Civil Engineering Reference
In-Depth Information
Fig. 6.12
Aerodynamic damping coefficient
Finally, let us adopt the following wind velocity variation of the relative aerodynamic damping
coefficient (see Fig. 6.12)
ω
=⋅
D
(
)
−
n
(
)
−
m
⎡
⎤
()
KVK
2.6
VV
exp
VV
V
i
=⋅
⋅
−
⎦
where
⎢
⎥
a
a
R
R
R
i
0
i
i
2
St
⎣
In this case (see Eq. 6.81)
⎡
2
⎤
Cov
Cov
σ
rr
rr
rr
yy
yz
y
θ
⎢
⎥
∞
⎢
⎥
()
(
)
2
∫
Cov
x
=
S
x
,
ωω
d
=
⎢
σ
Cov
rr
r
rr
r
r r
r r
⎥
zz
z
θ
0
⎢
⎥
2
Sym
.
σ
⎢
rr
⎥
⎣
⎦
θθ
⎡
⎤
000
000
⎡
⎤
⎡
⎤
00
0
⎢
⎥
⎢
⎥
⎢
⎥
2
()
2
2
()
2
2
0
x
0
0
x
0
0
0
0
=
φ
⋅
σ
+
φ
⋅
σ
+
⎢
⎥
⋅
σ
⎢
⎥
⎢
⎥
z
r
z
r
η
η
η
1
1
2
2
3
⎢
⎥
⎢
⎥
⎢
⎥
2
3
()
00
x
000
000
φ
⎢
⎥
⎣
⎦
⎣
⎦
⎣
r
⎦
θ
and thus:
⎡
⎤ ⎡
⎤
00
0
0
0
0
⎢
⎥ ⎢
⎥
()
⎢
2
⎥ ⎢
2
()
2
2
()
2
⎥
Cov
x
=
0
σ
0
=
0
φ
x
⋅
σ
+
φ
x
⋅
σ
0
rr
r
r r
z
r
η
z
r
η
zz
1
1
2
2
⎢
⎥ ⎢
⎥
⎢
⎥ ⎢
⎥
2
2
()
2
00
0
0
x
σ
φ
⋅
σ
⎣
rr
⎦
⎣
r
⎦
θ
η
3
3
θθ
From Eqs. 6.83 and 6.84 (and taking it for granted that
λλλ
==) the following variance
z
θ
contributions are obtained
