Civil Engineering Reference
In-Depth Information
Fig. C.1
Typical decay recordings as obtained from section model tests; top diagram:
vertical displacements; lower diagram: torsion
,
,
2
z zz
2
K
M
K
M
CM
ω ζ
2
CM
θ
Introducing
=
ω
=
ω
=
,
=
ω ζ
and that
θ
θ θ
z
zzz
θ θ θ
2
r
=
LjLj
Lj
Lj
and
λ=⋅
, then the equation of motion is reduced into
r
§
·
ª
C
C
º
ª
º
K
ae
ae
ae
¨
zz
z
θ
2
z
¸
«
2
»
θ
ωζ
−
−
«
ω
−
»
zz
z
¨
M
M
M
K
¸
10
01
ª º
«
»
«
»
z
z
z
2
Lj 0
⋅ +
λ
⋅ +
λ
⋅ =
¨
¸
«
»
« »
«
»
r
r
C
C
¨
¬ ¼
¸
«
»
«
»
ae
ae
ae
2
θ
z
θθ
0
θθ
−
2
ωζ
−
ω
−
¨
¸
«
»
«
»
¨
θθ
θ
¸
M
M
M
¬
¼
¬
¼
©
¹
θ
θ
θ
(C.11)
H
and
A
,
j
1,2,3
It is convenient to replace the aerodynamic load coefficients
=
, in
*
H
and
*
A
called aerodynamic
Eq. C.7 with the non-dimensional quantities
derivatives and defined by:
