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本文研究柔性旋转带冠叶片的接触振动问题.应用Frobenius方法计算旋转带冠叶片横向振动的动频和模态函数,并给出了模态函数正交性的证明.提出了利用叶片的弯曲动刚度描述的等效接触刚度来确定相邻旋转叶片接触刚度的方法,在此基础上,采用Galerkin截断将叶片的偏微分运动微分方程离散为常微分方程描述的旋转带冠叶片的分段线性动力系统.然后应用平均法,计算了旋转带冠叶片在尾流激励下的主共振响应,并分析当相邻叶冠间隙、尾流激励力幅值、叶片厚度和长度作为可调参数时系统的动力学响应与非线性行为,揭示了旋转带冠叶片的碰撞振动机理以及叶冠结构参数与叶片振动抑制之间的关系.
In this paper, the problem of contact vibration of flexible rotating crown blades is studied.The dynamic and modal functions of the transverse vibration of rotating crown blades are calculated by Frobenius method, and the orthogonality of modal functions is also proved. Stiffness of the adjacent contact to determine the contact stiffness of the adjacent rotating blade method, on this basis, the use of Galerkin truncation of the leaf partial differential equation of motion is discreted by the ordinary differential equations describe the rotary blade with a piecewise linear dynamic System.And then, averaging method was used to calculate the main resonance response of rotating crown blades under wake excitation, and the influence of adjacent crown clearances, wake excitation amplitude, blade thickness and length as the adjustable parameters Dynamic response and nonlinear behavior, the mechanism of collision vibration of rotating crown blades and the relationship between structural parameters and blade vibration suppression were revealed.