Introduction

Circular cylindrical shells are very stiff structural elements with optimal use of the material. Therefore, they are also very light. This is one of the reasons why they are used for rockets (see Figure 13.1). Similarly to other thin-walled structures, the main strength analysis of circular cylindrical shells is a stability analysis; in fact, these structural elements buckle much before the failure stress of the material is reached.

In this chapter, the stability and the postcritical behavior of circular cylindrical shells under the action of axial static and periodic loads are investigated. Because of the strongly subcritical nature of the pitchfork bifurcation associated with buckling, even if the static compression load is much smaller than the critical load, shells collapse under small perturbation with a jump from the trivial equilibrium configuration to the stable bifurcated solution. Moreover, circular cylindrical shells subjected to axial loads are highly sensitive to geometric imperfections.

Periodic axial loads generate large-amplitude asymmetric vibrations due to period-doubling bifurcation of axisymmetric small-amplitude vibration. Period-doubling bifurcation arises for frequency of axial load close to twice the natural frequency of an asymmetric mode; this is usually referred as parametric instability. In fact, most of the studies are based on Donnell's nonlinear shallow-shell theory, so that axial loads do not appear directly in the equations of motion obtained with this shell theory, where only radial loads are directly inserted. They appear through boundary conditions, giving the so-called parametric excitation in the equation of motion.