free free dynamics chech

[engroma]

I am carrying out a free free dynamic check to an assembly model to verify that it acts as a rigid model, honestly I don't have clear how to interpret my output results.
I mean the first 6 modes have got a frequenty of 1E-4 magnitude or lower, but the shape of the 6 animated models don't recall me the 6 modes of a beam (example).
The others modes (the 7th the 8th etc) have got values higher that 1 Hz and I thought that a rigid body without contraints shouldn't have futher modes.
Someone could clarify the subject or advice me some papers.

Thanks

Regards

Engroma

 

[GBor]

The first 6 modes should be theoretically infinite translation along each of the global axes and three virtually infinite rotations about the three global axes. They will not look like the bending modes that you probably recall from school. The software that you are using will likely have some error checking that limits the deflection and provides some answer so that your computer doesn't lock up in a never-ending convergence loop.

The 7th, 8th, etc. modes are probably meaningless for frequency, but may start to look like what you would expect from the bending mode shapes (a jumprope about each of the three major axes followed by two max/mins, etc.)

As for a text...do a google search and you will probably get a google of hits.



Garland E. Borowski, PE
Engineering Manager
Star Aviation

 

[corus]

The 1st 6 will be zero as Gbor says, but if it is a rigid body then presumably it has infinite stiffness and as the frequency is related to root(k/m) then the frequency will be infinite too, for some mass m.

corus

 

[jhardy1]

As gbor and corus point out, the first 6 modes of an unrestrained body should have zero frequency, and will correspond to the 6 "free body" modes (three global translations, and three global rotations).

Modes 7 and above should correspond to the free vibration modes of the unrestrained ("floating") object. Think of tossing a long flexible stick violently in the air - as well as flying as a projectile, it will probably "flex" in a shape similar to the first mode of a simply-supported beam, but in a way such that the centre of mass does not move laterally. That is, as the mid-span flexes to the left, the tips flex to the right. You can see this behaviour in slow motion footage of a javelin throw, for example.

Whether any of these higher modes are relevant to your analysis depends on what you are trying to achieve.

Hope this helps!

 

[spongebob007]

If I understand you correctly I think you are not interpreting the results correctly or using the term rigid body correctly.

In a free-free modal analysis, the first six modes are all rigid body modes that will have infinite translations with an essentially meaningless frequency that is in effect 0Hz. These modes are the six translations and six rotations. You are not interested in these and for the sake of analysis, you should set your first shift point for the eigenvalue solver to 1Hz or higher. The higher modes are real free-free natural frequencies of the structure.


All continuous structures have an infinite number of natural frequencies and there is no such thing as a structure that will behave as a rigid body over the entire frequency spectrum. Say your FEA model gives the first non-zero free-free frequency as 50Hz then that is a real resonant mode of the structure. The structure will NOT behave as a rigid body when excited at or near 50Hz.

Now if a structure has a fundamental frequency at least 3X the forcing frequency, the structure will behave approximately as a rigid body, that is the vibration maginfication will be ~1.

I think you may be confusing the concept of "rigid body" with "static" response. When the ratio of the driving frequency to the natural frequency of the structure is below say .3 then response=input. The structure behaves in a static (or quasi-static to be more correct) manner. It may also behave as a rigid body, but not necessarrily.

 

[GregLocock]

This has probably been said above, I'll put it in perspective from a practical testing POV.

The first 6 modes should be of very low frequency. The mode shapes may line up with the axes of the model or not. It doesn't much matter.

Your other modes will be flexural, and will be similar to the ones you'd expect from a more heavily constrained system. They should look 'sensible', and will be somewhat higher in frequency than a restrained model, usually.

If your model contained a hinge or an additional free body then you would have more than 6 of the very low frequency modes, so it sounds to me like you have proved that the model is not a mechanism and has only one free body.





Cheers

Greg Locock

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