Civil Engineering Reference
In-Depth Information
Fig. 5.7
Vortex shedding induced response characteristics at different levels of
structural eigen-damping
Experiments show that vortex induced vibrations are greatly affected by the damping
properties of the structure, as shown on the left hand side diagram in Fig. 5.7. The
motion induced self-limiting and damping dependent nature of vortex induced vibrations
is further illustrated on the diagram to the right in Fig. 5.7. Thus, it has been customary
to ascribe the motion induced part of the load to the structural displacements and the
velocity, i.e.
(
)
mz
=
.
Extensive research has been carried out on the investigation of vortex shedding
induced vibrations. In the following it is the theory first developed by Vickery & Basu
[18, 19] that will be presented. The motivation is convenience, as it is the only
comprehensive stochastic frequency domain theory currently available, rendering a
solution at any setting of the mean wind velocity. An alternative approach applicable at
resonance has been presented by Ruscheweyh [20].
In the theory as developed by Vickery & Basu the description of the net motion-
independent cross sectional load spectra and corresponding co-spectra are shape-wise
shown in Fig. 5.5. Mathematically they are given by
qqxt r
,, ,
mm
r
, where
or
=
mm
⎡
(
)
2
⎤
2
B
ˆ
⎧
⎫
⋅
σ
1/
⎛
−
ωω
⎞
⎪
⎪
⎢
q
z
⎥
2
s
1
2
exp
⋅
−
⎛
⎞
⎨
⎬
⎜
⎟
2
⎢
⎥
ρ
V
b
b
()
()
⎜
⎟
⎡
S
S
⎤
⎝
⎠
ω
ω
⎪
⎪
z
z
⎢
⎩
⎭
⎥
⎝
⎠
q
z
⎢
⎥
=
⋅
⎢
(5.33)
⎥
2
(
)
⎢
⎥
πω
⋅
2
2
B
ˆ
⎧
⎫
⎣
q
⎦
⎢
⋅
σ
⎥
s
1/
θ
⎛
−
ωω
⎞
⎪
⎪
q
θ
s
⎢
exp
⎥
⋅
−
⎨
⎜
⎟
⎬
b
b
⎢
⎥
⎪
⎝
⎠
⎪
θ
θ
⎩
⎭
⎣
⎦
and
