# Modal Analysis: Interpreting ANSYS Results

1. Dec 30, 2013

I have been easing my way into ANSYS and doing some modal analyses. The component I am modeling is a body of revolution with N=15 slots in it. The cross section looks much like the one in post #1 of this thread.

I started out by modeling the full 360° ring and requested the first 6 Modes shapes. The results were fairly easy to interpret: Here are the first 6 mode shapes and their corresponding frequencies.

Then, I decided to try to make use of symmetry: since a 360°/15 sector repeats 15 times, I used a "cyclic symmetry" model with this sector. So I again requested the first 6 mode shapes. The results are a little confusing to me now. They are instead reported in terms of mode shapes, harmonic indices, and corresponding frequencies (see screenshot below). There are 66 such entries and I am a little befuddled as to how I can relate them to the results I got from the full 360° model (which I have since deleted).

I am reading through Chapter 6 of the ANSYS Mechanical APDL Advanced Analysis Guide (page 157 of this pdf) but it is not quite clicking.

It says that for a nodal diameter d, and model with N sectors (in this case 15), and harmonic index k, we have:

d = m*N ± k ​

I understand (I think) that "nodal diameters" are essentially the same as mode shapes. The first mode shape has 1 node and 0 nodal diameters (at least for a circular membrane fixed at its perimeter).

But looking at my results, I am still not sure of how to get from "here to there." "Here" being a solution in terms of mode shapes, k's, and frequencies. And "there" being a solution in terms of Mode shapes and frequencies like for the 360 ring.

Any guidance is much appreciated.

Thanks,
KC

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2. Dec 31, 2013

### AlephZero

Something is wrong there. My calculator says 360/15 = 24, not 15.

Maybe that is just a typo, or maybe it explains why you can't understand how the sector model and the full model relate to each other!

Try this, to understand what's going on:

Take your sector model, and make a full model by rotating the sector around the axis.

Run the full model and ask for a lot of modes, say 50. That may take a while to run, but you only have to do it once.

Then, run your sector model, and with luck there should be an option to request the modes in a given frequency range (i.e the range that covers all the modes you got from the full model) for each harmonic index, not the same number of modes for each index.

From the PDF you linked, apparently there is a post processing option to "expand" the mode shapes from the sector model to the full structure. You should be able to see what's going on by comparing the full and sector models.

Note that most of the modes occur in pairs, which have the "same" mode shape but rotated around by an angle. The amount of rotation is arbitrary, so it will probably be different in the sector and full models, but you should still be able to match up the modes visually.

If you ran your full model for 6 modes, you probably got the the lowest frequencies of 504, 504, 506, 506, 623, 623, which isn't really enough modes to see what is happening

3. Dec 31, 2013

### AlephZero

One other comment: if you want to see the simplest possible "nodal diameters" (literally, radial lines), do this exercise on an axisymmetric structure - e.g. a circular disk (with no holes, etc!) or a circular ring.

4. Dec 31, 2013

Hi Aleph!

You are correct: 360/15=24. Perhaps it was bad wording, but that is what I was trying to convey (i.e. fifteen 24 degree sectors).

I have seen the circular membrane articles and that's how I have inferred that they are similar to Mode shapes...but they are not quite the same. However, I am still unclear as to what the nodal diameter equation above has to do with the results that are reported by ANSYS in the cyclic model. It doesn't report ND's, it reports harmonic indices.

I am going to run another full solution right now as you suggested with many mode shapes.

The PDF id help for MAPDL. I am using Workbench and I am quite a novice to both. I will try to find the equivalent commands.

I should be back in a half hour with new ANSYS results! Happy New Year!

5. Dec 31, 2013

### AlephZero

The idea of nodal diameters is easiest to understand if the model is a continuous piece of material (i.e. not a set of blades with gaps in between them).

If you plot the displacements normal to the surface of the model, you literally see radial lines (well, approximately radial, they may be curved) running right across the disk through the center, where the displacement is 0. Each line is a nodal diameter, and there can be 0, 1, 2, 3, .... of them.

