Geology Reference
In-Depth Information
strong wind excitation, a well known problem,
e.g. limiting the cantilever method of bridge
construction, can be reduced substantially by the
application of TLCGD. If lateral horizontal and
torsional vibrations dominate, the U- or V-shaped
plane TLCGD is perfectly suited to increase the
effective damping of the bridge. Tall supporting
columns of bridges in seismic zones should be
effectively damped by TLCGD mounted on top,
analogous to tall buildings as discussed above.
The analytical investigation is based on a modal
approximation of the bridge dynamics, selecting a
rigid plane cross section with a TLCGD attached.
Modal tuning is performed with respect to the
dominating horizontal or alternatively rotational
motion. Classical Den Hartog tuning is performed
before fine tuning the multiple degree of freedom
main structure with several TLCGD attached in
state space.
Again the TLCGD dynamic equations have to
be adapted to the possible lateral deflection of a
bridge cross-section, which comprises of the two
translational displacements w and v and the rota-
tion ϑ about the (horizontal) bridge axis ( x -axis),
see Figure 6a. Eq.(1) with absolute accelerations
prescribed renders for sufficiently small rota-
tional angles, ϑ 1 , a linearized equation of
motion for the TLCGD stroke u , see e.g. Reiterer
et al. (2006)

d
H
ϑ
ω
2
w
H

2
u
+
2
ζ ω
u
+
ω
1
κ
+
κ
A
κ
u
=
A A
A
1
1
2
ω
2
2
A
A
B
(
)


κ
v
g
ϑ
κ
d
+
κ
ϑ
A
1 2
B
+
2
H
L
cos
β
2
H
L
sin
β
B
cos
β
+
2
H
κ
=
,
κ
=
,
κ
=
1
2
L
eff
eff
eff
(32)
with the geometry dependent factors κ 1 and κ 2 .
The interaction forces are obtained by the basic
law of conservation of momentum and generalized
conservation of the moment of momentum of the
fluid body with respect to the moving reference
point A . Introducing the geometry dependent
', ( )
b) symmetric cross section of the bridge with absorber forces applied, note the distinct centers of mass
and stiffness. (Adapted from Reiterer et al. (2006)).
Figure 6. a) Free body diagram of symmetrically designed TLCGD with moving reference frame y z
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