在轴向应力波传播和反射过程中弹性有限长圆柱壳非对称动态屈曲

Non axisymmetric dynamic buckling of finite elastic cylindrical shells in propagating and reflecting of axial stress waves

本文讨论弹性有限长圆柱壳端部受冲击载荷作用，在轴向应力波传播和反射过程中的非对称动态屈曲问题。通过建立和求解扰动方程得到了动态屈曲的分叉条件，临界载荷和屈曲模态。数值结果表明：当壳壁厚不很薄时，轴对称屈曲临界载荷比非轴对称临界载荷高；反之，轴对称临界载荷会比非对称临界载荷低；由于应力波的反射，临界载荷降低，因而更容易发生屈曲，屈曲模态也有其不同特点。

In this paper, non axisymmetric buckling of finite elastic cylindrical shell, which is impacted on the end by axial step loads, is discussed with the aid of the stress wave propagating and reflecting. By solving the disturbed equations, the bifurcation condition of the dynamic buckling, critical buckling load and buckling mode are obtained. The results show that when the thickness is not very small, non axisymmetric critical buckling load is higher than axisymmetric one; that when the thickness is very small, non axisymmetric buckling can occur first and that since the wave is reflected on the other end of the shell, the critical buckling load decreases further. The results are in agreement with the physical phenomenon in experiments.