Finding natural frequency of a steel flat

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is there a straight formula for finding one of the natural (preferably fundamental) frequency of a steel flat with dimension say, L=1000 mm, B=100 mm and Thickness T=10 mm ? The flat is fixed at both ends by bolts and two weights of equal magnitude are suspended at 1/4 and 3/4 (i.e. 250 mm and 750 mm) of the flat.

I am yet to find understandable solution to the above problem on the net; so I had to post it to this forum. Please help, I am lost.
 

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SteamKing
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is there a straight formula for finding one of the natural (preferably fundamental) frequency of a steel flat with dimension say, L=1000 mm, B=100 mm and Thickness T=10 mm ? The flat is fixed at both ends by bolts and two weights of equal magnitude are suspended at 1/4 and 3/4 (i.e. 250 mm and 750 mm) of the flat.

I am yet to find understandable solution to the above problem on the net; so I had to post it to this forum. Please help, I am lost.
This article gives an engineering approach to estimating the fundamental frequency of a shaft under various end conditions and loadings:

http://www.impactap.com/joe/Chapter%207.pdf [Broken]

Dunkerley's method is outlined in this article:

http://www.freestudy.co.uk/dynamics/free vibrations.pdf

Basically, you can calculate the natural frequency of the beam under just its own weight, and under the deflection due to each point load, separately, and then find the overall frequency by using Dunkerley's formula. This formula tends to underestimate the actual value of the frequency. There are more complicated approaches to finding the natural frequency, but this should give a close approximation.
 
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