Effect of damping on variable added mass and lift of circular cylinders in vortex-induced vibrations

For many decades now, the idea of Vortex-Induced Vibrations (VIV) being modeled as a lock-in phenomenon of a mass-spring-dashpot system with an ideal added mass term has prevailed. In 2000, it was suggested by Vikestad et al. [1] that VIV may be modeled as a resonance phenomenon with variable natural frequency due to a variable added-mass term. In this paper, the variable added-mass approach is used for analysis of VIV at various added damping values. Additionally, Vandiver's damping coefficient c∗ is used [2] to correlate damping to lift. The findings are that: 1. The oscillation frequency is in unity with the mean of the natural frequency with variable added mass for each period of oscillation during VIV lock-in no matter the damping value. 2. The time-averaged variable added mass coefficient is shown to vary with an increasing damping coefficient, where below a reduced velocity of approximately seven, increased damping indicates increased added mass. After a reduced velocity of approximately seven, however, increased damping results in decreased added mass. 3. Vandiver's damping coefficient c∗ plotted against the nondimensional amplitude follows very closely to c∗A/D = max lift coefficient = square root of 0.79 [3]. A handful of cases did exceed square root of 0.79 but only marginally.