Civil Engineering Reference
In-Depth Information
q
mz
=
or
Experimental investigations of the single point
process (
θ
) on stiff
r
≈ show that fluctuating loads are more or less narrow banded
centred at a vortex shedding frequency
f
, as illustrated in Fig. 5.5.a. The properties of
the shedding frequency are characteristic to the cross section of the line-like structure. It
is proportional to the mean wind velocity
V
and inversely proportional to the across wind
width
D
. Thus,
0
models where
V
f
t
=⋅
(5.31)
s
D
where
St
is the Strouhal number, which is available for a good number of typical
structural cross sections in the literature. Two-dimensional investigations also show that
q
has a more or less random distribution in the span-wise direction, as illustrated on
the right hand side of Fig. 5.4. and indicated by the decaying co-spectrum in Fig. 5.5.b.
Fig. 5.5
Load characteristics associated with vortex shedding
Turning to a flexible structure it is assumed that the properties of
f
are maintained,
i.e. that Eq. 5.31 still holds. The situation is illustrated in Fig. 5.6. Assuming that
V
is
slowly increasing (from zero), then
f
will increase accordingly, and resonance will first
occur when
f
becomes equal to the lowest eigen-frequency with respect to vibrations in
the across wind direction or torsion. Further increase of
V
will cause resonance to occur
when
f
is equal to the next eigen-frequency, and so on. Theoretically, resonance will
occur when
f
is equal to any eigen-frequency
f
. According to Eq. 5.31, the event that
f
f
=
will occur when the mean wind velocity has a value given by
s
i
