Special design of tuned liquid column-gas dampers for the control of spatial structural vibrations

Abstract

The relevant low-frequency modes of plan-asymmetric tall buildings and those of bridges consist of coupled translational and torsional motions. We consider the locations of the modal centers of velocity of either the rigidly assumed floors or of the bridge cross-sections to be crucial for selecting the design and the “optimal” position of the liquid absorbers. Such a tuned liquid column-gas damper, TLCGD consists of a sealed rigid piping system that is partially filled with liquid (preferably water), whose dynamics can be derived using the nonstationary Bernoulli equation properly extended to account for the relative streamline in a moving reference system. Although both the construction and working principle of TLCGDs differ from tuned mass dampers (TMD), a geometric analogy exists between these absorber types. Consequently, in a first step modal tuning is performed by means of a transformation of the TMD optimal parameters, e.g., of the Den Hartog formulas, possibly followed in a second step by fine-tuning in state-space. Such a U- or V-shaped sealed liquid column-gas damper, i.e., with the gas-spring effect taken into account, is found suitable for applications in moderately plan-asymmetric buildings (the floors’ modal center of velocity falls outside of the floor plan) and for bridges with dominant horizontal vibrations. The novel design of a torsional sealed liquid column-gas damper, TTLCGD, turns out to have even higher efficiency in effectively damping strongly asymmetric buildings, where the floors’ modal centers of velocity lie inside of the floor plan: in that case of an alternative design, the mid-plane of the U-shaped TLCGD is bent to a cylindrical surface that might be “nearly closed” such that the trace in the floor becomes approximately a loop. For bridges with dominating vertical flexural vibrations, a novel pipe-in-pipe design of the VTLCGD provides the vertical control force rendering the additional efficient damping. The evident features of TLCGDs are no moving mechanical parts, cheap and easy implementation into civil engineering structures, simple modification of the natural frequency and even of the damping properties, low maintenance costs, little additional weight in those cases where a water reservoir is required, e.g., for the sake of fire fighting, and with a performance comparable to that of TMDs of the spring-mass- (or pendulum-)-dashpot type.