Tuned Liquid Column Gas Damper in Structural Control - Design Optimization of Active and Passive Structural Control Systems - page 157

In the following section moderate asymmetry
is assumed, thus the popular plane U- or V-shaped
TLCGD is perfectly suited as the proper ab-
sorber. If the position of the TLCGD is given with
respect to its reference point A

u T = θ , where r S denotes the radius of inertia
with respect to the mass of the properly selected
floor (the top floor is always eligible). For mod-
erate asymmetry the plane TLCGD is preferred,
for strong asymmetry the redesigned torsional
TLCGD, TTLCGD, is recommended. Since the
multiple purpose building considered is asym-
metric, its center of mass and the center of stiffness
do not coincide. An arbitrary distribution of floor
mass and stiffness furthermore causes the mass
and stiffness centers not to be aligned vertically
along the x -axis.

=

, , 0 and
its angular orientation by the angle γ with respect
to the y -axis, rotation of the floor about the verti-
cal x -axis is denoted θ , see Figure 2b, proper
generalization of Eq. (1) renders

y z
A A



2

θ
ω

 

2

u + 2 ζ ω u + ω 1 − κ u =

A A A 1 2

A

e ' − κ a ⋅ , κ = κ cos β (12)

A A 1

Figure 2. a) Top floor of a moderately asymmetric building: Position of the velocity-center C V is outside
of the floor plan. Rotation exaggerated. b) TLCGD in horizontal general motion. Unit vector e ' in di-
rection of its trace. Instant position of the fluid mass center C f marked. c) Torsional TLCGD (TTLCGD)
in plan view. The pipe encloses the modal center of velocity C V . (Adapted from Fu et al. (2010)).