Dynamic stability of a thin cylindrical shell with top mass subjected to harmonic base-acceleration

This paper considers the dynamic stability of a harmonically base-excited cylindrical shell carrying a top mass. Based on Donnell’s nonlinear shell theory, a semi-analytical model is derived which exactly satisfies the (in-plane) boundary conditions. This model is numerically validated through a comparison with static and modal analysis results obtained using finite element modelling. The steady-state nonlinear dynamics of the base-excited cylindrical shell with top mass are examined using both numerical continuation of periodic solutions and standard numerical time integration. In these dynamic analyses the cylindrical shell is preloaded by the weight of the top mass. This preloading results in a single unbuckled stable static equilibrium state. A critical value for the amplitude of the harmonic base-excitation is determined. Above this critical value, the shell may exhibit a non-stationary beating type of response with severe out-of-plane deformations. However, depending on the considered imperfection and circumferential wave number, also other types of post-critical behaviour are observed. Similar as for the static buckling case, the critical value highly depends on the initial imperfections present in the shell.