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 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.
>
>
>
>
>
>
>
>
> _______________________________________________
>
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>
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