旋转薄圆盘的行波动力学特性分析

Dynamic Characteristics Analysis of Traveling Waves for Rotating Thin Disks

旋转圆盘是广泛应用于旋转机械装置中的基本结构元件,圆盘在高速旋转状态下会表现出与低速或非旋转状态下迥异的力学性能。本文对高速旋转薄圆盘横向振动的行波动力学特性进行了分析,建立了考虑离心力引起的薄膜内力影响下的动力学控制方程以及相应的边界条件。采用伽辽金法数值模拟了旋转圆盘前、后行波振动频率和动力屈曲失稳临界转速随着圆盘几何参数如半径比、厚度的变化规律,以及材料参数对于振动频率和临界转速的影响等。本文的数值计算可以同时给出圆盘旋转的前、后行波频率,并且结果与实验结果吻合良好。

As the elementary structures, thin disks are widely employed in many rotating machines and equipments. There always exhibits distinct mechanical behaviors of a rotating disk with high-speed comparing to a rotating disk with low-speed or a non-rotating disk. Taking into account the membrane stresses due to centrifugal effect, the dynamic governing equation and boundary conditions for the rotating disk with high-speed were derived. Based on Galerkin＇s Method, the analysis on the dynamic characteristics of traveling waves for rotating disk vibration was presented. The results of frequencies for the forward and backward traveling waves dependence upon the geometrical and material parameters of thr rotating disk were obtained numerically. The effects of geometrical and material parameters on the critical speed of rotating disk dynamic instability were discussed. The numerical results of both forward and backward traveling frequencies were obtained to show good agreements with some experimental data.