尾流激励下功能梯度叶片动力学行为研究

Dynamics behavior analysis of functionally graded blades under the trail excitation

为探究尾流激振力作用下旋转功能梯度叶片的振动特性,本文建立了具有任意预置角的旋转功能梯度叶片模型,并对其动力学行为展开研究。基于改进Fourier级数对旋转叶片的振动位移场进行拟合,采用罚函数实现叶片任意边界约束,尾流激振力展开为多项正弦谐波叠加的形式,通过Ritz法对旋转叶片的振动问题进行求解。经过与文献中结果对比验证了方法的收敛性和正确性,并给出新的计算结果和关键参数分析。研究表明:通过改变功能梯度叶片的组分分布可以调整其固有频率;叶片各阶固有频率会随转速、轮毂半径、预置角的增加而增大;在转速范围一定时,谐次越高的尾流激振力谐波引起的临界转速也越多。

To investigate the effects of trail excitation on the vibration characteristics of rotating functionally graded blades,a dynamic model of rotating functionally graded blades with arbitrary presetting angles is established,and the dynamic behavior of the model is analyzed.The vibration displacement functions of rotating blades are fitted based on an improved Fourier series.A penalty function is adopted to realize the arbitrary boundary constraints of the blade.In addition,the trail excitation is expanded as sinusoidal harmonics.The vibration problem of rotating blades is solved using the Ritz method.By comparison with the results in the literature,the convergence and correctness of the present method are demonstrated,and new results of computation and key parameter analyses are given.The results show that the natural frequencies of the functionally graded blades can be adjusted by changing the distribution of components,and the natural frequencies of blades increase with the rotation rate,rotating radius,and presetting angle.Additionally,in a certain range of rotation speeds,the higher the harmonic order is,the higher the critical speed caused by the harmonic of wake exciting force.