Civil Engineering Reference
In-Depth Information
T
ˆ
(
)
buffeting part of the cross sectional loading is
⎡
qqq
⎤
VB
/2
Bv
,
⎦
Bv
=⋅
=
ρ
⋅
⋅
⎣
y
z
θ
q
q
then its Fourier transform is
⎡ ⎤
⎢ ⎥
a
q
y
ˆ
(
)
(
)
x
,
a
VB
/ 2
a
ω
=
⎢ ⎥
⎢
⎢
⎣ ⎦
=
ρ
⋅
B a
⋅
(6.55)
q
q
q
v
z
a
q
θ
where
T
(
)
[
]
x
,
a
a
a
ω
=
(6.56)
v
u
w
(
)
x
,
The cross spectrum
S
Δ
ω
is then given by
qq
1
(
)
(
)
(
)
⎡
*
T
⎤
x
,
lim
x
,
x
,
S
Δ=
ω
a
ω
⋅
a
ω
qq
⎣
q
1
q
2
⎦
T
π
T
→∞
2
ρ
VB
1
⎛
⎞
ˆ
ˆ
*
(
)
T
(
)
T
⎡
⎤
lim
x
,
x
,
=
⋅
B
⋅
a
ω
⋅
a
ω
⋅
B
(6.57)
⎜
⎟
q
⎣
v
1
v
2
⎦
q
2
T
π
⎝
⎠
T
→∞
2
VB
⎛
ρ
⎞
ˆ
ˆ
(
)
T
=
⋅
BS B
⋅
Δ
x
,
ω
⋅
⎜
⎟
qv
q
2
⎝
⎠
(
)
x
,
SS
0
where
= ≈ ,
see Eq. 6.17, and introducing Eq. 6.40, then the content of the normalised modal load
matrix (
N
mod
by
N
mod
)
S
Δ
ω
is defined in Eq. 6.37. Adopting the assumption that
v
uw
wu
⎡
⎤
%
$
⎢
⎥
()
()
⎢
S
⎥
S
ω
=
⎢
ω
(6.58)
ˆ
ˆ
ˆ
Q
Q
ij
⎥
⎢
⎥
$
%
⎣
⎦
is given by
{
}
ˆ
ˆ
ˆ
T
()
2
(
)
T
()
⎡
⎤
∫∫
φ BI S Bφ
x
x
,
x
dx dx
⋅
⋅
⋅
Δ
ω
⋅
⋅
i
1
q
v
v
q
j
2
1
2
⎣
⎦
2
2
⎛
⎞
ρ
VB
L
exp
()
S
ω
=
⋅
⎜
⎟
ˆˆ
(
) (
)
⎜
⎟
Q
ij
2
2
2
MM
ω
⋅
ω
⎝
⎠
i
i
j
j
2
2
3
3
⎛ ⎞
BB V
⎛ ⎞
V
ρρ
ˆ
2
J
=
⋅
⋅
⋅
⎜ ⎟
⋅
⎜ ⎟
⎜ ⎟
⎝ ⎠
⎝ ⎠
ij
22
mmB
B
ω
ω
i
j
i
j
(6.59)
