Vortex-induced vibrations of stepped cylinders with varied spanwise arrangements and diameter ratios

Vortex-induced vibration (VIV) presents a significant challenge in the design of offshore risers and pipeline systems. Compared to bare uniform risers, the attachment of large-diameter buoyancy modules significantly modifies hydrodynamic characteristics and, consequently affects the fatigue damage of the risers. To improve the understanding and optimization of system VIV, this study experimentally investigates the hydrodynamics and response mechanisms of stepped cylinders under both concentrated and staggered buoyancy module configurations with different diameter ratios (D/d = 1.25, 1.5, 2, D: buoyancy module/large cylinder diameter; d: bare pipe segment/small cylinder diameter) in uniform flow. The results show that stepped cylinder in concentrated configurations exhibits a distinct "dual lock-in" phenomenon, where the frequency in the second lock-in region is notably higher than in the first region. At small and intermediate diameter ratios (D/d = 1.25 and 1.5), the distinct vibration response branches are respectively dominated by the small and large cylinder segments. However, for increasing to the large diameter ratio condition (D/d = 2), the dominance of the large cylinder segment becomes more pronounced. For staggered configurations, the dynamic behavior diverges with diameter ratios: systems with D/d = 1.25, 1.5 exhibit single lock-in characteristics resembling low-mass-damping uniform cylinders, whereas a dual lock-in response emerges at D/d = 2. During the transition between two lock-in regions, the stepped cylinder exhibits shift in vibration frequency and wake pattern, causing a phase jump between the lift force and structural response; this discontinuity alters the effective added mass coefficient, leading to dual lock-in. The mechanism governing VIV responses lies in the dynamic competition between large and small cylinder segments. This competition intensifies wake interactions and amplifies nonlinearity in both hydrodynamic forces and structural vibrations.