Environmental Engineering Reference
In-Depth Information
Using the resonance curves of a harmonically excited SDOF oscillator, Den
Hartog derived the optimal frequency and the damping ratio as in Eq.
12.4
-
12.5
.
Hereby, l* is the ratio between effective mass of TMD and modal mass of the
structure. f
H
is the natural frequency of the structure.
1
1
þ
l
f
D
;
opt
¼
f
H
ð
12
:
4
Þ
s
3l
8
ð
1
þ
l
Þ
3
D
D
;
opt
¼
ð
12
:
5
Þ
The same procedure can also be used with the tuning criterion of Warburton,
who has enlarged the criterion of Den Hartog also for other stochastic excitations
such as earthquake. The tuning parameters of a TMD attached to a stochastically
excited SDOF can be calculated by Eq.
12.6
-
12.7
.
p
1
l
=
2
f
D
;
opt
¼
f
H
ð
12
:
6
Þ
1
þ
l
s
l
ð
1
l
=
4
Þ
4
ð
1
þ
l
Þð
1
l
=
2
Þ
D
D
;
opt
¼
ð
12
:
7
Þ
12.3.4 Tuned Liquid Dampers
Tuned liquid dampers such as tuned sloshing damper (TSD) and tuned liquid
column damper (TLCD) count also as TMD. Figure
12.7
shows a wind turbine
with a TSD and TLCD. These dampers have naturally very low fundamental
frequencies and therefore can be easily tuned to the tower frequencies of wind
turbines. As these dampers use commonly water as auxiliary masses and do not
need any mechanical elements like springs or joints, they feature a better alter-
native to other vibration mitigation methods for wind turbines.
12.3.4.1 Tuned Sloshing Dampers
The TSD consists of an open tank filled with a Newtonian liquid such as water
with antifreeze. Depending on the tank geometry and liquid depth, different natural
frequencies can be achieved. In order to control the vibrations effectively, TSD
should be installed like TMD and pendulum damper near the tower top, for
instance in the nacelle. As the turbine tower starts to vibrate, the movement of
TSD tank causes the liquid to slosh and develop waves, which dissipate the
oscillation energy. Hereby, the fundamental frequency of TSD depends on non-
linear phenomena, which are caused by sloshing and tank-liquid interaction.
