Coupled nonlinear dynamics of a top-tensioned riser with internal flow under multi-frequency parametric and vortex-induced excitations

The dynamic response of risers in complex marine environments is governed by a confluence of factors, including waves, ocean currents, and internal flow effects. Although the internal flow is critical for accurately capturing riser vibration characteristics under real operational conditions, it has often been underestimated in previous research. To address this gap and provide a more comprehensive understanding of riser vibration behavior, this study establishes a dynamic model for risers based on Euler-Bernoulli beam theory, incorporating the effects of multi-frequency parametric excitation and internal flow, and introduces the Van der Pol wake oscillator model to simulate vortex-induced vibrations. The governing equations are discretized via the Galerkin method and solved analytically using the method of multiple scales. Numerical examples investigate the influence of internal flow velocity, internal flow density, and top tension on riser vibration characteristics. The results indicate that increasing internal flow velocity induces saddle-node and Hopf bifurcations, with more pronounced bifurcations at higher velocities. Furthermore, elevated internal flow density alters the nontrivial solution domain, impacting both response amplitudes and bifurcation patterns. Variations in top tension significantly impact vibration amplitude and bifurcation behavior, with higher top tension leading to period-doubling and chaotic phenomena.