For a model that is approximately a circular disk, you can also get approxmiately circular lines where the displacement is zero. it can be useful to "name" the modes by the number of diameters, and the number of circles. Where I work we often call the modes with no nodal circles the "first family" of modes, those with one circle the "second family", etc, but I don't know now widely used that naming system is.

If you plot the magnitude of the displacements, not the component normal to the surface, the diameters may not be so clear, because the motion in the circumferential direction actually has its maximum value at those positions.

For a cyclic structure with "holes" in it, it can be harder to identify what is happening, because the notional position of some nodal diameters may be within the "holes" so there is nothing to plot. The more nodal diameters relative to the number of "holes", the worse this gets.

Finally, the "harmonic index" is not exactly the same as the number of nodal diameters. If your model has say 10 sectors, the modes with harmonic number 2 say may have 2, 12, 22, 32 ... nodal diameters. This may well show up with harmonic number 0, where you may apparently have one nodal diameter in each sector, instead of zero nodal diameters. Of course modes with high numbers of nodal diameters usually also have high frequencies and may not be very interesting for that reason.

6. Dec 31, 2013

Hi again Aleph,

Thanks for that. I think that I am on board with you when it comes to what the nodal diameters are, but there is still my lingering question (which I apologize if you have already answered, I am just not seeing it):

Why doesn't ANSYS give me the same results for the sector model as for the full ring? It's the same thing ... I have to imagine that it is giving me the same results, but I am just not reading them correctly.

See results from full ring and sector below. (The last table has the sector results ranked by increasing frequency).

Thanks again,
KC

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7. Jan 1, 2014

Oooo......I went ahead and refined the mesh on both models as the default was very coarse. Now I think I see what is going on ... I think. You can see in screenshot below that when I take the sector results and rank them according to frequency, they match up within ~1% to those from the full model (for the first 30 modes or so). So it seems like the results from the full ring are simply all modes across all harmonic indices but they are reported in order of increasing frequency instead of increasing harmonic index.

Sound correct? I think it makes sense the way ANSYS is reporting it now.

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8. Jan 1, 2014

### AlephZero

That's right.

If you make a sector mesh so the nodes (grid points) on the two boundaries match up exactly (i.e. the program doesn't need to do any "magic" interpolation procedures at the boundaries), and then make a full model by rotating the sector mesh around the axis, you should get exactly the same frequencies, however coarse or fine the mesh is.

In real life, often you are only interested in the modes for a small number of harmonic indices, so excluding modes from the other indices (by not calculating them) can save a lot of human post processing time, as well as reducing the computer solution time.

9. Jan 1, 2014

Great. This makes sense. Interestingly, accepting the coarse default mesh on both models did not make this evident. This Workbench and it is using a "free" meshing method which might be contributing to the discrepancy since there is nothing guaranteeing an identical mesh on both. By overly refining the mesh I was able to alleviate most of the error between the two models.

Thanks again AlephZero. BTW, what is your experience with FEA/CFD? Do you use ANSYS for work? Or some other program? Do you use it for turbomachinery?

10. Jan 1, 2014

### AlephZero

The commercial cores I's using at present are mainly Nastran, plus a bit of Abaqus and LS-Dyna3D. I've used several other commercial FE codes in the past, but not Ansys.

For many applications (including cyclic symmetry) we use codes written in-house - some of which I helped to write. As a company, we have a long history of wanting to do stuff that isn't commercial software yet - and the effort needed to verify that "leading edge" commercial software actually does what it says in the users guide can be very non-trivial!

My main involvement in CFD is when the aerodynamic data that CFD gurus give us to use for structural analysis doesn't make any sense - which can be an "interesting learning experience"

Ih the past I spent a few years working on finite element modeling for heat transfer problems (again, a mix of commercial software and in house) but I'm not involved much with that any more.

11. Jan 11, 2014