柔索牵引起重臂平面外失稳特征方程的统一表达及其应用

The uniform expression of the out-of-plane buckling characteristic equation for the crane jib tensioned by flexible cables

本文研究了带有柔性牵索的起重臂的平面外稳定性,通过建立起重臂起升平面外失稳临界状态下的弯曲微分方程,引入边界条件、变形协调方程及固支点侧向受力平衡方程,推导出起重臂平面外失稳特征方程的一般解析表达式,解析计算结果与ANSYS数值结果完全吻合。随后,探讨一般失稳特征方程在水平臂、双钢绳及单钢绳牵引起重臂极限情况下的退化形式。最后,指出所推导的一般失稳特征方程可作为各类柔性钢绳牵引下起重臂平面外失稳特征方程的统一表达。

The analytical expression of the buckling characteristic equation was obtained by establishing the bending differential equation under the critical buckling state.To solve the equation,the boundary condition,the deformation compatibility condition and the equation of force equilibrium at the cable fixed joint are used.The analytical results agree well with the results obtained by the general commercial finite element software ANSYS.Then,the different degeneration forms of the buckling characteristic equation under different limited cases including the horizontal jib,the jib tensioned by both single cable and two cables were discussed.Accordingly,the buckling characteristic equation can be considered as the uniform expression for the crane jib tensioned by flexible cable.