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
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
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
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
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
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
RE: Natural Frequency of a pinned-pinned beam
RE: Natural Frequency of a pinned-pinned beam
RE: Natural Frequency of a pinned-pinned 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
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.