The stability of non-homogeneous elastic cylindrical thin shells with variable thickness under a dynamic external pressure

Abstract

The stability of elastic cylindrical thin shells of variable thickness along the directrix and of elastic properties varying continuously depending on the thickness coordinates, subject to a uniform external pressure which is a power function of time, was investigated. Firstly, fundamental relations and the modified Donell-type stability equations of the non-homogeneous elastic cylindrical thin shells with variable thickness were derived. Applying Galerkin's method, a differential equation having a variable coefficient depending on time wass obtained and by applying the method of Sachenkov and Baktieva (1978) to these equations, general formulas for static and dynamic critical loads, corresponding wave numbers, and the dynamic factor were obtained. The appropriate formulas for elastic cylindrical thin shells made of homogeneous and non-homogeneous materials with uniform thickness were specifically obtained from these formulas. Finally, performing the computations, the effects of linear and sinusoidal variation of shell thickness, linear, parabolic, and exponential variation of elastic properties, and the variation of variation factor due to time on critical parameters were investigated.