Experiments and Analytical Study of Multi-modal Vortex-Induced Vibrations of Bridges

Modal frequencies of super-long-span bridges are often closely spaced, allowing multiple vortex-induced vibration (VIV) modes to be excited simultaneously. Existing VIV theories are largely single-mode and thus cannot capture the multi-modal responses of such bridges. Within overlapping lock-in regions, mode competition commonly occurs: one mode becomes dominant while others are suppressed.To investigate this, a multi-degree-of-freedom suspended sectional model exhibiting symmetric and anti-symmetric modal characteristics is developed, and wind-tunnel tests are conducted across a range of wind speeds. The experiments reveal rich nonlinear behaviors in the overlapping lock-in ranges, including mode competition and multi-stability.Based on the wake-oscillator concept, a two-degree-of-freedom wake-oscillator model is derived, and the averaging method is applied to obtain a reduced theoretical framework that captures the nonlinear multi-modal dynamics during lock-in.Theoretical analysis indicates that the mode competition may exhibit two stable equilibrium, and the final state is determined by both the wind speed and the initial excitation condition.