风力机叶片非线性挥舞分析

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.

ANALYSIS OF NON-LINEAR FLAP VIBRATION OF WIND TURBINE BLADES

The nonlinear governing equation of flap vibration is established by considering the blade as a rotating Euler-Bernoulli cantilever beam with variable sections on the hub.The unsteady aerodynamic forces acting on the blade are derived by using the Greenberg’s expressions.Considering the bending rigidity and line density are variable along the elastic axis and the expressions of modes can’t be derived directly,we introduce an assumed-mode method to compute modes functions.By using these modes functions as a functional base,the Galerkin procedure is applied to the governing equation in order to discrete the continuum model.The dynamic response is analyzed by decomposing the flap vibration as static displacements and dynamic ones.Influences of the rotating speed,the wind velocity,and the rotating angle to flap characteristics are discussed.The study shows that:1) the influence of the rotating speed on vibration characteristic is dramatic,but those of the wind velocity and the rotating angle are negligible;2) the static displacement increases proportionally with the wind velocity,but the aerodynamic damping decreases with the wind velocity;3) the nonlinear flap vibration under lower wind velocity attenuates,and it becomes a quasi-periodic vibration through a periodic vibration with increase of the wind velocity.