Frequency response mode of vibration

1. Mar 19, 2012

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
ωn=$\sqrt{k/(M + 0.23m)}$

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

2. Mar 19, 2012

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.

3. Mar 19, 2012

roldy

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

4. Mar 19, 2012

OldEngr63

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