Environmental Engineering Reference
In-Depth Information
m top
L
m
EI
Figure 29: Structural model of a fl exible wind turbine system.
Figure 30: Frequency areas of 1P and 3P for the V90, with the designed natural
frequency at 0.31 Hz between 1P and 3P to prevent dynamic interaction.
For this model consisting of a uniform beam with a top mass and a fi xed base,
the following approximation for the calculation of the fi rst natural frequency
is valid:
3.04
4
EI
( 14 )
2
nat
f
2
3
p
(
m
+
0.227
m
L L
)
top
with f nat is the fi rst natural frequency (Hz), m top the top mass (kg), m the tower
mass per meter (kg/m), L the tower height (m) and EI is the tower bending
stiffness (N m 2 ).
The 1P and 3P areas can be plotted in a fi gure to visualize the zones in which
the support structure natural frequency should not lie. In Fig. 30 this is shown for
the V90 from Table 2 in the previous section.
The natural frequency will change through the next steps of design. It will need
to be checked against this diagram to make sure it falls within the area between 1P
and 3P.
For more detailed determination, the natural frequency will of course be calculated
using a fi nite element model of the structure.
 
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