Natural Frequency of a pinned-pinned beam 1

[ForrestLowell]

Somewhere in my math i am a factor of 10 off for my natural frequency for a beam. What is the equation for the natural frequency of a pinned-pinned beam. Thanks

 

[JAE]

OK - from my dynamics book - for a simple span

L = span
m - mass of beam
EI - EI of beam
N = node number (1, 2, 3, )
[ω] = natural frequency
[Π] = Pi

[ω] = (N²[Π]² / L²) x [√](EI / m)

 

[GregLocock]

Quick check use 1/2/pi*sqrt(k/m) where k is the stiffness of the centre of the beam and m is say 2/3 the total mass of the beam. It won't be right, but it'll be close.

If it is uniform pinned pinned then f1=1/2/pi*(96*E*I/M/L^3) where M is total mass of beam.

Cheers

Greg Locock

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

 

[271828]

THe easiest form to remember is:

Calculate the deflection at midspan of the beam due to the uniform load corresponding to the uniform mass. Call this Delta.

Then fn = 0.18*sqrt(g/Delta)

This gives fn in Hz. Using USC units, g = 386 in./sec.^2 and Delta is in in.

THis equations actually works pretty well for all kinds of situations. For example, you can check the lateral period of a building using it and get pretty close to what your computer program should compute.

 

[GregLocock]

m in JAE's formula is mass per unit length, I think

Cheers

Greg Locock

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

 

[JStephen]

In JAE's formula, the pi^2 term is about 10.

Check that mass vs weight is not confused. In English units, check if a g-c term is required for lbm/ lbf conversion. Foot (length) vs. inches (E, I) could be another source of problems.

 

[miecz]

The [ω] calculated by JAE's formula has the units radians/sec. To get cycles per second, you need to divide [ω] by 2[π]. So the natural frequency in cycles per second is [ƒ]=(N[²][π]/2)[√](EI/m)

 

[JAE]

miecz, JStephen, and GregLocock - thanks for the clarifications!

 

[271828]

And I rest my case that fn = 0.18*sqrt(g/Delta) is the easy way to remember this, LOLOLOL!!! Forget that form from the vibrations book--I did about 2 minutes after I learned it.

 

[GregLocock]

Yeah yeah, we get it. I once used 'your' formula to predict the frequency of a troublesome bending mode on a rather badly made car, it was right to within 10% much to the irritation of the other engineer.

Cheers

Greg Locock

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

 

[271828]

I wish I could take credit for it, LOL, but I can't. The AISC Design Guide 11 on Floor Vibrations uses it. It's an exact solution for a simply supported beam with uniform mass and uniform EI.

In some ways, I'm conflicted about its use because it misleads folks who aren't vibe specialists.

An example:

I was giving a seminar on floor vibrations several years ago and calculated fn for a composite beam (steel beam with concrete slab) and someone asked the question "What loads go into w for calculating Delta? Precomposite DL, that plus superimposed DL, etc.?" Representing the mass as a "load" really threw him off.

He never would've gotten confused if we were using the form with "m" instead.