Civil Engineering Reference
In-Depth Information
Appendix D
DETERMINATION OF INDICIAL
FUNCTIONS FROM AERODYNAMIC
DERIVATIVES
Aerodynamic load contributions in the along-wind, the across-wind and the pitching
moment directions
T
()
t qq
θ
q
=
¬
ª
º
generated by the interaction between the
¼
ae
y
z
ae
T
()
=
¬
r
have first been
developed in a quasi-steady format in chapter 5.1, where the definition of positive
r
θ
and
q
θ
comply with the usual aerodynamic conventions shown in Fig. 1.3.a. Since the
determination of aerodynamic derivatives and the corresponding indicial functions are
taken from wind tunnel aero-elastic section model tests, this is also the sign convention
chosen for the presentation below. However, the use of indicial functions will generally
only be relevant in a time domain solution in a finite element format, and in such a
format all displacement and load quantities are vectors. This format has been presented
in chapter 9. It should however be noted that the choice of sign convention for
displacements and forces has no consequences to the determination of indicial functions
as long as any displacement component and its corresponding load component has
identical directions. Thus, from a quasi-steady theory (see Eq. 5.8)
()
t
ª
r
r
r
θ
º
wind field and the motion of the structure
y
z
()
()
q
t
Cr
t
Kr
t
(D.1)
=
+
ae
ae
ae
where for simplicity the horizontal spanwise (axial)
r
degree of freedom and
corresponding
q
load component have been omitted as they have no relevance for a
line-like type of structure, and
(
)
ª
º
½
2
DC
DC
′
BC
0
−
−
−
D
D
L
°
«
»
°
V
ρ
(
)
«
»
C
=
−
2
BC
−
BC
′
+
DC
0
ae
L
L
D
°
2
«
»
°
«
»
2
2
−
2
BC
−
BC
′
0
«
M
M
»
°
¬
¼
¾
°
°
(D.2)
00
00
DC
′
ª
º
D
°
V
2
ρ
«
»
K
=
BC
BC
′
°
«
»
ae
L
2
°
«
2
»
00
′
¬
¼
¿
M
