Simple natural frequency calculation 3

[bgoo]

It's been a while for me to do a vib calculation. I was trying to determine the resonance frequency of the structure. The structure is basically a beam hanging vertically down from the ceiling. The lower end of the beam is attached with a mass. I found a simple equation from Steinberg, natural frequency (fn) = [1/(2 pi)]* sqrt(K/m) or alternatively fn = [1/(2 pi)]* sqrt(g/deflection)

My question is whether this equation is applicable to any mounting orientation of the beam.

Note: Steinberg has an example of using this equation to calculate the natural frequency of the beam which is mounted horizontally. For my case where the beam is mounted vertically, would this equation still applicable? Also how should the deflection be calculated if the equation can be used for vertical orientation.

Thanks for any help.

 

[ivymike]

If I read your equation right, it's using the static deflection of the beam due to gravity to estimate the stiffness of the beam. If you have a relatively stiff beam, that may be hard to measure. Other than that, the natural frequency would remain essentially unchanged regardless of orientation (assuming stiffness/mass is such that the "pendulum" behavior is not significant).

 

[bgoo]

I should add...I want to determine the resonance frequency of the vertically mounted beam when it is excited horizontally.

Thanks

 

[bgoo]

Ivymike,

I think it make sense. The deflection was only used to determine the stiffness, which is what the fn depends on. It sounds like if I know the stiffness and the mass of the system, I would know the fn. This is independent of orientation...or g field.

Thanks a lot.

 

[GregLocock]

I agree with the above. One way to think about the effect of g is that in a linear passive system it is impossible to change the frequency of a signal. g is DC, so can only affect the 0 Hz response of the system.

g appears in your second equation as a sort of scaling factor.

I suppose it is obvious that for that to work you have to know the beam deflection when horizontal?

Cheers

Greg Locock

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

 

[WCFoiles]

If the beam is hanging from the ceiling one has to determine if the beam behaves basically as a rigid body or a flexible body. The support stiffness at ceiling may have a large effect.

Do you expect the motion to be pivoting about the ceiling? If so this sounds like a pendulum with a stiffness at the support.

If it is cantelevered and the beam acts flexibly the standard beam equations should work.

It could be a combination of the two, depending upon the circumstances.

Regards,

Bill

 

[tomirvine]

I have posted a paper with formulas for beam natural frequencies at:

http://www.vibrationdata.com/tutorials2/beam.pdf

Tom Irvine

http://www.vibrationdata.com

 

[bgoo]

WCFoiles,

It is what I am going to do next, determine the stiffness of the mounting bracket (which support the cylinder to the ceiling).

Thanks.