旋转轴和转子的应力
Stress in Rotating Disks and Cylinders
摘要：
经典的旋转弹性圆盘或圆柱体中的应力问题的解，如弹性理论的标准文本中所解决的，有两个特点：使用的动力学方程只在惯性参考系中有效，在应变的定义中，位移梯度中去掉了二次项。我表明，在惯性参考系的动力学方程是有效的，这是不正确的，因为它们是一样大的线性项，保持下降的二次项。我提供了一个替代配方的问题，通过转换的动力学方程的参考系的磁盘/气缸，在那里下降的二次项位移梯度是合理的。分析表明，经典教科书中应力应变的推导必须解释为在介质的共转坐标系中进行。
英文摘要：
The solution of the classic problem of stress in a rotating elastic disk or cylinder, as solved in standard texts on elasticity theory, has two features: dynamical equations are used that are valid only in an inertial frame of reference, and quadratic terms are dropped in displacement gradient in the definition of the strain. I show that, in an inertial frame of reference where the dynamical equations are valid, it is incorrect to drop the quadratic terms because they are as large as the linear terms that are kept. I provide an alternate formulation of the problem by transforming the dynamical equations to a corotating frame of reference of the disk/cylinder, where dropping the quadratic terms in displacement gradient is justified. The analysis shows that the classic textbook derivation of stress and strain must be interpreted as being carried out in the corotating frame of the medium.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
