MAX DEFLECTION ALLOWED IN A MACHINE IN MODAL ANALYSIS. 2

[Sarikahirpara]

HELLO,

I am performing modal analysis to find natural frequency and their deflection. What does these deflection values at different modes indicates? Also If modal testing is done on a machine constraining the base of the machine. How much deflection is allowed in such case?

 

[FEA way]

Those values are normalized and thus not physical. They are relative so they only show you which region will deflect/stress more. You would have to run a frequency response (harmonic) analysis with actual load to get real displacements.

 

[Sarikahirpara]

@FEA way, Thank you for your reply. I understood it but then how do we interpret the result then, if we don't know the actual values of stress and deflection and then what is the use of modal analysis then? what can we interpret with frequency?

 

[FEA way]

Modal analysis has many uses but the main one is to obtain the natural frequencies of the model that can be compared with operating frequencies to avoid resonance. Mode shapes are deformation patterns associated with those frequencies and contour plots of displacements or stresses can show you critical regions. The first mode shape represents the most flexible orientation of the structure. Other uses of modal simulations include dynamic analyses based on model superposition and checking connections and boundary conditions in the model - any unconstrained parts will fly away and rigid body modes will be shown as mode shapes with eigenfrequencies close to 0 Hz.

 

[ThomasH]

The deflection from a natural frequency analysis can be a value that gives you the modal mass.

If the value is normalized for max deflection the peak value is probably 1.0. But it can also be based on mass. If you then have a peak deflection 0.01, the modal mass can be 1 / 0.01^2 = 10000 kg.

I assume that this can be software dependent but that also means that you need to know your software

 

[Sarikahirpara]

@FEA WAY AND @THOMASH, THANK YOU BOTH FOR YOUR RESPONSE. CAN YOU PLEASE SUGGEST SOME TEXT TO UNDERSTAND MODAL ANALYSIS AND ITS USE FOR FURTHER HARMONIC RESPONSE ANALYSIS. I AM WORKING ON A MACHINE ASSEMBLY AND I AM TRYING TO FIND OUT THE VIBRATIONS AND STRESSES DURING THE OPERATIONS USING ANSYS SOFTWARE.

 

[FEA way]

Documentation of your FEA software is usually the best source of information but there are some practical books too. I would especially recommend those written by D. Madier and V. Adams but also some NAFEMS publications.

 

[3DDave]

Modal analysis is generally used to determine the frequencies the item is sensitive to amplifying. The deflection is related to the amount of time the item is subject to the frequency and how much damping there is.

Look at the cases of the Millennium Bridge or the Tacoma Narrows Bridge for examples where the modal analysis would predict the kind of deflections but depending on the external forces the deflections were either unnoticed or catastrophic.

 

[GregLocock]

Tacoma is a bad example as it was an aerolastic issue, not a structural resonance that would be found in a modal.

Cheers

Greg Locock


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[ThomasH]

@Sarikahirpara

Start with something simple, like a simply supported beam. Calculate the natural frequencies, with Ansys and by hand. Don't skip "by hand" because you need to know that your model is correct.

Then you apply a frequency dependamt load on the beam and calculate the response. You should see peak response at the natural frequency och frequencies.

The advantage with this is that you can check it "by hand". That is not always possible for "real" models. As for suggesting a text regarding modal analysis, I don't have a specific preference. There are several good ones.

 

[3DDave]

Greg,

I expect the Tacoma Narrows bridge mode that it was experiencing at failure would be found. That no one previous to construction identified the source of energy for that is a separate issue. As far as the structure is concerned it doesn't matter if it is the deflection in a wind or someone pushing on the structure - force is applied and the deflection is amplified at certain frequencies.

 

[GregLocock]

Hmm.

https://www.physics.utoronto.ca/~poppitz/poppitz/PHY1530_files/dangreenpaper.pdf

Money quote "As Billah and
Scanlan complained 13 years ago,2 physics textbooks have
called this large scale oscillation an example of a resonance,
when it was clearly not. Already in the report by Ammann,
von Karmen, and Woodruff3 to the Federal Works Agency
that investigated the collapse
a report issued only four
months after the collapse, it was recognized that the collapse
was due to an example of negative damping, just as in the
musical instruments we have mentioned. This conclusion
was based on wind tunnel experiments carried out at the
California Institute of Technology, which clearly showed the
exponential growth of the oscillations."

The period of the oscillations is due to the frequency of vortex shedding at that windspeed, the pressure variation of which was enough to twist the airfoil.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[JoshPlumSE]

Greg -

The wind issue (which was some kind of vortex shedding related to the wind hitting those girders) was NOT an issue of the wind gusts blowing at the natural frequency of the bridge. That is correct, it was the "vortex shedding" that occurred at a frequencies that excited one of the bridge's natural frequency. I think that paper is getting into a lot of esoteric with its semantics.

This type of issue isn't really discussed much in Structural Engineering of buildings. But, is very common with Aerospace structures. What did we call it there. I think the term was "flutter" where an air flow issue (like vortex shedding) causes resonance with the wing or tail structure. Now, this doesn't necessarily mean that the vortex shedding occurred at the natural frequency of the structure. But, it may have been some multiple of the frequency, so that every 2nd, 3rd or 4th cycle, the vortex sheds leading to progressive amplification.

That being said, the mode of vibration that was excited by the vortex shedding should be easily apparent in a modal analysis of the structure.... the key is that no one knows whether that will be a problem until you know the frequency at which the vortex sheds. And, how that impulse can interact with the fundamental modes of the building.

Reasonably tricky. But, in the end, it is still technically correct to say that the Tacoma Narrows Bridge failed due to a resonance between wind effects and one of the torsional modes of the bridge.