As water depths for oil and gas exploration and extraction increase, structures such as flexible risers, mooring lines, and umbilical cables are increasingly being used in subsea environments. Compared to conventional fixed-type structures and vertical risers, the dynamics of flexible risers is significantly more complex. In particular, these flexible structures may be prone to dynamic instabilities. Furthermore, there has been increasing interest on safety, which makes it imperative to design more robust risers in order to avoid situations where the static configurations of risers can lose their stability.

The focus of this work, therefore, is to provide a comprehensive study of the dynamics, stability, and vibration of flexible risers. We use Kirchhoff's theory of an extensible, flexible rod that resists torsion to develop a set of nonlinear equations for the dynamics of risers. Furthermore, we extend our model to take into account the cross-sectional shearing by using a Cosserat rod theory. The resulting model incorporates drag and the effects of the fluid being transported internally besides all other forces acting on the risers. We perform static analyses and linear stability analyses for a variety of applications of risers such as a catenary-type riser, a lazy wave-type riser, a steep wave-type riser, and a vertical riser.

Based on configurations obtained from static analysis, we perform a comprehensive investigation regarding their stability. First, we identify the effects of external current and internal fluid on the stability of a static configuration and find an interesting phenomena where the internal fluid being conveyed can destabilize some static configurations. We also suggest a potential means to stabilize the destabilized configurations. Furthermore, we look into the torsional stability of risers in order to capture the critical point where the twisted or hockled configurations are observed under certain conditions and the effects of design parameters on the onset of the resulting torsional instability. Finally, we investigate the variation in the dynamic characteristics of a flexible riser as the riser transitions from a vertical riser to a catenary-type riser and also find a potentially efficient way to remove the instability for vertical risers by introducing a small horizontal offset. Our principal results from this work are expected to provide effective and useful guidelines for the design of marine flexible risers.