Deep water risers are usually so long that significant currents will excite a natural bending mode that is much higher than the fundamental bending mode. Since, deep water currents usually change in magnitude (and direction) with depth; it is possible that multiple modes of the riser can be excited into vortex induced vibration (VIV). This makes deep water riser VIV prediction much more complex than that for the short riser spans typically of fixed platforms in shallow water. For a pinned-pinned beam with varying tension, stiffness, and mass, the nth natural frequency is given by solving the following equation: 
Where, T(s) is the tension, EI(s) the bending stiffness, mt(s) the mass per unit length, and ?n the nth natural frequency of the structure: For this configuration the nth mode shape of the riser is: 
And the curvature along the riser us expressed by the following relationship. 
The riser stress can be calculated using the abovementioned equation and general long beam theory of elasticity. The shedding frequency of the fluid passing the riser is; 
Where, St is the Strouhal number, which is function of the Reynolds number and roughness of the structure, and V denotes the current velocity. All riser vibration modes with a natural frequency within a frequency band around fs are assumed to be excited. The frequency band for cross-flow and in-line is respectively. The fatigue damage at location x of the riser then can be calculated using the following relationship: 
The fatigue damage Dr(x) due to excitation frequency, ?r, is given by: 
Where, Sr,rms(x) is the RMS stress due to the rth mode, m, and K are material fatigue constants. Experiences in deepwater riser design show that often, a deepwater riser will fail to meet the fatigue design criteria due to VIV. So, generally designers may choose one of the following methods to overcome this problem:
- Redesign the riser either by changing the mass, increasing the tension, or changing the whole riser design
- Add a VIV suppression devices to reduce the vibration
REFERENCES
- DNV-RP-F204, Riser Fatigue.
- Subsea Pipelines and Risers, Elsevier Science Ltd, 2005.
- SHEAR7 Program Theoretical Manual, Massachusetts University of Technology, 2005.
