Dynamic analysis of long-span bridges with vibration control systems: A novel reduced-order model and comparative study

Abstract

Long-span bridges, especially suspension bridges, are highly vulnerable to wind-induced vibrations, such as vortex-induced vibrations (VIVs), which necessitate the use of mechanical dampers for control. While a full finite element model (FEM) of the bridge with vibration control systems ensures accuracy of dynamic analysis, it is often computationally expensive due to the large number of degrees of freedom (DOFs). This study presents a reduced-order model that strikes a balance between computational accuracy and efficiency of dynamic analysis, making it ideal for the parametric design of damping devices. The model is based on the modal truncation method, retaining only a limited number of lower-order modes of the undamped bridge to capture the dominant vibration responses induced by wind loads. To compensate for the impact of point-wise control forces and minimize errors from modal truncation, quasi-static correction modes are introduced based on the static deformations of the bridge under unit forces applied at each damper location. The proposed model is applied to the modal analysis of a long-span suspension bridge equipped with damped outriggers and tuned mass dampers (TMDs) to suppress VIVs. The model is compared to both the full FEM and the conventional modal truncation method. Results show that the quasi-static correction significantly improves the accuracy of damping computations, reducing errors by up to 71.2% compared to the uncorrected modal truncation method. Most notably, the computational efficiency improves dramatically compared to the full FEM, with the number of DOFs reduced by approximately two orders of magnitude. Furthermore, a combination of damped outriggers and TMDs tuned to a single mode is sufficient to supply damping for all the bridge vibration modes subjected to VIVs.