Vibration Control in Cable-Stayed Bridge Towers Using an EL-FRF Model for MTLD-Structure Interaction

This study proposes a novel analytical framework, termed the Euler-Lagrange Frequency Response Function (EL-FRF), for modeling the dynamic interaction between structures and multi-tuned liquid damper (MTLD) systems. Derived from Euler-Lagrange equations and incorporating nonlinear shallow-wave theory via equivalent tuned mass damper (TMD) analogies, the EL-FRF provides a non-dimensional transfer function to evaluate broadband vibration suppression under wind loads. Key innovations include its multi-degree-of-freedom formulation for MTLD, enabling optimization of parameters such as tank count (N = 5–15), frequency bandwidth (R = 0.2–0.3), and center mass ratio (~ 60%), demonstrating superior robustness over single-tuned liquid dampers (STLD). Validated through parametric simulations showing 20–30% greater amplitude reductions, the EL-FRF is applied to the tower of the Bai Chay cable-stayed bridge in Vietnam, where MTLD outperforms the existing STLD with reduced damper layers and enhanced lateral vibration control. This method advances passive damper design, offering a versatile tool for structural engineers in seismic and wind-prone regions.