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以凸肩叶片为研究对象,应用Donnell’s简化壳理论建立模型的非线性振动方程,考虑了几何非线性、阻尼、凸肩接触面正压力、摩擦力等因素。采用Galerkin法将振动微分方程离散到模态坐标上,分别应用数值法和近似解析法对方程组求解,得到系统的频率响应曲线,并讨论了系统周期解的稳定性。结果表明,由于凸肩接触面之间摩擦力方向周期性改变,导致系统的振动特性产生不连续性,以摩擦力为正、负方向分别绘制一条频率响应曲线。则随着摩擦力方向T/4周期变换一次,系统的振动也以T/4为周期在两条频率响应曲线上来回跳跃,从而有效抑制叶片的振动响应,提高叶片使用的安全性。
Taking the shoulder blade as the research object, the nonlinear vibration equation of the model is established by using Donnell’s simplified shell theory. The geometric nonlinearity, damping, positive pressure at the shoulder contact surface and frictional force are considered. The Galerkin method is used to discretize the vibration differential equations to the modal coordinates. The equations are solved by numerical method and approximate analytic method respectively, and the frequency response curves of the system are obtained. The stability of the system periodic solutions is also discussed. The results show that due to the periodic change of the frictional force between the contact surfaces of the shoulders, the vibration characteristics of the system are discontinuous. A frequency response curve is plotted in positive and negative directions respectively. The vibration of the system jumps back and forth on the two frequency response curves with a period of T / 4 as the T / 4 cycle of the frictional force changes once, thereby effectively suppressing the vibration response of the blade and improving the safety of the blade.