Intrinsic features of flow-induced stability of a square cylinder

Vortex-induced vibrations and galloping of an elastically mounted square cylinder are investigated for cylinder mass ratio m * = 2–50, damping ratio ζ = 0–1.0, mass-damping ratio m * ζ = 0–50 and flow reduced velocity U r = 1–80. We home in on the effects of m *, ζ , m * ζ , $({m^\ast } + m_{a\textrm{0}}^\ast )\zeta$ and $({m^\ast } + m_{ae}^\ast )\zeta$ on the critical reduced velocity U rc marking the onset of galloping, where $m_{a\textrm{0}}^\ast $ is the quiescent-fluid added mass ratio and $m_{ae}^\ast $ is the effective added mass ratio. Vibration responses, forces, vibration frequencies and added mass ratios are studied and discussed. The different branches of vortex-induced vibrations have different dependencies of $m_{ae}^\ast $ on U r . The $m_{ae}^\ast $ in the initial branch is positive and drops rapidly with U r , but that in the lower branch is negative and declines gently. In the galloping regime, $m_{ae}^\ast $ jumps from negative to positive at the onset of galloping, declining slightly with increasing U r . Our results and prediction equations show that when ζ = 0, U rc is independent of m * for m * ≥ 5, albeit slightly higher for m * = 3. The latter is ascribed to mode competition. When ζ > 0, U rc linearly increases with increasing ζ . Detailed analysis substantiates that m * ζ or $({m^\ast } + m_{a\textrm{0}}^\ast )\zeta$ does not serve as the unique criterion to predict the galloping occurrence. Here, we propose a new combined mass-damping parameter $({m^\ast } + m_{ae}^\ast )\zeta$ in the relationship between galloping onsets and structural properties, which successfully scales all data of U rc at different m * and ζ values.