The more practical case of vortex-induced vibration in two degrees of freedom has been presented. The mass ratio is low and equal to m*=1.78. The response amplitude showed three branches namely, the initial branch, the super-upper branch and the lower branch. The reason for the appearance of the super-upper branch is owed to the power increase. The fatigue damage in two degrees of freedom has been compared with that in one degree of freedom. The results showed the in-line fatigue damage can not be neglected especially in the initial branch and the super-upper branch. The in-line fatigue damage could be a main contributor under low reduced velocity and distinctly have a positive influence on that in cross-flow direction in the super-upper branch.
The problems of vortex-induced vibration (VIV) have been paid more attention in recent years due to the demand of petroleum industry moving towards deep water. Many efforts have been devoted to the prediction of VIV of deepwater marine risers and free span pipelines response mainly in the cross-flow direction for structural design according to the fatigue damage criterion. Vandiver (1987) discovered that there was an interaction between inline vibration and cross-flow VIV that showed as a chart of ‘eight-offigure’. Moe and Wu (1990) carried out two studies for systems enabling x-ymotion of a cylinder, the mass ratios in the xand y directions were quite different, and also the natural frequencies were set in the ratio fx/fy=2.18. Under these special conditions, they found a broad regime of reduced velocity Un(where Un = U/fND, U =freestream velocity, fN= natural frequency; D= diameter) over which resonant amplitudes were found (with transverse normalised amplitude close to Ay/D=1, Ayis the response amplitude in cross flow direction), but without any evidence of distinct response branches.