long lead screws

A recent email about a 1/2"-13 12' long leadscrew caught my attention. I
modeled it in SolidWorks, imported into Algor (FEA program) and analyzed 1 g
case and the lowest 5 modes of vibrations.
Results are as follows:
for a .407" diameter (minor diameter 1/2-13) CRS rod, 12 feet long,
rigid support at one end and sliding fit at other end (axial motion allowed)
deflection 1 g is .512 inch at center
1st modal frequency is 4 Hz
2nd 5 Hz
3rd 11.2 Hz
4th 13.8 Hz
5th 22 Hz

Even adding a few supports won't help much, as there are two nodes between
the ends for the 5th mode.

I suppose you could tension the screw, like a big guitar string. That might
be fun to analyze too.

I understand this is a rotating nut design, so the screw won't be twisting.
But the force applied into the screw by the nut will make it bounce around
quite a bit. Sorry I can't analyze what happens with axial impulse, yet.

And when the nut is at one end of the screw it will sag by .5 inch.

Let us know how the long screw works.

Elliot