Civil Engineering Reference
In-Depth Information
induced. Comparing
()
det
H
ω shown in the top left hand side diagram of Fig. 6.10 to that which
is shown in Fig. 6.9 it is seen that the resonance frequency associated with the second mode shape (in
torsion) is no longer precisely at
2
rad s
, but slightly below. It is also seen that the resonance peaks
are reduced, and particularly the peak associated with
0.8
ω = rad/s. The standard deviation
of the dynamic responses in the across wind direction (
r
) and in torsion (
r
θ
) at various mean wind
velocities are shown on the two left hand side diagrams in Fig. 6.11. The circular points joined with a
fully drawn line are based on the development shown above, i.e. they contain the effects of
aerodynamic derivatives, while the broken line represents the situation that aerodynamic derivatives
are ignored. As can be seen, the difference is considerable for the respone in the across wind vertical
direction, but in torsion only at the highest mean wind velocity setting. It should be noted that the
applicability of quasi static aerodynamic derivatives is in many cases questionable, and they should in
general be replaced by values obtained from wind tunnel tests. The covariance coefficient between
the dynamic responses
r
and
r
θ
is shown on the top right hand side diagram in Fig. 6.11, and again,
circles and fully drawn line contain the effects of aerodynamic derivatives while for the broken line
no motion induced effects have been included. The changes of the resonance frequency associated
with the second mode shape (in torsion) at increasing mean wind velocities is shown on the lower
right hand side diagram in Fig. 6.11. As can be seen, the reduction of the resonance frequency from
0
φ
at
1
V
V
40
ms
is slightly less than 15 % (which without further iterations implies an
overestimation of the torsion response).
=
to
=
Fig. 6.11
Top and lower left: dynamic response in vertical direction and torsion. Top
right: covariance coefficient. Lower right: resonance frequency associated with 2
nd
mode. Full lines: including motion induced effects. Broken lines: without motion induced
effects.
