基于大挠度板理论的旋转轮盘振动及动力学特性研究

Study on Vibration and Dynamics Characteristics of Rotating Disk Based on Large Deflection Plate Theory

摘要: 将轮盘简化为内圈固定–外圈自由的等厚弹性圆板模型，通过运用基尔霍夫薄板理论在固定坐标系里建立了轴对称旋转轮盘的大挠度横向自由振动方程。运用两次伽辽金法获得轮盘自由振动的振型。在临界转速附近，施加一个横向载荷，得到旋转轮盘的受迫振动方程，进而分析了不同转速下的轮盘动态特性。结果表明：相同的节径数对应的振型相同，但是相位有所区别；不同转速下的受迫振动响应曲线总体呈周期分布，转速越高，同一时间段内的周期越短。在一定工况下动态响应可以大致反映轮盘的振动形式，且振幅最大值的变化趋势与转速大小没有直接关系。

Abstract: The disk was simplified as the same thickness elastic circular plate model fixed at the inner ring and free at the outer ring, and the large deflection transverse free vibration equation of axis sym-metry rotating disk was established in the fixed coordinate system based on the Kirchhoff theory of thin plates. The free vibration mode of disk was obtained by using the Galerkin method two times. A transverse load was applied near the critical speed; the forced vibration equation of rotating disk was established, and then the dynamic characteristics of the disk under different rotating speeds were analyzed. The results showed that the same diameter number corresponds to the same vibration mode of disk, but the phases of two vibration modes are different. The forced vibration responses of the disk under different rotating speeds are periodically distributed, and the higher the rotating speed, the shorter the period in the same time. The dynamic characteristic of the disk under the certain condition is roughly presented by the dynamic response, and the changing trend of the maximum amplitude of the disk has no direct relationship with the rotating speed.