Hello Hank,
Thank you very much for the content of this message. I suppose their will
be no more bad formulated questions neither answers, with this message in
mind.
I told Jim SMxxxx, If one ask you how paradise looks like, Just tell him how
to get there, he will find out most of it himself. If you have'nt been
there, dont make them believe you have been there..
As far as I am concerned there are no stupid questions, just stupid answers.
That was also the mean raison I started joking on the subject.....
Time to dig up the calculators Guys Just remember Ham is much more then
just playing
" Chicken Bander ".
Thanks again Hank, at least this is a good start for some, and a good
reminder for other ( included myself ).
Take care mate.
Jos on4kj.
 Original Message 
From: <kr7x@comcast.net>
To: <towertalk@contesting.com>
Sent: Monday, August 11, 2003 10:05 PM
Subject: [TowerTalk] antenna element vibration damping  how
> 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 nontapered 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.
>
>
>
>
>
>
>
>
> _______________________________________________
>
> See: http://www.mscomputer.com for "Self Supporting Towers", "Wireless
Weather Stations", and lot's more. Call Toll Free, 18003339041 with any
questions and ask for Sherman, W2FLA.
>
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>
