Civil Engineering Reference
In-Depth Information
are the so-called cross sectional admittance functions. They are frequency dependent
functions characteristic to the cross section in question.
In general, they may be determined from section model wind tunnel experiments,
either directly from pressure tap measurements around the periphery of the cross section,
or from time series of drag, lift and moment forces on the model that are otherwise used
to determine mean load coefficients, in which case it is necessary to assume that the
length scales of the fluctuating forces are identical to the appropriate length scales of the
turbulent flow components. Cross sectional admittance functions have been theoretically
developed for a thin airfoil by Sears [15], but since Sears solution is complex and
contain cumbersome Bessel functions, approximate expressions, usually of the following
type have been suggested (first by Liepmann [16])
myz
,,
1
⎧
⎨
nuw
θ
=
()
(
A
ω
=
(5.21)
mn
b
mn
,
)
=
1
aB V
/
+
ω
⎩
mn
a
b
where
and
mn
are cross sectional dependent constants. As can be seen,
mn
⎫
()
(
A
A
1
01
ω
ω
≤
mn
⎪
⎪
)
()
==
(5.22)
⎬
⎪
mn
lim
A
0
ω
=
⎪
⎭
mn
ω
→∞
and thus, its main effect is to filter off load contributions at high frequencies. (Other
expressions may be expected for complex cross sections.) The second major
improvement to the frequency domain application of the buffeting theory is to replace
the content of
a
C
and
a
K
with the so-called aerodynamic derivatives. That is dealt
with in the next chapter.
5.2 Aerodynamic derivatives
As derived from the buffeting theory
a
C
and
a
K
are given in Eqs. 5.13
and 5.14. They are three by three matrices containing all the eighteen coefficients that
are required for a full frequency domain description of motion induced dynamic forces
associated with structural velocity and displacement. The modal frequency domain
counterparts to
a
C
and
a
K
are first fully presented in Eq. 4.62 in chapter 4.4.
(Basic assumptions are given in Eq. 4.59.
a
M
is in the following considered
negligible.) The essential theory presented below was first developed in the
field of aeronautics and later made applicable to bridges by Scanlan &
Tomko [17]. Following their notations, rather than the more general use of
