Flow-induced vibration and force characteristics of a downstream cylinder with two degrees of freedom influenced by upstream cylinder wake

A study on 2-DOF vibration characteristics and aerodynamic forces of a downstream cylinder in staggered arrangements is conducted, with cylinder center spacings of L/D = 2.5–6.0 longitudinally and T/D = −2–0 transversely (where L and T denote longitudinal and transverse spacings, D denotes cylinder diameter). The investigation covers reduced velocities (U_r = U/(f_nD)) from 12.5 to 72.1, where U is wind speed and f_n is natural frequency. Three distinct vibration forms are observed: Wake-Induced Vibration (WIV), Wake-Induced Flutter (WIF), and horizontal vibration induced by the laminar separation and turbulent reattachment (LSTR) flow pattern at inner lift peak positions, termed LHV. For WIV, tandem arrangements yield predominantly vertical oscillations with peak amplitudes reaching 1.83D, whereas staggered arrangements produce comparable horizontal and vertical responses at higher wind speeds. WIF characteristics include rapid amplitude growth and frequency reduction with increasing wind speed. Under the staggered arrangement of (2.5, −0.4), two distinct horizontal vibration regions emerge, driven by inner shear layer oscillation frequency lock-in and flow separation-reattachment, respectively. Force measurements during oscillation indicate unsteady characteristics in tandem arrangements but quasi-steady features in staggered cases. Additionally, consistent force-displacement phase differences observed in WIV under staggered arrangements provide valuable experimental data for future theoretical model development and validation.