... 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...

..., velocity is proportional to displacement. Furthermore, drag is proportional to the square of the velocity (assuming no waves). Equating the approximated drag force with that of the simplified model gives 61 ∫ − d ∕ 2 0 [ x ( 2 z d + 1 ) ] 2 d z = y 2 d e...