匀速转动内悬臂梁稳定性研究

本文采用了凯恩简化模型并提出大范围平动和转动共同作用下的连续体梁模型；通过两种模型分析了匀速转动内悬臂梁的稳定性；指出了匀速转动内悬臂梁存在动力柔化现象，动力柔化的原因在于梁的大范围平动；提出了匀速转动内悬臂梁的内转半径和外转半径的概念，指出匀速转动内臂梁的内转半径和外转半径比值存在一定关系时，系统为一阶稳定，研究表明，同时作大范围平动和转动的柔性梁存在柔化和刚化的分界点，需要在实际应用中予以注意。

Analysis of Stability for Internal Cantilever Beam with Even Rotational Speed

In this paper, Kane simplified model was used and a beam model undergoing large range movement and large range rotation was presented. With both of the two models, the stability of an internal cantilever beam with even rotational speed was studied. It is pointed out that an internal cantilever beam has dynamic softening phenomena during rotation with even speed, and the dynamic softening phenomenon is ascribed to the large range movement of the beam. The concepts of internal radius and external radius are put forward. When the ratio of the internal radius to the external radius satisfies some relation, the dynamic system of the internal cantilever is stable. The study indicates that the flexible beam undergoing large translation and rotation can have dividing point of dynamic stiffening and dynamic softening, it should be considered during application.