Abstract For the investigation of the initial post-buckling of a column built in at one end, clamped in rotation with a flexible support at the other, the stability of the bifurcation point is studied using the Fourier series. The second-order variation of the potential energy is proved to be semi-positive-definite at the bifurcation point. When the disturbance matches the buckling mode, the fourth-order variation is positive for some flexible support stiffness, and negative for other flexible support stiffness. Based on the Koiter's initial post-buckling theory, the condition on the flexible support stiffness conducive to the unstable branch path is derived. The unstable branch paths indicate that the buckling load of the column will be sensitive to the imperfections

中文翻译：

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具有柔性支撑的弹性柱的分叉点稳定性和初始后屈曲

摘要 为了研究一端内置柱子的初始后屈曲，另一端用柔性支撑旋转夹紧，使用傅立叶级数研究了分岔点的稳定性。证明势能的二阶变化在分岔点是半正定的。当扰动匹配屈曲模式时，四阶变化对于某些柔性支撑刚度为正，而对于其他柔性支撑刚度为负。基于Koiter的初始后屈曲理论，推导出有利于不稳定分支路径的柔性支撑刚度条件。不稳定的分支路径表明柱的屈曲载荷将对缺陷敏感