旋转梁与弹性圆结构碰摩的稳定性分析
Stability analysis of rotating beams rubbing on an elastic circular structure
摘要：
本文用Routh-Hurwitz准则分析了由柔性圆环上的旋转梁组成的系统的稳定性。所展示的模型已通过使用能量方法在旋转框架内得到充分发展。考虑的梁具有两个自由度（dofs），弯曲运动以及牵引/压缩运动。将考虑环的面内变形。发散和模式耦合因此在旋转坐标系中被强调，为了简化对所有这些现象的理解，梁的自由度将首先被单独处理，然后一起处理。弹性环上的径向旋转载荷的动力学可以产生发散不稳定性以及后临界模式耦合。此外，梁在环上的弯曲摩擦运动也会导致模式耦合和轨迹转向现象。摩擦的存在似乎使系统不稳定，只要光束的旋转速度大于零。最后，将研究光束与环内表面法线之间的角度对系统稳定性的影响，从而突出频移现象。
英文摘要：
This paper presents the stability analysis of a system composed of rotating beams on a flexible, circular fixed ring, using the Routh-Hurwitz criterion. The model displayed has been fully developed within the rotating frame by use of an energy approach. The beams considered possess two degrees of freedom (dofs), a flexural motion as well as a traction/compression motion. In-plane deformations of the ring will be considered. Divergences and mode couplings have thus been underscored within the rotating frame and in order to simplify understanding of all these phenomena, the dofs of the beams will first be treated separately and then together. The dynamics of radial rotating loads on an elastic ring can create divergence instabilities as well as post-critical mode couplings. Moreover, the flexural motion of beam rubbing on the ring can also lead to mode couplings and to the locus-veering phenomenon. The presence of rubbing seems to make the system unstable as soon as the rotational speed of the beams is greater than zero. Lastly, the influence of an angle between the beams and the normal to the ring's inner surface will be studied with respect to system stability, thus highlighting a shift frequency phenomenon.
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