Civil Engineering Reference
In-Depth Information
(
)
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
()
*
*
*
*
S
ωγ
=⋅
HH
+ ⋅
γ
HH
+
HH
+ ⋅
γ
HH
η
LL
21
21
LM
21
22
22
21
MM
22
22
22
2
2
⎛⎞
m
⎛⎞
m
ω
ω
2
(
)
2
2
2
1
1
C
′
9375
BC C
′′
150
BC
′
2.4
γ
=
=
,
γ
=
=
and
γ
=
=
.
⎜
⎝⎠
⎜
⎝⎠
LL
L
LM
L
M
MM
M
m
m
ω
ω
1
1
2
2
Since we are mainly aiming at calculating the content of the covariance matrix
2
⎡
Cov
⎤
σ
∞
rr
rr
zz
z
(
)
(
)
⎢
θ
⎥
xL
2
∫
L
2 ,
d
Cov
=
=
S
ωω
=
⎢
rr
r
rr
2
⎥
Cov
σ
0
⎣
rr
rr
⎦
z
θ
θ θ
it is only the absolute values that are of interest.
Fig. 6.10
Top left: absolute value of frequency response function. Top right: cross
spectrum between vertical and torsion response components. Lower left and right:
spectra of components in vertical direction and torsion.
30
Vms
.
=
The absolute value of the determinant of the non-dimensional frequency at a mean wind velocity
30
Vms
of
is shown in the top left hand side diagram in Fig. 6.10. The top right hand side
diagram shows the amplitude of the cross spectrum between
r
and
r
θ
=
while the two lower diagrams
show the spectral densities of
r
and
r
θ
30
Vms
. As can be
seen, there are traces of modal coupling. In this case the coupling effects are exclusively motion
, all at a mean wind velocity of
=
