Nonlinear Analysis of Bidirectional Vortex-Induced Vibration of A Deepwater Steep Wave Riser Subjected to Oblique Currents

An improved three-dimensional(3D)time-domain couple model is established in this paper to simulate the bidirectional vortex-induced vibration(VIV)of a deepwater steep wave riser(SWR)subjected to oblique currents.In this model,the nonlinear motion equations of the riser are established in the global coordinate system based on the slender rod theory with the finite element method.Van der Pol equations are used to describe the lift forces induced by the x-and y-direction current components,respectively.The coupled equations at each time step are solved by a Newmark-βiterative scheme for the SWR VIV.The present model is verified by comparison with the published experimental results for a top-tension riser.Then,a series of simulations are executed to determine the influences of the oblique angle/velocity of the current,different top-end positions and the length of the buoyancy segment on the VIV displacement,oscillating frequency as well as hydrodynamic coefficients of the SWR.The results demonstrate that there exists a coupled resonant VIV corresponding to x-direction and y-direction,respectively.However,the effective frequency is almost identical between the vibrations at the hang-off segment along x and y directions.The addition of the buoyancy modules in the middle of the SWR has a beneficial impact on the lift force of three segments and simultaneously limits the VIV response,especially at the decline segment and the hang-off segments.Additionally,the incident current direction significantly affects the motion trajectory of the SWR which mainly includes the fusiform and rectangle shapes.