Civil Engineering Reference
In-Depth Information
Furthermore, it has been considered convenient to normalise
a
C
and
a
K
with
2
22
/ 2
i
ω
is the in-wind (mean wind velocity dependent)
resonance frequency associated with the mode shape (number
i
) from which they have
been extracted. Thus,
ρω
/ 2
and
ρω
, where
i
i
2
2
B
B
ρ
ρ
2
ˆ
ˆ
()
()
V
⎡
V
⎤
C
=
⋅
ω
⋅
C
and
K
=
⋅
ω
⋅
K
(5.24)
⎣
⎦
ae
i
ae
ae
i
ae
2
2
where
⎡
*
*
*
⎤
⎡
*
*
*
⎤
PP
P
PP
P
1
5
2
4
6
3
⎢
⎥
⎢
⎥
ˆ
ae
ˆ
ae
*
*
*
*
*
*
HH
H
HH
H
C
=
⎢
⎥
and
K
=
⎢
⎥
(5.25)
5
1
2
6
4
3
⎢
⎥
⎢
⎥
*
*
2
*
*
*
2
*
BA
ABA
BA
ABA
⎢
⎥
⎢
⎥
⎣
5
1
2
⎦
⎣
6
4
3
⎦
*
*
*
PHA k
=− that are usually called
aerodynamic derivatives. The values that emerge from the buffeting theory are obtained
by comparison to Eqs. 5.13 and 5.14, rendering quasi-static aerodynamic derivartives
,
,
,
16
It is the non-dimensional coefficients
kkk
DV
D
V
V
⎡
⎛
⎞
⎤
2
C
C
′
C
C
′
−
−
+
−
⎢
⎜
⎟
⎥
D
L
D
M
()
()
()
BBV
BBV
BV
ω
ω
ω
⎝
⎠
⎢
i
i
i
⎥
*
*
*
⎡
PHA
PHA
⎤
1
1
1
⎢
⎥
⎢
⎥
0
0
0
*
*
*
⎢
⎥
⎢
⎥
2
2
2
2
2
2
⎢
⎥
⎢
⎥
⎛
⎞
⎛
⎞
⎛
⎞
D
V
V
V
*
*
*
PHA
⎢
C
C
C
⎥
⎢
⎥
′
′
′
⎜
⎟
⎜
⎟
⎜
⎟
3
3
3
D
⎜
()
⎟
L
⎜
()
⎟
M
⎜
()
⎟
=
⎢
BB V
ω
B V
ω
B V
ω
⎥
⎢
⎥
⎝
⎠
⎝
⎠
⎝
⎠
*
*
*
i
i
i
PHA
PHA
⎢
⎥
⎢
⎥
4
4
4
0
0
0
⎢
⎥
⎢
⎥
*
*
*
⎢
⎥
⎢
5
5
5
⎥
DV
V
V
⎛
⎞
⎢
⎥
CC
′
2
C
2
C
⎢
*
*
*
⎥
−
−
−
PHA
⎜
⎟
LD
L
M
⎣
⎦
()
()
()
⎢
BB V
BV
BV
⎥
6
6
6
ω
ω
ω
⎝
⎠
i
i
i
⎢
⎥
0
0
0
⎢
⎥
⎣
⎦
(5.26)
As shown in Eq. 5.26, the aerodynamic derivatives will be functions of the reduced
velocity
()
⎡
⎣ ⎦
. It should be noted that in the determination of the reduced
velocity [or the non-dimensional resonance frequency
VVB
ω
()
ˆ
B
VV
/
] the resonance
ωω
=
i
i
()
frequency
is a function of the mean wind velocity,
V
. To start off with, i.e. at
ω
i
V
(
)
,
is the eigen-frequency in still air conditions. It is then only dependent
V
=
0
ω
i
V
=
0
V
0
on the relevant structural properties. At
the aerodynamic derivatives contained in
a
K
will have the effect of changing the total stiffness of the combined structure and
≠
