Multimodal vortex-induced vibration mitigation and design approach of bistable nonlinear energy sink inerter on bridge structure

Large-scale structures, e.g., long-span bridge structures, are prone to induce multi-modal vibrations due to their densely spaced low modal frequencies. Due to the limited frequency bandwidth of linear dynamic absorbers, they are incapable of effectively mitigating vibrations across multiple modes. To this end, the bistable nonlinear energy sink inerter (BNESI) is used to mitigate the multimodal vortex-induced vibration (VIV) of the beam structure. The highly nonlinear equilibrium differential equations of the beam-BNESI system are numerically solved, and the simulated annealing (SA) algorithm is employed to determine the optimal VIV reduction ratio and BNESI parameters. In comparison to the cubic-type nonlinear energy sink inerter (CNESI), BNESI is found to possess more stable equilibrium positions, smaller stiffness coefficients, and higher VIV mitigation efficiency. The selection of design modes has been found to influence the efficiency of multimodal VIV mitigation, with the use of the intermediate modal order as the design mode resulting in the highest efficiency for multimodal VIV mitigation. The performance-based multimodal VIV mitigation design can be realized with three parameters, i.e., inertance ratio, damping coefficient, and stiffness coefficient. Moreover, the performance-based multimodal VIV mitigation approach and models proposed in this study demonstrate a high level of precision.