentric effect of blade cross-section is considered,and two improved wind turbine blade beam elements are derived by the finite element theory.Relevant finite element computation programs are compiled with the correctness and accuracy verified by several typical examples.(4)The changes in the dynamics of wind turbine structures due to small damage mistuning of the blades are studied,and a damage indicator for blades is proposed.The finite element model of NREL 5MW is established by using the improved beam element,and the effects of blade mistuning on the vibration modes of the wind turbine are analyzed.The results of this study are the first to show that small blade mistuning can cause mode jumping in the NREL5 MW wind turbine,and the mechanism of mode jumping in wind turbines is further explored.Taking advantage of the fact that the small damage mistuning of the blades are sensitive to some mode shapes of the wind turbine,a damage indicator of wind turbine blades based on the vibration correlation coefficient is proposed,and the effectiveness of the indicator is verified by some cases.(5)Through numerical calculation and modal tests,a conclusion of possible mode localization of mistuned wind turbines is drawn.Firstly,the effects of manufacturing error and damage mistuning of the blade 1 on mode shapes of NREL 5MW wind turbine are examined,and the results show that mode localization phenomenon occurs in the first-order flapwise mode in NREL 5MW wind turbine.Then,the effects of manufacturing error and damage mistuning of actual blade 1 on mode shapes of wind turbine are also examined by modal tests,It is demonstrated that the mistuning of actual blade1 can cause modal localization in the mistuned wind turbine structure which are consistent with the numerical simulation results. |
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