论文标题
旋转均匀弹性圆柱的同步旋转：线性和弱的非线性分析
Synchronous whirling of spinning homogeneous elastic cylinders: linear and weakly non-linear analyses
论文作者
论文摘要
通过考虑轴的横截面中的完全变形，可以重新审视细长和均匀（连续的）弹性轴的固定旋转，并在末端旋转，并在末端旋转，并在末端旋转。研究了针对任何波长的同步正弦扰动的稳定性，并通过考虑几何和材料（超弹性）非线性来衍生出屈曲振幅的分析表达。对于任何弹性本构定律，分叉在长波长域中是超临界的，对于有限的非线性材料参数，在短波长限制中次临界。
Stationary whirling of slender and homogeneous (continuous) elastic shafts rotating around their axis, with pin-pin boundary condition at the ends, is revisited by considering the complete deformations in the cross section of the shaft. The stability against a synchronous sinusoidal disturbance of any wave length is investigated and the analytic expression of the buckling amplitude is derived in the weakly non-linear regime by considering both geometric and material (hyper-elastic) non-linearities. The bifurcation is super-critical in the long wave length domain for any elastic constitutive law, and sub-critical in the short wave length limit for a limited range of non-linear material parameters.
