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将风力机叶片简化为绕轮毂旋转的变截面Euler-Bernoulli悬臂梁,基于Greenberg公式给出非线性气动力,建立叶片挥舞振动非线性控制方程.由于变截面梁的弯曲刚度和线密度是沿梁轴线变化的函数,无法给出模态函数解析式,论文提出使用假设模态法计算的模态函数,作为基函数对控制方程进行Galerkin截断,通过将挥舞振动分解为静态位移和动态扰动合成,对其进行动态响应分析,同时讨论了叶轮转速、风速和旋转位置对振动特性的影响.研究表明:(1)叶轮转速对叶片挥舞特性影响显著,风速和叶片转角对振动特性影响很小.(2)静态位移随风速增加而增大,大体上成线性关系,气动阻尼随风速增加而减小.(3)风速较低时,非线性挥舞振动表现为衰减振动,随着风速增加,振动由衰减振动演化为周期运动,再由周期运动演化为拟周期运动.
The wind turbine blade is simplified as a variable section Euler-Bernoulli cantilever rotating around the wheel hub, and the nonlinear aerodynamic force is given based on the Greenberg formula to establish the nonlinear governing equation of blade waving vibration. Because the bending stiffness and linear density of the beam are variable, Axis function can not give the analytic formula of modal function. In this paper, the modal function calculated by the hypothetical modal method is proposed as Galerkin truncation of the governing equation as a basis function. By decomposing waving vibration into static displacement and dynamic perturbation, The dynamic responses of the blade were analyzed and the influence of the rotational speed, the wind speed and the rotational position of the impeller on the vibration characteristics were also discussed.The results show that: (1) The impeller speed has a significant influence on the waving characteristics of the blade, while the wind speed and the blade angle have little influence on the vibration characteristics. 2) The static displacement increases with the increase of wind speed, which is generally linear, and the aerodynamic damping decreases with the increase of wind speed. (3) When the wind speed is low, the nonlinear vibration waving is attenuated. As the wind speed increases, Vibration is evolved from damping vibration to periodic motion, and then from periodic motion to quasi-periodic motion.