旋转均匀弹性圆柱体的同步涡动：线性和弱非线性分析
Synchronous whirling of spinning homogeneous elastic cylinders: linear and weakly non-linear analyses
摘要：
考虑轴截面的完全变形，重新研究了两端具有销-销边界条件的细长均匀（连续）弹性轴的定常涡动。对任何波长的同步正弦扰动的稳定性进行了研究，并通过考虑几何和材料（超弹性）非线性，推导出了弱非线性状态下屈曲振幅的解析表达式。对于任何弹性本构关系，在长波长范围内分叉都是超临界的，而对于有限范围的非线性材料参数，在短波长范围内分叉是亚临界的。
英文摘要：
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.
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。
