This paper presents an analytical investigation on dynamic buckling of cylindrical shells with general thickness variations under exponentially increasing external pressure over the time. Different from the previous studies in literatures, the shell thickness varies arbitrarily and is common in actual engineering, which leads to failure of the existing methods. A new analytical method is first developed to solve the fourth-order governing partial differential equations with variable coefficients for the shell subjected to varying external pressure. Then the asymptotic formulae for dynamic buckling loads considering general thickness variations are derived and expressed by geometry sizes of the shell and thickness variation functions. To validate the presented results, two specific non-axisymmetric thickness cases are discussed in detail. The critical dynamic buckling loads show a great agreement with the previous ones by other researchers for simple and axial thickness variation situation. Finally, example calculations and parametric discussion are performed, and influences of thickness variation types, speed of external pressure and the power exponent of time on the critical dynamic buckling loads are discussed.

中文翻译：

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外压呈指数增加的一般厚度变化圆柱壳的动态屈曲分析研究

本文介绍了在外部压力随时间呈指数增加的情况下，具有一般厚度变化的圆柱壳的动态屈曲的分析研究。与以往文献研究不同的是，壳体厚度随意变化，在实际工程中普遍存在，导致现有方法失效。首次开发了一种新的解析方法来求解受变外压的壳的四阶变系数控制偏微分方程。然后推导了考虑一般厚度变化的动态屈曲载荷的渐近公式，并用壳的几何尺寸和厚度变化函数表示。为了验证所呈现的结果，详细讨论了两种特定的非轴对称厚度情况。对于简单和轴向厚度变化的情况，临界动态屈曲载荷与其他研究人员先前的非常一致。最后，通过实例计算和参数讨论，讨论了厚度变化类型、外压速度和时间幂指数对临界动态屈曲载荷的影响。