Effect of geometry on the stability of cylindrical clamped shells subjected to internal fluid flow

In this paper, the nonlinear stability of circular cylindrical shells subjected to internal incompressible flow is studied by means of the Donnell nonlinear shallow shell equations and a linear fluid–structure interaction model. Specifically, the effect of varying the thickness-to-radius (h/R) and length-to-radius (L/R) ratios is investigated. In general, the system loses stability by a subcritical pitchfork bifurcation, leading to a stable divergence of increasing amplitude with flow; no oscillatory solutions are found. Increasing the value of the circumferential wavenumber for shells with the same h/R ratio reduces the natural frequency and enhances the subcritical behaviour of the shell. Interesting results are found for different L/R cases in which the solution changes from subcritical to supercritical nonlinear behaviour.