natural frequency of a pinned-pinned beam

huangyhg

natural frequency of a pinned-pinned beam
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
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)

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
the easiest form to re  
m in jae's formula is mass per unit length, i think
cheers
greg locock
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.
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 ?=(n2π/2)√(ei/m)
miecz, jstephen, and greglocock - thanks for the clarifications!
and i rest my case that fn = 0.18*sqrt(g/delta) is the easy way to re  
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
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.