... into account the main intrinsic nature of VIV for low mass ratio structures in lock-in regions, added mass, and nonlinear fluid damping. Based on the simplified model, a closed-form solution of fatigue damage is suggested for the case of a riser with uniform mass and cross-section oscillating in a uniform flow...

... (taken as positive upwards). Due to the limitations of the simplified model, three-dimensional effects are not considered. Using the deep water approximation of classical linear wave theory ( 7 ) the horizontal wave particle velocity u and acceleration u ̇ are expressed as 4 u = a ω...