Civil Engineering Reference
In-Depth Information
()
()
V
i
r
V
and
λ
=− ⋅ + ⋅
ζ ωω
, from which the in-wind damping ratio
ζ
, resonance
r
r
r
r
()
()
r
V
r
V
frequency
ω
and phase angle
ψ
may be quantified. The difference between
observed in-wind values of
ψ and their corresponding still-air counterparts
will then contain all the effects of motion induced interaction between the section model
and the flow. Since
ζ ,
ω
r
r
r
( )
V
Lj
has been idealised into a single harmonic component it is
necessary to assume that the motion induced part of the loading is dominant and narrow-
banded, and that the buffeting contribution is insignificant or it has been filtered off. The
general equation of motion that contains all the relevant motion induced effects as
expressed by the aerodynamic derivatives is then given by
M Lj C Lj K Lj C Lj K Lj
⋅ +⋅ +⋅ ≈ ⋅ + ⋅
(C.5)
ae
ae
where
ª º
C
C
ª º
ae
ae
T
¬ ¼
³
Ʒ
Ʒ
dx
=
⋅
⋅
(C.6)
« »
« »
K
K
« »
¬ ¼
ae
ae
L
exp
Since the testing strategy only allows for the determination of six of the altogether eight
motion induced load coefficients in the present set-up it is necessary to make a
simplification. The following is adopted:
HH
A
0
0
H
A
ª
º
ª
º
1
2
3
C
K
=
«
and
=
«
(C.7)
»
»
ae
ae
A
¬
¼
¬
¼
1
2
3
H
and
A
are discarded. Thus,
I.e.,
ª
CC
H
º
2
ª
º
φ
φ φ
H
ae
ae
CC
θ
zz
z
z
1
z
2
«
»
θ
C
³
dx
=
=
«
»
(C.8)
ae
2
«
»
φφ
A
φ
A
«
»
¬
¼
¬
ae
ae
¼
L
z
1
2
θ
θ
z
exp
θ
θθ
and
ª
0
K
º
0
0
φφ
H
ª
º
ae
z
3
z
θ
θ
K
«
»
³
dx
=
=
(C.9)
«
»
ae
2
«
»
A
0
K
φ
«
»
¬
¼
3
¬
ae
¼
L
θ
exp
θθ
The equation of motion is then given by:
ª
CC C
º
−
−
ª
K
K
º
ª
M
0
º
−
0
0
ªº
z
ae
ae
z
z
z
zz
z
θ
θ
«
»
«
Lj
Lj
»
Lj
«
»
⋅ +
⋅ +
⋅ =
(C.10)
«»
0
KK
0
M
«
»
−
−
C
C
−
C
«
»
«
»
¬¼
¬
¼
¬
θ
ae
¼
θ
¬
ae
ae
¼
θ
θθ
z
θ
θθ
