I have used the Ansys workbench to carry the modal analysis of one motor stator and under the free modal analysis, the first 6 mode frequency are all zero, it is ok because of the first 6 mode does not consider the deformation.

However why the adjacent two mode frequency are almost the same, it is queer.(Under the free modal analysis.)

The following the is free modal analysis result:

1.  0.
2.  0.
3.  1.556e-003
4.  4.0131e-003
5.  5.1746e-003
6.  6.3977e-003
7.  875.86
8.  876.46
9.  1662.2
10. 1663.2
11. 2309.2
12. 2311.
13. 3541.8
14. 3542.9
15. 4058.6
16. 4062.2
17. 5459.2
18. 5461.6
19. 5844.8
20. 5852.9

The first non-zero modal is as this: enter image description here

  • $\begingroup$ Did you use a symmetry boundary condition in your analysis? If you use symmetry and do not force the harmonic index to 0, you will see results very similar to this. $\endgroup$
    – Tristan C.
    Commented Mar 29, 2023 at 9:29
  • $\begingroup$ @TristanC. I did not use this condition, I use the whole motor stator model and without any constrain, and set the whole stator as one part. $\endgroup$
    – fhrl
    Commented Mar 29, 2023 at 10:15
  • $\begingroup$ @AJN, I have submitted the topology of the stator, it is more than symmetric, so why the result is 2 plets rather than 18 plets? $\endgroup$
    – fhrl
    Commented Mar 29, 2023 at 12:27
  • $\begingroup$ Is your question "why are the mode pairs not exactly the same frequency and only approximately the same"? $\endgroup$
    – AJN
    Commented Mar 29, 2023 at 14:19
  • 1
    $\begingroup$ @AJN is on the right track. Heavily symmetrical systems have groups of very similar modes that differ by one 'feature'. They can't be at the same frequency as they would act as harmonic dampers, that is , the mode would split into two frequencies, differing by one feature. I suggest you do some hand calculations with 3 dof systems to get an idea. $\endgroup$ Commented Mar 29, 2023 at 20:50

1 Answer 1


If a structure has 2 eigenmodes with the same eigenfrequency, then every linear combination of those modes is also an eigenmode with that same frequency.

Suppose one mode is east-west bulging and the other is north-south bulging, then northeast-southwest bulging is also a mode, and so is every other compass angle.

The solver will jshow just 2 modes out of those infinite options. Typically 2 orthogonal ones. It could have shown another set of 2 modes, as long as together they "span" the space of all modes with that freqeuncy.

FEM solvers often show slightly different frequncies even for a perfectly symmetric shape, presumably because the meshing is not quite symmetric or other numerical effects.

You mention having 18 teeth, and that you might expect to see 18 similar modes. If you ask for more modes, I bet such sets if modes will pop at higher freqeuncies. This set of 2 modes is just from the ring itself.


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