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Natural Frequency of a pinned-pinned beam

Natural Frequency of a pinned-pinned beam

Natural Frequency of a pinned-pinned beam

(OP)
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

RE: Natural Frequency of a pinned-pinned beam

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 = (N2Π2 / L2) x √(EI / m)

 

RE: Natural Frequency of a pinned-pinned beam

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

SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

RE: Natural Frequency of a pinned-pinned beam

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.

RE: Natural Frequency of a pinned-pinned beam

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

Cheers

Greg Locock

SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

RE: Natural Frequency of a pinned-pinned beam

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.

RE: Natural Frequency of a pinned-pinned beam

The ω calculated by JAE's formula has the units radians/sec. To get cycles per second, you need to divide ω by 2π.  So the natural frequency in cycles per second is ƒ=(N²π/2)√(EI/m)

RE: Natural Frequency of a pinned-pinned beam

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

RE: Natural Frequency of a pinned-pinned beam

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.

RE: Natural Frequency of a pinned-pinned beam

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

SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

RE: Natural Frequency of a pinned-pinned beam

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.

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