Optimization of tuned mass dampers for multiple mode vortex-induced vibration mitigation in flexible structures: An application to multi-span continuous bridge

Abstract

Tuned mass dampers (TMDs) have proven effective in suppressing structural vibration. In existing research on vortex-induced vibration (VIV) control of flexible structures, only one mode is commonly considered at the time, and only basic aerodynamic force models, which can struggle to model amplitude-dependent damping, are considered. However, flexible structures, such as multi-span bridges, exhibit multiple modes with closely spaced frequencies. Neglecting secondary modes may introduce calculation inaccuracies, as these modes can impose additional stiffness, thereby influencing the performance of TMD. This paper presents a framework to optimize the performance of multiple TMDs in the context of multi-mode VIV control for a flexible structure. A multi-span bridge is used as a case study, and the secondary modes and nonlinear aerodynamic effects are considered. The governing equations for the force-structure-MTMDs system are derived in modal coordinates using a polynomial model to model the aerodynamic force. A novel method to calculate the contribution of each mode to determine the minimum number of secondary modes to be considered is proposed. The optimal parameters of MTMDs are obtained using a global optimization method and compared with mode-by-mode design results. Robustness analysis is conducted to verify the effectiveness of the optimization framework. The results show that the polynomial model accurately predicts the amplitude after TMD installation. Secondary modes significantly affect the optimal parameters of TMDs, and the optimized results exhibit better control performance than the mode-by-mode design results.