部分充液柔性转轴的动力稳定性

Dynamic Stability of Flexible Rotating Cylinder Partially Filled with Liquid

讨论了腔内部分充液的细长柔性转轴的动力稳定性．通过选择特征量和估计控制方程、边界条件中所有项的量级，把腔内流体的三维流动问题简化为二维流动问题．使用Ｂｅｒｎｏｕｌｉ－Ｅｕｌｅｒ梁的弯曲来描述转轴的变形以及二维转子的结果后，可以得到转轴失稳判别的解析表达式．本文工作发展了Ｃｒａｎｄａｌ的结果．

This paper discusses dynamic stability of a flexible slender rotating cylinder partially filled with liquid in its chamber. By choosing characteristic scales and estimating the orders of magnitude of all the terms in governing equations and boundary conditions,the three dimensional flow problem of the internal fluid can be simplified to a two dimensional flow problem. When the deformation of the cylinder is described by Bernoulli Euler beam bending and the results in the two dimensional rotor are used,unstable critical rules analytically can obtain. This investigation developed Crandall's result greatly.