The governing equation of a step cylindrical shell's vibration displacements in radial direction under axial impact load was established and solved considering boundary conditions and consistency conditions to obtain its bifurcated conditions of dynamic buckling after stress wave reflecting. The relations among the critical buckling load,the position where the stress wave front reached the step cylindrical shell and the ratio of thickness to radius of the step cylindrical shell were acquired through numerical calculation. The numerical results showed that the axisymmetric buckling of the step cylindrical shell appearing is easier than its non-axisymmetric buckling occurring; the buckling occurring at the fixed end after the stress wave reflected by the fixed end passing through the division surface is harder than that before the reflected stress wave passing through the division surface be,while the buckling occurring at the impacted end is easier; the critical buckling load increases with increase in the ratio of thickness to radius and the ratio of thicknesses; for a step cylindrical shell and a constant thickness cylindrical one with the same mass,the step cylindrical shell's buckling is easier before the stress wave reflected by the fixed end passing through the division surface,while the step cylindrical shell's buckling is harder after the reflected wave passing through the division surface.%建立并求解了阶梯圆柱壳径向位移控制方程,考虑边界条件及相容条件,得到应力波发生反射后阶梯圆柱壳的动态屈曲分叉条件.通过数值计算,分别给出了不同时间段屈曲临界载荷与应力波波阵面到达阶梯圆柱壳的位置、阶梯圆柱壳厚径比的关系.数值计算结果表明,阶梯圆柱壳发生轴对称屈曲相对非轴对称屈曲更容易;应力波传播经固定端反射,通过分界面后比通过分界面之前固定端部更难发生屈曲,而冲击端部较易发生屈曲.随着厚径比及厚度比的增大临界载荷也随之增大.质量相同的阶梯圆柱壳与等厚度圆柱壳,应力波经固定端反射通过分界面之前阶梯圆柱壳更易发生屈曲,而通过分界面之后阶梯圆柱壳更难发生屈曲.
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