面内阶跃载荷下薄板弹性动力屈曲差分解

根据薄板微元的动力平衡分析导出薄板动力屈曲控制方程,由屈曲瞬间能量转换率守恒条件得出一个压缩波前屈曲变形的附加约束方程,由此得到求解薄板动力屈曲问题的完备定解条件.以受载边夹支的薄板为倒,利用有限差分法得出了薄板前三阶动力屈曲模态和相应的两个特征参数值,并对比分析了薄板静、动力屈曲的差别.分析表明,薄板动力屈曲过程中产生屈曲动能,比静力屈曲要吸收更多的外部能量.

Difference solution to elastic dynamic buckling of thin plates subject to in-plane step load

The governing equations for dynamic buckling of plates were derived through the analysis of dynamic balance for the element of plates.The supplementary restraint equation for buckling defor-mation at the front of the compression wave was obtained by means of the conservation criterion for the rate of the energy transformation in the buckling instant,then the sufficient conditions were achieved for solving the dynamic buckling problem of plates.Taking the plates as an example,clamped at the loading end,the first three dynamic buckling modes for plates and the corresponding values of the two characteristic parameters were solved and the differences between the static buckling modes and the dynamic buckling modes were compared and analyzed with the finite difference method.The analysis shows that the plates generate the buckling kinetic energy in the process of dynamic buckling,which requires more external energy than the static buckling.