Analytical and numerical biaxial bending analysis of deepwater riser due to vortex-induced vibration

Previous studies of analysis and prediction of marine risers responses usually focus on vortex-induced vibration (VIV) of cross-flow (CF) direction rather than in-line (IL). Recent studies show that responses of IL direction tend to dominate in some cases. Responses of long riser due to biaxial bending of IL and CF VIV are investigated. Closed-form formulas are derived for estimating maximum normal stress due to the biaxial moment of CF/IL VIV and relations for estimating biaxial stress using CF values are presented. Analytical results are compared with numerical results of the time domain model and a good correlation is observed. It is shown that for tension and bending-controlled modes of vibration if the ratio of displacement amplitude of IL to CF direction is, respectively, higher than 0.22 and 0.35, normal stress due to biaxial bending is noticeably more than one directional (CF) bending stress. For a case study, the maximum biaxial stress along the riser is about 20 and 40% higher than the maximum CF stress along the length of the riser for bending and tension-controlled modes of vibration, respectively. Such results can be important not only directly in design issues, but also they may be noticeable in fatigue analysis.