壳板凸肩叶片的非线性振动特性

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。

NONLINEAR VIBRATION CHARACTERISTICS OF SHROUDED BLADE FOR CYLINDRICAL PANEL

A shrouded blade is investigated in this paper. Using Donnell’s nonlinear shallow-shell theory, the nonlinear equation of vibration is obtained, in which the geometric nonlinearity, damping, shroud contact normal load and friction between shrouds are taken into account. Discretized by a Galerkin method, the nonlinear mode equations are studied by using numerical and analytical methods, then nonlinear frequency-response curves are obtained. The stability of periodic solutions of the system is also analyzed. The results show that the periodic changes in the direction of the friction force between shrouds cause the discontinuity of vibration characteristics of the system. In order to describe the inherent vibration characteristic of the system, two frequency-response curves are drawn, which respectively adopts the positive and negative directions of the friction force. With the changes of the direction of a friction force in a period of T/4, the vibration of the system also jumps between these two curves with a period T/4, this effectively suppress the response amplitude of a shrouded blade, and improves its safety.