双特征参数法与最优模态法在弹性直杆动力屈曲问题中解的一致性

采用求解最优模态的方法,分别对弹性压应力波作用下受载端夹支和简支两种边界条件直杆的动力屈曲问题进行了探讨,研究中所设的屈曲模态不仅满足边界条件,而且满足文献所得的波前附加约束条件。研究发现屈曲模态中放大最快的模态所对应的临界力参数和惯性项的指数参数与双特征参数法所得的结果是一致的,即用双特征参数法求解所得屈曲模态就是最优模态。另外,计算表明,最低阶动力屈曲载荷远高于静力屈曲载荷,确定动力屈曲载荷时应计及横向惯性。

THE IDENTICALNESS OF THE DYNAMIC BUCKLING RESULTS OF ELASTIC BARS BETWEEN THE TWIN-CHARACTERISTIC-PARAMETER SOLUTION AND THE PREFERRED MODE SOLUTION

By use of the method of the preferred mode,theoretical analyses of dynamic buckling for elastic bars subjected to axial compression,with the loaded end clamped but movable in axial direction or simply supported,were performed.The supposed buckling modes fulfill not only the boundary condition,but also the supplementary restraint equation given in literatures.Research shows that the critical-load parameter and the dynamic characteristic parameter of the most amplified mode are in accordance with the results given by the Twin-characteristic-parameter solution.That is to say,the dynamic buckling modes given by the Twin-characteristic-parameter solution are also the preferred mode of buckling.Calculation results shows that the first order of the critical load of dynamic buckling is much higher than the static critical load with the same boundary condition.So the transverse inertia should be considered in the calculation of the critical load of dynamic buckling.