Civil Engineering Reference
In-Depth Information
Under these circumstances the equation above may be rewritten into the following fourth order
polynomial
(
)
ˆ
ˆ
4
2
2
ˆ
ˆ
σ
−−
1
ζ
σ
− =
β
0
r
r
z
z
where
12
2
⎛
⎞
∫
dx
φ
z
()
ˆ
φ
x
⎜
3
⎟
σ
4
m
D
g
ζ
ρ
λ
q
ˆ
ˆ
zr
z
z
L
z
z
ζ
=
⋅
⋅
and
β
=
⋅
⎜
⋅
⎟
⋅
⋅
2
2
52
74
2
2
K
bK
a
ρ
B
∫
dx
2
π
m x
∫
φ
St
φ
⎜
⎟
a
z
a
z
z
zz
z
⎜
z
⎟
⎝
⎠
L
L
exp
(
)
ˆ
r
aD
and where
. Thus, the reduced standard deviation of the vortex shedding
induced dynamic response is given by
σσ
=
r
z
z
z
12
⎧
12
⎫
2
⎡
⎤
ˆ
ˆ
1
⎛ ⎞
1
−
ζ
−
ζ
⎪
⎪
ˆ
⎢
2
⎥
ˆ
σ
=
+
+
β
⎨
⎜ ⎟
⎬
r
z
⎜ ⎟
2
2
⎢
⎥
⎪
⎝ ⎠
⎪
⎣
⎦
⎩
⎭
Fig. 6.16
Vortex shedding induced dynamic response
