Predicting buckling from vibration: an analytical, numerical, and experimental verification for cylindrical shells

Kurzfassung

This thesis explores an empirical vibration correlation technique for predicting the buckling load of imperfection-sensitive cylindrical shells. As the title implies, the research addresses analytical, numerical, and experimental aspects of the mentioned methodology. Within the scope of the analytical work, the emphasis is given to provide an analytical foundation for the referred technique. Firstly, the equations describing the free vibrations of an axially loaded cylinder are revisited through a linearized theory of shells. Subsequently, the reviewed equations are rearranged, expressing a parametric form of the applied load as a quadratic function of a parametric form of the loaded natural frequency. Afterward, the typical static behavior of an imperfection-sensitive structure is evaluated, establishing the link between the minimum magnitude of the parametric form of the applied load and the effective knockdown factor of the experiment. Towards a numerical verification based on finite element models, two theoretical cylindrical shells are defined. At first, the critical buckling load and the fundamental natural frequency for different load levels are determined and compared to the analytical results for verifying the numerical models. The finite element models are then extended contemplating geometric nonlinearities, more realistic boundary conditions, and three magnitudes of a measured mid-surface imperfection. These numerical results are considered for analyzing the variation of the natural frequency in the surroundings of buckling and verifying the vibration correlation technique. Finally, the applicability and the robustness of the methodology are further validated through three experimental campaigns. Five cylindrical shells, being three of them nominally equal, were tested. The test program covered different buckling test facilities, internal pressure levels, and in-plane imperfections. Besides, each specimen was tested for buckling for comparing the corresponding estimated and experimental buckling loads. The experimental work corroborates that the evaluated vibration correlation technique provides appropriate and conservative estimations for imperfection-sensitive cylindrical shells considering different design details and test conditions.