List members:
The phenomina you are witnessing is called vortex shedding or oscillation. It
is a function of natural frequency of the element, in this case a cylindar with
l/d >25, and the weight per unit length plus the wind velocity.
For those who wish to see some illustrations go to:
http://www.itsc.com/movvkv.htm
http://www.mecaconsulting.com/vortex_shedding.htm
For a ton of sites use google and type in "vortex shedding" .
For those interested further now come some formulas:
for straight cylinder nat freq (f)= C/2*Pi*L Sqrt(E*I*g/w)
C=3.515 for 1st mode
L= length of element
E=Modulus of elasticity of element material
I=Moment of Inertia of element cross section
g= acceleration of gravity
w= element weight per unit length
IF the element is tapered then:
f = 3.52*De/48*Le Sqrt(E*g/2*w)
De= equivalent dia of tapered element
Le= equivalent length of tapered element
De=D+Dend/2
Le= L*Sqrt(2*De/De+D)
The critical velocity to induce oscillation is:
v= f*D/S S=Strouhal number =0.2
D= D or De
As can be seen as the natural frequency goes up the critical velocity goes up
When you add a rope inside an element then you have increased the mass which
increases the unit weight without modifying any other component which will
reduce the natural frequency and there by decreasing the critical velocity.
This helps explain why these things occur at lower velocities.
IF you taper the element then you reduce both the diameter, reduce the I and
the w and reduce the length. The upshot is that the natural frequency normally
increases thus the critical velocity increases.
This occurs again at the next harmoinc natural frequency. The force generated
at natural or resonant frequencies of structures increase/decrease very quickly
at the resonant frequencies with very little change in velocity. So as the wind
starts and if the critical velocity is reached vortex shedding and its
accompaning oscillations occur. As you pass through the critical velocity point
then the vibration will damp out. If the wind speed continues to rise it is
likely that it will approach the 2nd harmonic frequency velocity and the
oscillations will occur with additional node and so on.
Which is better as far as mass increase via rope in the element or tapered
elements ? Who knows.
Which ever mechanism you choose it would be advantageous to have a fundamental
natural frequency that would be high enough to exceed normal wind velocities at
a given location. However this on a commercial basis would be very difficult.
In general if you use straight non-tapered elements use rope inside if tapered
then I would think that the taper would be very dramatic as to lessend Le and
De but not to the detriment of the I or stiffness of the section to withstand
design wind and ice loadings. See not an easy answer with all kinds of
comprimises.
This is my 1 euro input but I hope it expands the understanding behind this
type of vibration.
73
Hank Lonberg, P.E.,S.E. / KR7X
Lonberg Design Group, Ltd.
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