The non-linear dynamics of thin walled shell structures

This paper discusses the non-linear oscillations and dynamic instabilities of thin walled shells subjected to harmonic loads. Due to the presence of strong non-linearities and high sensitivity to small variations in control parameters, thin shells may display a complex dynamic behavior and, despite the recent advances in this field, there is still a lack of satisfactory solutions to this class of problems. There are several complicated issues relating to the dynamics of such structures. In this work some of these topics are addressed, namely shell discretization processes, influence of modal coupling on non-linear vibration modes, modal interaction between different non-linear vibration modes, imperfection sensitivity and fractal basin boundaries. To this end, the theory for quasi-shallow shells is used to study the non-linear vibrations and instabilities of thin cylindrical shells under axial load.