Natural Frequency Equation 2

[jaydigs]

I'm analyzing a flag pole for wind loads and wanted to see what the critical wind speed was for vortex shedding. I'm using Vc = fd/s where f=natural freq, d=diameter of pole, and s=Strouhal number. I'm assuming the pole could be modeled as a cantilevered beam with fixed end? Also, I've found a few equations for f, all of which differ slightly. Can anyone tell me if the following sounds correct:

w (or f) = (1.875)^2 sqrt[EI/mL^4]

Since the mass is just the mass of the pole can you just use that? Most of the examples I've seen have an object serving as the mass, being acted by springs, and dampers, etc...

Thanks in advance!

 

[desertfox]

Hi jaydigs

Look at this website and use the first formula case. the formula looks slightly different but you could compare answers,

http://www.roymech.co.uk/Useful_Tables/Vibrations/Natural_Vibrations.html

desertfox

 

[jaydigs]

Thanks for the link....that's a great site btw!

 

[desertfox]

hi jaydigs

your welcome

desertfox

 

[jaydigs]

I wonder how accurate it is to consider a flagpole as a cantilevered beam? It sort of sounds reasonable because it is fixed on on end and at 90deg to the ground, but, it isn't leaning out from a structure, and in a perfect world the only load is compressive, from it's own weight, unlike the true cantilevered beam which has to support an overhung load.

 

[desertfox]

Hi jaydigs

Good point, however I assume your just after the natural frequency of the beam, if thats things going to vibrate then its going to do so because of wind or some other tranverse load, in that circumstance (wind loading) it would be loaded just like a beam.

desertfox

 

[jaydigs]

Well I reviewed about 5 different equations and kept getting 1 of 2 answers. Then it hit me, some equations were using rad/sec and others were using Hz (Duh!) That explains why I got around 70, and around 11, I was off by a factor of 2Pi. I ended up getting a critical speed of 4.3 m/s. Does this mean that at 4.3 m/s my pole is going to vibrate at it's natural freq due to vortex shedding? The wind blows on average around 5 m/s in my area, and since we already have one of these poles mounted and haven't had any issues I wonder if I'm not missing something here?

 

[desertfox]

Hi jaydigs

have a look at this report on lamp poles it also refers to some standards which might be relevant:-

http://www.utility-security.com/por... Repository/article-HarmonicResonance-083.pdf

desertfox

 

[GregLocock]

Reasons why you may not have a problem -

foundation is soft so your calculated frequency is wrong.

Pole is stiff enough that the aero forces are not significant.

pole material is damped.

flag damps pole motion.

flag halyards act as a vortex suppressor (bit of a long shot)

luck.







Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.