Which formula for Natural Frequency?

[wchowe]

I have been designing a box. This box will see vibration and I want to make sure the welds hold up. I went to look at the panels as rectangular plates and found that there are several formulas I can use depending on which book I open. They do not yield the same answer, so which do I put my faith in?
Rothbart's Mech Design (pg 6-62), gives
Fn=Cn x h/a^2 x 10^4 x Km
Mark's CD-rom gives
Fmn=(pi/2)x(gD/hd)^.5 x(m^2/a^2 + n^2/b^2)
Mark's hard copy (eq3.4.124 on pg 3-74) gives
Fmn=((pi^2)x((m/a)^2 + (n/b)^2)x(D/m)^.5)/2pi
finally can't you argue that a plate is a rectangular beam and use?
fn=(1/2pi)x((3EI/L^3)/(w/g))^.5
Above I use ^to raise to a power.

 

[tomirvine]

Well, here are some suggestions.

1. Make sure the formula is appropriate for your boundary conditions.

2. Determine whether the formula is for a square or rectangular plate.

3. Decide whether you are interested in the fundamental mode only or in several modes.

In addition, I recommend that you use a plate formula rather than a beam formula. The comparsion of a plate to a beam is only valid for a few special cases.

Sincerely, Tom Irvine

http://www.vibrationdata.com