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## [TowerTalk] antenna element vibration damping - how

 To: [TowerTalk] antenna element vibration damping - how k4oj@tampabay.rr.com (Jim White, K4OJ) Mon Aug 11 22:56:01 2003
 ```Thanks, Hank! That was interesting. ..more importantly, now I remember why I dropped out of engineering school! :-) Jim, K4OJ kr7x@comcast.net wrote: > 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. > > > > > > > > > _______________________________________________ > > See: http://www.mscomputer.com for "Self Supporting Towers", "Wireless > Weather Stations", and lot's more. Call Toll Free, 1-800-333-9041 with any > questions and ask for Sherman, W2FLA. > > _______________________________________________ > TowerTalk mailing list > TowerTalk@contesting.com > http://lists.contesting.com/mailman/listinfo/towertalk > ```
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