Vortex-induced vibration mitigation in long-span bridges using a nonlinear energy sink inerter: Theoretical framework and application

Long-span bridges, with their exceptionally low modal frequencies, are prone to wind-induced vibrations, notably vortex-induced vibrations (VIVs). Conventional linear dynamic vibration absorbers like tuned mass dampers (TMDs), and nonlinear dynamic absorbers such as nonlinear energy sinks (NESs), often struggle to mitigate VIV effectively at low frequencies due to excessive static displacements and limited achievable mass ratios. To overcome these challenges, this study proposed a novel vibration control device—a quasi-zero-stiffness nonlinear energy sink inerter (QZS-NESI). By introducing a positive linear stiffness component, the QZS-NESI achieves a quasi-zero stiffness configuration that compensates for static loads while maintaining low restoring forces. Meanwhile, the inclusion of the inerter provides a mass amplification effect, effectively reducing the static displacement requirement. The complexification-averaging (CX-A) technique was used to obtain the slow-flow dynamic model and steady-state dynamic model of the original system, which approximated by the CX-A method has been demonstrated to possess accuracy comparable to that of the original system. Moreover, this method enabled the direct determination of the steady-state amplitude and phase difference of the dynamic system, thereby elucidating the bifurcation structure of the system under varying parameters. The mechanical damping and VIV-related aerodynamic damping were identified as critical parameters significantly influencing the emergence of unstable branches. The Xihoumen Bridge, with a main span of 1650 m, was chosen as the reference bridge to evaluate the VIV control efficacy of the NESI system. Findings underscored the exceptional capacity of NESI for displacement reduction and broadband vibration mitigation.