natural frequency of a massless beam with a point mass

[bogor04]

Hi there
How to calculate natural frequency of a massless cantilever beam with a point mass? The point mass located from the fixed end to the free end (from x=0 to x=L). I know the formula for the point mass at the end (x=L) from shock and vibration hand book by Harris. But It would be easy to have the the formula to calculate all the natural frequencies for example 100 points between x=0 and x=L.
Many thanks in advance

 

[ivymike]

um, if the beam is massless, then isn't the answer the same as what you'd get if you just used a shorter beam in the formula you have?

 

[IRstuff]

Is this for school?

TTFN

 

[tomirvine]

As a reminder, I have posted a paper with formulas for beam natural frequencies at:

http://www.vibrationdata.com/tutorials2/beam.pdf

Tom Irvine

http://www.vibrationdata.com

 

[tomirvine]

If you have other configuration than those covered in my paper, then you need to use the Rayleigh, Rayleigh-Ritz, or finite element method.

I have posted additional papers on these topics at:

http://www.vibrationdata.com/StructuralFE.htm

http://www.vibrationdata.com/StructuralDC.htm

Tom Irvine

 

[electricpete]

I agree with ivymike. Redefine L to be the varying distance between the point of attachment and the point mass. Pretend that is how long the beam is... ignore any length beyond the point mass because it doesn't change anything.

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