Wave Period Modulation and Spacing Effects on Flow-Induced Vibration of Tandem Flexible Cantilevered Cylinders Under Combined Current-Wave Conditions

• Spacing governs tandem cylinder flow-induced vibrations in pure currents. • Wave period dominates pure-wave responses via dynamic amplification. • Wave-current interaction induces distinct asymmetric cylinder responses. • Long waves enhance upstream vibration but disrupt downstream wake coherence. • Wave modulation fundamentally alters effective lock-in behavior in combined flows. Flow-induced vibration (FIV) of marine slender structures is strongly affected by wake interference and environmental unsteadiness. Building upon previous studies that have primarily focused on pure-current environments, this study extends the investigation to wave–current combined conditions that are more representative of realistic offshore settings, and examines the FIV response of two tandem flexible circular cylinders arranged in a cantilevered configuration, with the upper ends fixed in air and the lower sections freely submerged in water. Four spacing ratios in reattachment regime are examined under pure current, pure wave, and wave–current combined conditions, covering multiple reduced velocities and regular wave periods and their combined effects. Spanwise RMS displacement distributions in both the in-line (IL) and cross-flow (CF) directions are analyzed together with time–frequency and frequency-ratio characteristics. Under pure current excitation, the CF response exhibits a clear non-monotonic dependence on spacing, with peak amplitudes occurring at intermediate spacings due to wake interference. In contrast, pure-wave excitation leads to weak spacing sensitivity, indicating limited persistent wake effects. Under combined loading at lock-in conditions, the vibration response is strongly modulated by wave period: short-period waves introduce broadband, multi-modal features with limited amplitudes, whereas long-period waves promote coherent, first-mode-dominated responses and significantly alter spacing dependence, with distinct behaviors for upstream and downstream cylinders. These results highlight the coupled roles of wake interference and wave-induced modulation in governing FIV of tandem flexible cylinders.