Issues with modal analysis

General Questions
1

Good morning,

I am trying to perform a modal analysis of a simply supported beam, like this tutorial: PrePoMax (CalculiX FEA) - Tutorial 3 - Modal analysis of a beam - YouTube

The first analytical solution of the natural frequency is 208.9 Hz;
In PrePoMax the first three are: 167 Hz, 187 Hz and 433 Hz.

Is this issue due to the analytycal solution limitations?

I tried with a cantilever beam, with the proper constant values. I got the same ‘‘divergent’’ results.

2

It should be closer to the analytical solution if it’s just a beam. Can you share the files and analytical solutions ? There might be a mistake somewhere.

3

I shared the cantilever beam with its analytical solution, too.
3 elementi

4

Notice that this first mode shape is in the direction perpendicular to the normal bending of the beam. The analytical solution actually applies to the second mode shape in this case and thus the discrepancy is smaller. When I was preparing that tutorial, I tried different cases and a long simply-supported beam with a square section turned out to be the best for comparison with an analytical solution.

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5

Thank you. If I wanted to know the analytical solution of the first torsion mode, around Z_axis, how could be the formula?

6

Check the book “Formulas for Natural Frequency and Mode Shape” by R.D. Blevins. You should find all the necessary equations there.

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