Civil Engineering Reference
In-Depth Information
If a quasi-static approach is adopted, then
c
and
k
are given by (see Eqs. 5.13
ae
ae
0
0
and 5.14):
0
0
0
0
0
0
⎡
⎤
⎢
⎥
(
)
02
DC
DC
BC
000
−
−
′
−
⎢
⎥
D
D
L
⎢
⎥
(
)
V
ρ
02
−
BC
−
BC
′
+
DC
000
⎢
⎥
L
L
D
c
=
(9.52)
ae
⎢
⎥
0
2
2
2
⎢
02
BC
BC
′
000
⎥
M
M
⎢
⎥
0
0
0
0
0
0
⎢
⎥
⎢
⎥
0
0
0
0
0
0
⎣
⎦
000000
000
⎡
⎤
⎢
⎥
DC
BC
′
00
−
⎢
D
⎥
⎢
000
′
00
⎥
2
−
V
ρ
L
k
=
(9.53)
⎢
⎥
ae
0
2
2
000 00
000000
000000
BC
′
⎢
⎥
M
⎢
⎥
⎢
⎥
⎢
⎥
⎣
⎦
If a modal approach with aerodynamic derivatives is adopted, then (see Eqs. 5.24 and
5.25)
00
0
0 00
⎡
⎤
⎢
⎥
*
*
*
0
P
P
P
0
0
−
⎢
⎥
1
5
2
⎢
⎥
2
*
*
*
B
ρω
0
HH
−
H
0
0
i
⎢
5
1
2
⎥
c
=
(9.54)
ae
0
2
⎢
⎥
*
*
2
*
0
BA
BA
B A
0
0
−
−
5
1
2
⎢
⎥
00
0
0 00
⎢
⎥
⎢
⎥
00
0
0 00
⎣
⎦
00
0
0 00
⎡
⎤
⎢
⎥
*
*
*
0
P
P
P
0
0
−
⎢
⎥
4
6
3
⎢
⎥
22
B
*
*
*
ρω
0
HH
H
0
0
−
i
⎢
⎥
6
4
3
k
=
(9.55)
ae
0
2
⎢
⎥
*
*
2
*
0
BA
BA
B A
0
0
−
−
6
4
3
⎢
⎥
00
0
0 00
⎢
⎥
⎢
⎥
00
0
0 00
⎣
⎦
where
ω is the relevant frequency of motion (i.e. the mean wind velocity dependant
resonance frequency of mode
i
). It should be noted that if a quasi-static approach is
i
