Multiple tuned liquid column dampers for reducing coupled lateral and torsional vibration of structures

This paper presents a theoretical investigation on the performance of multiple tuned liquid column dampers (MTLCD) for mitigating the coupled lateral and torsional vibration of a long span bridge which can be modelled as a two degrees-of-freedom structure. The cross section of the bridge has a vertical axis of symmetry but with the vertical offset between the elastic centre and the mass centre of the bridge. The external dynamic force and moment are applied at the elastic centre of the bridge. The proposed MTLCD consists of two sets of liquid column dampers with one tuned to the lateral frequency of the bridge and the other tuned to the torsional frequency of the bridge. The equations of motion for the coupled lateral and torsional vibration of the bridge with MTLCD are first presented. The nonlinear damping property of MTLCD is linearized using the equivalent linearisation technique. Extensive parametric studies are then carried out in the frequency domain to find beneficial parameters of the MTLCD for achieving maximum reduction of coupled lateral and torsional vibration of the bridge. The parameters investigated herein include water mass distribution between the two dampers, distance from the centre line of the MTLCD to the rotational axis of the bridge, ratio of horizontal length to total length of liquid column, head loss coefficient, and frequency tuning ratio. The performance of the MTLCD in reducing buffeting response of the bridge due to turbulent wind is finally investigated. This study shows that the performance of MTLCD in reducing the lateral and torsional displacements of the bridge depends on the head-loss coefficient and the frequency-tuning ratio significantly. It is also demonstrated that the aeroelastic effects due to the interaction between turbulent wind and bridge motion is a crucial factor affecting the performance of MTLCD in reducing buffeting responses of the bridge.