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^ + mₐ₀^ )ζ and (m^ + mₐₑ^ )ζ on the critical reduced velocity U rc marking the onset of galloping, where mₐ₀^ is the quiescent-fluid added mass ratio and mₐₑ^ 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 mₐₑ^ on U r . The mₐₑ^ 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, mₐₑ^ 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^ + mₐ₀^ )ζ does not serve as the unique criterion to predict the galloping occurrence. Here, we propose a new combined mass-damping parameter (m^ + mₐₑ^ )ζ in the relationship between galloping onsets and structural properties, which successfully scales all data of U rc at different m * and ζ values.