natural frequency of a steel plate

huangyhg

natural frequency of a steel plate
here is my problem:  i working on a pump station containing 3 large pumps.  
-a shaft extends 17 feet below each pump through a bearing which is mounted in the middle of a 3 ft x 3ft x 3/4" steel plate.  
-the pump shaft operates at 1750 rpm.  
the pump manufacturer wants me to determine the natural frequency of the steel plate to ensure that resonance does not occur and result in undue vibration in the plate.  any assistance would be greatly appreciated as i don't have a copy of roark's book in my office.
as you pose the question it seems the excitation should be mainly from eccentricity of the shafts acting on the plane of the plate.
anyway, you need to model the plate plus support in a program able to do dynamic analysis and extract the first natural modes of vibration. place the holes in the plate, just in case. and then give the results to the manufacturer., risa 3d, etabs, sap 2000 and many more programs able to do dynamical analyses may provide what you want.

the natural frequency of the plate will heavily depend on the masses that are connected to it (the bearing and what else?). also it will depend on the vibration mode: the vertical movement could be unimportant, if the bearing allows for that (and if the bearing doesn't, then there is an additional constraint on the plate strongly influencing the frequency). you could be worrying about the flexural vibration of the shaft, but i guess this wouldn't matter for the plate, as the bearing will allow freely for that rotation.
so you should better specify your problem to get closer advice.
prex
if you can work out a mass for the stuff in the middle of the plate, and add the mass of 1/6 of the plate, and work out the stiffness of the plate, then you will be as close as an uncorrelated fea model. f=1/2/pi*root(k/m)
  
cheers
greg locock
installing isolation mounts between the motors and the plates is out of the question ?