Dynamic Buckling of Cylindrical Shells with Arbitrary Axisymmetric Thickness Variation under Time Dependent External Pressure

This paper presents an analytical study on the critical dynamic buckling load of cylindrical shells with arbitrary axisymmetric thickness variation under uniform external pressure which is a function of time. Based on the Donnell simplified principle, the equilibrium and compatibility equations of cylindrical shells with arbitrary axisymmetric wall thickness under dynamic external pressure were derived. By using the method of separation of variables, the equations were transformed into ordinary differential equations in nondimensional form. Combining Fourier series expansion and the regular perturbation method, as well as the Sachenkov–Baktieva method, analytical formulas of the critical buckling load of cylindrical shells with arbitrary axisymmetric thickness variation under dynamic external pressure that varies as a power function of time were obtained. Using these analytical formulas, the critical dynamic buckling load of cylindrical shells with linearly and parbolically varying thickness were computed. The influences of thickness variation parameter and loading speed of external pressure on the critical buckling load were also discussed. The method was also applied to cylindrical shells with a classical cosine form thickness variation, by introducing the reduction factor of critical dynamic buckling load. The buckling capacity of these cylindrical shells under dynamic external pressure was discussed considering the effects of loading speed and thickness variation parameter.