An equation-based co-simulation framework for vertical tuned liquid column gas dampers and comparison with tuned mass dampers

Vertical tuned liquid column gas dampers (VTLCGDs) are emerging passive dampers for the vertical vibration control of large-span structures. However, their finite element implementation remains challenging because the effective inertial participation mass differs from the total liquid mass due to the liquid height difference and liquid–gas coupling, complicating mechanically consistent modelling. This study develops an equation-based ANSYS–MATLAB co-simulation framework for evaluating the vibration control performance of VTLCGDs. A unified dynamic formulation is established based on the concept of effective inertial participation mass for representative passive devices, including tuned mass dampers (TMDs), tuned liquid dampers (TLDs), and tuned liquid column damper (TLCD)-type systems. In the proposed time-step-based co-simulation framework, structural responses and equivalent damper forces are exchanged between the finite element model and the damper governing equations. Two control force evaluation schemes are investigated: a displacement–velocity formulation suitable for TMDs and a displacement–velocity–acceleration formulation for liquid-based dampers with non-uniform inertial mass participation. A simplified equivalent TMD model based on the liquid height difference mass is also proposed for preliminary engineering assessment. The proposed framework is evaluated using a 21.8 m corridor structure under pedestrian-induced excitations. The VTLCGD achieved a maximum acceleration reduction of 31.08%, compared with 36.88% for the conventional TMD. The co-simulation results agreed well with the direct finite element simulations, with acceleration response errors remaining within 4%, while the simplified equivalent model showed errors below 3%. These results demonstrate that the liquid height difference governs the effective inertial mass of VTLCGD systems. The proposed framework enables mechanically consistent finite element implementation of liquid-based passive dampers without explicitly resolving the internal liquid–gas flow field, while providing a unified effective-mass representation for engineering applications.