Civil Engineering Reference
In-Depth Information
The variation of
ˆ
r
σ with the mean wind velocity at three levels of structural eigen-damping is
shown in Fig. 6.16. As can be seen, the vortex shedding induced dynamic response is self-limiting
and strongly damping dependant.
The maximum vortex shedding induced dynamic response will occur slightly above
V
, but
R
z
for practical calculations the maximum value of
σ
may be obtained by setting
VV
=
, in
r
z
R
z
which case
g
=
1
and
K
=
K
. As shown on the lower right hand side diagram in Fig. 6.15,
z
a
a
z
0
the maximum value of
σ
is rapidly reduced with increased structural eigen-damping.
r
z
T
[
]
If
φ
=
00
φ
then
12
12
⎧
⎫
2
⎡
⎤
ˆ
ˆ
⎛ ⎞
1
−
ζ
1
−
ζ
⎪
⎪
ˆ
⎢
2
⎥
ˆ
σ
=
+
+
β
⎜ ⎟
⎨
⎬
r
θ
⎜ ⎟
2
⎢
2
⎥
⎪
⎝ ⎠
⎪
⎣
⎦
⎩
⎭
where
ˆ
r
σσ
=
a
θ
and
r
θ
θ
12
2
∫
⎛
⎞
φ
dx
θ
()
x
5
σ
ˆ
φ
⎜
⎟
4
m
ζ
ρ
D
λ
g
ˆ
ˆ
r
q
θ
θ
θ
L
θ
θ
ζ
=
⋅
⋅
and
β
=
⋅
⋅
⋅
⋅
⎜
⎟
4
2
52
74
2
2
B
K
∫
2
m x
∫
bK
St
a
ρ
φ
dx
π
φ
⎜
⎟
a
θ
a
θ
θ
⎜
θθ
⎟
θ
θ
⎝
⎠
L
L
exp
