Vortex dynamics and amplitude modulation in vortex-induced vibration of a low-aspect-ratio stepped cylinder

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An experimental study is conducted to investigate the vortex-induced vibration (VIV) of stepped cylinders with Reynolds numbers (Re=1150–7750) to clarify the mechanisms of amplitude modulation controlled by the diameter ratio (D*=1.3–3.0) and coverage ratio (R=10%–100%). By integrating dynamic response measurements with time-resolved particle image velocimetry and proper orthogonal decomposition (POD) analyses, the global VIV response is categorically mapped into three regions: inert, suppression, and enhancement. It is found that the response amplitude of the stepped cylinder is modulated by the dynamic competition between the staggered geometric parameters. In the inert region (D*≤1.9 and R≤50%), weak geometric discontinuities preserve a canonical plain cylinder like response. In the suppression region (emerging at D*>1.9 with moderate coverage 30%≤R≤50%), increasing (D*) enlarges the mismatch between the wake-development scales of the large- and small-diameter sections, as reflected by the increased vortex-formation-length difference and more dispersed POD energy distribution. This wake mismatch is accompanied by a reduction in the velocity-in-phase lift component, Clv, indicating weakened net fluid–structure energy transfer. Conversely, in the enhancement region (beyond a critical threshold of around R≥60%), an increase in R causes the large-diameter sections to dominate the overall wake, and the POD mode of the downstream vortex shedding is also dominated by the large cylinder. In addition, the “dual lock-in” phenomenon for stepped cylinders is further examined in the present low-aspect-ratio configuration. The observed “dual lock-in” is identified as a sequential resonance of the system natural frequency, in which the vortex shedding frequencies of the two sections successively approach the structural natural frequency while the cylinder remains in single-frequency motion. The traditional combined mass–damping parameter describes the peak response only under limited conditions. Nevertheless, for D*≤2.2, the measured amplitude remains strongly correlated with that estimated from the harmonic force-balance relation, with r>0.8 over most coverage ratios. These findings provide a unified interpretation of wake competition, energy transfer, and amplitude modulation in stepped-cylinder VIV.

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