Bifurcation phenomenon and multi-stable behavior in vortex-induced vibration of top tension riser in shear flow

Top tension riser is one of the most frequently used and vulnerable equipment in deep-sea petroleum engineering. With experiments and CFD simulations, researchers have found some hysteresis phenomenon and bistable behavior in vortex-induced vibration of the cylinders. However, there is still insufficient research on the bifurcation phenomenon and the multi-stable behavior of the riser vortex-induced vibration. In this study, based on the Van der Pol wake oscillator model, the vortex-induced vibration cross-flow governing equations of the riser fluid structure–coupled system in linear shear flow are established. Then the simplified multi-degrees-of-freedom model with 15-order modes is derived by the Galerkin method. Poincare map is utilized to obtain bifurcation diagram and identify the dynamic property of the top tension riser in a wide flow velocity range. Nonlinear dynamic behavior such as bistable behavior and even tristable behavior are discovered from the bifurcation diagram. Combined with the riser coupled system’s eigen analysis and the three-dimensional spectrum contour, it is found that there are various phenomena of mode interaction in the riser system, including 1:3 internal resonance phenomenon. Such study can provide reference and guide the design and optimization of riser structural parameters.