FEM - Stability Analysis

@jmateo,

I made a copy of your most recent project and made some small changes to fix the error. You can see it here.

The first mode natural frequency is now 7.6 Hz. It is slightly higher than I expected because the outer leg braces have been made larger.

It is only necessary to hit the structure once. If you put your hand on the structure you will feel it vibrate for a brief period of time. If you instrument the structure (with accelerators, displacement transducers, strain gauges etc) you will see a vibration signal. This vibration can be broken down into its constituents. All of the frequency modes will be present but in varying amplitudes. Typically the first mode is largest and subsequent modes get progressively smaller. This is called free vibration. A mass on a spring is an example of a free vibration.

What you are seeing in the SDOF video is an example of forced vibration. The shaker table forces the structure to vibrate at a given frequency. It starts slow and progressively gets faster. When the rate of forced vibration matches the natural frequency of the structure the structure will resonate.

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Thanks a lot for the explanations and also for the fix in the project

Then we have a first mode natural frequency of 7.6 Hz which seems to be fine.

However, I will need to make a report including the sources in which I have been based. I have not found any document in which relation between frequency and stability is explained. I understand you are based in your own experience and I do not doubt about it, but do you know where can I find further information so I can contrast the results with some written sources?

Thank you

Sorry I don’t know of any references.

Please keep in mind that the first mode frequency is not a measure of the structure’s stability (i.e. resistance to buckling or over turning). It is a measure of the structure’s flexibility. You can use the fact that the first mode is the structure’s most flexible mode to make some assessment about whether the structure is adequately braced in this direction.

In your application there appears to be sufficient bracing in the first mode direction. If you need to verify this then you will need to perform a non-linear analysis. A non-linear analysis will tell you what horizontal force is required to push the ring beam over to the point where is becomes unstable (if at all). I don’t believe this is necessary, I’m only mentioning it so that you understand what could be done if it was required.

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Yes, I understand frequency analysis in only about determinating the most flexible “direction” or vibration mode

About the non-linear analysis, I do not think it is necessary neither. Just because there will not be any horizontal force pushing the ring.

However, I actually would like to know how to do it. I already made some non linear analysis, but not considering any horizontal force, only the lead weight. That returned me the same results as linear analysis. So for verifying the pushing horizontal force needed I would need to play with horizontal loads right?

Thank you for everything. Already been so helpful

For a non-linear analysis you will need to make the following changes to your current half model linear project:

  1. Change to a nonlinear simulation type with
    Simulation > Properties > Nonlinear analysis > True
  2. Enable geometric nonlinear behavior with
    Model > Geometric behavior > nonlinear
  3. Enable nonlinear material behaviour with
    Model > Materials > Steel > Material behavior > Plastic
  4. Add a table to define the materials stress-stain curve after yield. You can find examples here
  5. Add a time dependent load e.g. 10000*t
    Model > Boundary Conditions > Loads
  6. Enable line search to give the solver a better chance to find a solution in the post buckling region.
    Numerical > Line Search > True

I may have forgotten a few steps but that’s probably enough to get you started.

Give it a go. If you have any trouble please let me know and I will see if I can help.

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Of course…I will try during the week

And I will give the results here. Thanks!