水平轴风机旋转叶片非线性动力学模型的建立及分析

 对不同风速下水平轴风力发电机旋转叶片的非线性动力学问题进行了研究，将水平轴风力发电机的旋转叶片简化为做定轴转动的柔性旋转悬臂梁，同时考虑叶片的气动力、弹性力和惯性力，建立了脉动风速作用下水平轴风力发电机旋转叶片的非线性动力学模型，利用牛顿定律建立了转动坐标系下叶片的动力学方程，并利用Galerkin离散方法将系统的运动偏微分方程离散为常微分方程。针对1/2亚谐共振-1:3内共振情形，考虑到方程中存在二次非线性项，采用渐进摄动法对该方程进行摄动分析，将其转化为直角坐标下的平均方程。通过数值模拟，得到这种共振情况下的二维相图、三维相图、波形图和频谱图，分析了风速的变化对旋转叶片振动的影响。数值结果表明，随着风速的增大，系统会重复呈现周期运动—混沌运动—周期运动。

Model Establishment and Nonlinear Dynamic Analysis of the Rotating Horizontal Axis Wind Turbine Blade

The nonlinear dynamics of the rotating blade of the Horizontal Axis Wind Turbine(HAWT) under the forces caused by the pulse wind is investigated in this paper. The blade is modeled as a rotating cantilever beam under the actions of aerodynamic forces, elastic forces and inertia forces. The nonlinear governing equation of motion for the rotating cantilevered blade under harmonic wind forces is obtained based on the Newton's law of motion. The Galerkin approach is used to transform the nonlinear partial differential governing equations of motion to a two-degree-of-freedom nonlinear ordinary equations. Due to the quadratic terms, the method of asymptotic perturbation is employed to transform the ordinary equation to the averaged equations in the case of 1/2 subharmonic resonance and 1:3 internal resonance. The planar phase portrait, the three-dimensional phase portrait, the waveform and the frequency spectrum of the averaged equations are obtained by numerical simulations. The influence of the mean wind speed and the stochastic wind speed on the system is studied. The results indicate that the motion of the blade of HAWT follows the following process: from periodic motion to chaotic motion and then to periodic motion.