章动角对旋转章动充液腔体运动稳定性的影响

Effect of Nutation Angle on Stability of a Spinning and Nutating Cylinder Filled with Liquid

旋转章动充液腔体的运动稳定性,主要分两大类。当Reynolds数很小时,出现转速衰减不稳定性,Reynolds数增大到一定程度,又出现共振不稳定性。本文考虑Reynolds数较大时的情况,此时腔内液体的惯性波振动与腔体的章动频率耦合即可发生共振不稳定性.当章动角增大时,共振频带又发生转移。采用变形参数法讨论章动角增大时弱非线性影响,很简明地得出特征值修正公式,并计算了液体力矩的变化曲线。

The stability of a spinning and nutating cylinder filled with liquid is mainly divided into two kinds. When Reynolds number is very small, it appears resonant instability; when Reynolds numlel increases to some value, it appears resonant instability. The condition of very large Reynolds number is studied in this paper. At this moment the inertial wave oscillation of liquid in cylinder coupling with the nutating frequency of cylinder, the cylinder will result in resonant instability. As increasing of nutation angle, the frequency band of resonance will shift. An approach of modified parameter is used to discuss the effect of weak nonlinear problem as nutation angle increases. A modified formula to liquid oscillation eigenvalue is simply derived, and calculation of the fluctuation curves of liquid moment is presented in this paper.