Frequency response mode of vibration

[roldy]

I'm working on an analysis problem using Abaqus. I would like to compare my results with an exact equation. My problem is modeled as a simply supported beam with a lumped mass at the end. The equation that I'm using for the exact solution is as follows:

k=3EI/L³
ω_n=$\sqrt{k/(M + 0.23m)}$

How do I incorporate the mode number to find what the exact solution is at say mode 2 or 3?

 

[OldEngr63]

That "exact" solution is probably only an analytic approximation for the first mode. Run the numbers and see which mode it compares with most favorably. I would bet it will be the first mode.

 

[roldy]

The exact solution does compare most favorably with the first mode results from Abaqus.

 

[OldEngr63]

Don't hold your breath on that being an exact solution. It is most likely obtained from a Rayleigh approximation.