Civil Engineering Reference
In-Depth Information
as an input for the dynamic analysis in FAST. TurbSim is a stochastic, full-
fi eld, turbulent-wind simulator. It uses a statistical or empirical model (as
opposed to a physics-based model) to numerically simulate time series of
three-component wind-speed vectors (Jonkman, 2009). TurbSim supports
the IEC Kaimal model (Kelley and Jonkman, 2007) that is used in this study.
More details on the Kaimal model can be found in Mardfekri and Gardoni
(2012).
In addition, FAST supports the JONSWAP/Pierson-Moskowitz spec-
trum (Dean and Dalrymple, 1991) to model linear irregular waves for given
signifi cant wave height and wave peak period. It then uses the Morison's
equation to determine the hydrodynamic forces on the tower. Current
loading is also incorporated in the Morison's equation. See Mardfekri and
Gardoni (2012) for more details on wave and current loading.
The deterministic predictions of the deformation, shear, and moment
demands on the support structure subject to seismic loading are developed
in this chapter following a consistent approach to the one that Mardfekri
and Gardoni (2012) used to compute deterministic predictions for wind,
wave, current, and turbine operational loadings, which is described above.
For given intensity and duration parameters of the ground motion and
frequency content of a fi lter, a synthetic ground motion is generated fol-
lowing Rezaeian and Der Kiureghian (2010). The generated ground motion
is then used as an input for a dynamic analysis also carried out using FAST.
Rezaeian and Der Kiureghian (2010) formulated the ground motion process
with a stochastic model as
T
u
ˆ
()
=
(
)
⎣
( )
⎦
yt
qt
,
a Ψ
t
t
≤<
+
t
t
1
[26.3]
m
m
where
t
stands for the time,
q
(
t
,
a modulating function that controls
the time-varying intensity of the process,
α
)
=
a unit
vector of the deterministic basis functions that controls the evolving fre-
quency content of the process and
u
Ψ
(
t
)
=
[
ψ
1
(
t
), . . . ,
ψ
n
(
t
)]
T
=
a vector of standard
normal random variable that provides the randomness that exists in real
ground motions. Following Rezaeian and Der Kiureghian (2010), we select
the gamma modulating function formulated as
=
[
u
1
, . . . ,
u
j
]
T
=
(
)
=
qt
,
a
0
if
if
t T
≤
0
[26.4]
(
)
α
−
1
[
(
)
]
=−
α
tT
2
exp
−−
α
tT
T t
≤
1
0
3
0
0
2
> 1, and
T
0
denotes the start time of the process. The deterministic basis
function is written as a function of the fi lter parameters,
This model has four parameters
α
=
(
α
1
,
α
2
,
α
3
,
T
0
), where
α
1
,
α
3
> 0,
α
λ
(
t
j
), as follows
[
()
]
ht t t
ht t
−
,
l
[
()
]
=
j
j
ψ
j
t
,
l
t
t
≤<
t
t
1
1
;
≤≤
j
n
[26.5]
j
n
n
+
n
∑
[
()
]
2
−
,
l
t
i
i
i
=
1
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