Vibration vs. Wave Propagation Analysis 4

[WARose]

The other day I was having lunch with a engineer I know. A subject we talked about began with me expressing frustration with displacement/modal based dynamic analysis (in programs like STAAD) that sometimes didn't predict vibrations (that occurred in real life) at other levels /locations of buildings. He suggested to me a wave propagation model could possibly solve those issues. I personally have never used such a model (I'm not even aware of any software that does). So I thought I'd ask here: has anyone here used such a technique? If so, were you satisfied with the results? Does it indeed "spread out" the vibration "better"?

 

[Tmoose]

Do you recall some details of project with "missed" vibration ?

 

[WARose]

[blue](Tmoose)[/blue]

Do you recall some details of project with "missed" vibration ?

Yes (in fact, I was asked to look at it to see what went wrong). It basically was a compressor on bolted down to a steel frame (up on the 4th floor of a building). It caused some noticeable vibrations at other levels that the model failed to predict. Looking at it, I think the main culprit was likely the estimate for the foundation stiffness at the column bases. Modifying that, I got a bit closer to what was observed in the field.

But that comes back to my original question: does a "wave propagation" model transfer these vibrations better? I would assume that it has similar boundary constraint issues (i.e. to a normal displacement/modal based dynamic analysis).......but, in the situation i describe above (i.e. the original model), I would assume (famous last words) that if it is propagating waves, it would have propagated them to the other levels (at least to some degree) regardless of the foundation stiffness assumption.

 

[GregLocock]

We used to use wave propagation models to model the interior of cars, for use with noise cancelling. Essentially that means the phase angle of the mode is no longer +/- 90 degrees, so you get travelling energy, whereas your standard modal assumes quadrature, hence no energy transfer. The problem as I see it is that we were working from real results, not dodgy computer models.



Cheers

Greg Locock


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[WARose]

Thanks Greg......good info.

 

[rob768]

Is this not related to the fact that what you get is related to forced vibrations, rather than resonance modes?

 

[WARose]

[blue](rob768)[/blue]

Is this not related to the fact that what you get is related to forced vibrations, rather than resonance modes?

Is this directed at me or Greg?

 

[GregLocock]

Rob - I think it is but I last worked on acoustic modal analysis in 1988, so I'm a bit hazy on that.

Cheers

Greg Locock


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[WARose]

Question (to anyone who may be interested).....reading more on this (wave propagation methods of vibration analysis), it appears that this sort of analysis is appropriate once forcing frequencies get above about 100-200 Hz or so (especially in the kilohertz range). One explanation I've seen is because such higher modes are involved. But using a typical FEA formulation, you only have as many modes as you have degrees of freedom. How does the fact its a wave propagation analysis change that? (Some of the material I've read shows frequency modulated stiffness matrices for elements. Not sure if that plays a role or not.)

 

[hacksaw]

you have to look at the accoustic velocity in the individual components to assess whether wave propagation is significant relative to the natural frequencies of your structure. This establishes the cut-off frequency of the accoustic propagation.

many times you can rely on the quasi-static analysis for frequencies below cut-off.

 

[WARose]

Since my original post, I've read a few books on this topic and I came away with a few questions (pardon if the answers seem obvious):

1. It would seem to me that at the right forcing frequency, this method (i.e. wave propagation analysis) would predict higher displacements, stress, etc than a normal modal analysis (with stiffness not modified by the wave number). Ergo this method becomes appropriate at certain cut-off frequencies. Do you agree with that?

I ask because a lot of FEA programs allow you to put in non-sinusoidal dynamic loads.

2. Is there a ceiling for that response? In impact loads, the max. response (the Dynamic Load Factor, or DLF) is about 2. However in vibration analysis, with sufficiently low damping, you can get values well in excess of that.

3. In mode conversion (i.e. converting axial waves to flexural waves at changes in geometry, etc)......is there a lot of energy loss in this process? Or is it minimal (depending on the level of damping)?

 

[hacksaw]

The traditional vibration and wave propagation models developed from the same physical models and equations. It is just a matter of how much calculation you are willing to do.

 

[electricpete]

Ergo this method becomes appropriate at certain cut-off frequencies. Do you agree with that

I'll give my simplistic thoughts fwiw (which probably duplicates what others have said and might miss some important).

There is a cutoff frequency which you could deduce from the speed of sound in a "structure" (*)
If the structure is a pure homogeneous material, then you could calculate speed of sound from material properties).

We remember the relationship among wavelength, frequency and speed of sound in the structure as follows:
wavelength = speed-of-sound / frequency

To predict behavior without considering waves, we need to have a wavelength much longer than the structure:
wavelength >> structure longest dimension.

subsitute our expression for wavelength:
speed-of-sound / frequency >> structure longest dimension.

Rearrange:
frequency << speed of sound / structure longest dimension

If frequency is low enough to satisfy this requirement (or equivalently structure small enough to satisfy this requirement), the structure can be analysed without considering wave behavior.

* Now the question: what is the "structure" of interest. I think it is the element size selected for the FEA. I think that is what hacksaw was getting at... you can analyse higher frequencies with your model if you refine to decrease the mesh size.

=====================================
(2B)+(2B)' ?

 

[GregLocock]

The problem with that approach is that for typical engineering structures the modes of interest are not simple functions of material properties alone. For example the effective speed of sound, that is wavelength*frequency, of a beam in bending is not constant. So that approach is useful in some instances, but not in general except as some sort of very high upper bound.[pre][/pre]

Cheers

Greg Locock


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[WARose]

Could someone just directly answer my questions?

 

[GregLocock]

I was put off answering because of your comment about DLF. It is a neat party trick, but virtually meaningless in the real world. More accurately, the maximum deflection, hence strain,hence stress, of an undamped SDOF system caused by a given force being applied is twice that of the steady state response. There's so many gotchas in that analysis that I'd be more than happy to see it removed from every dynamics text.

Also I don't know the answers.

Cheers

Greg Locock


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[hacksaw]

The simple answer to the question you've raised is "no",

what your friend is dealing with are the degenerate modes, no, birth certificates and photo id's not required, it is just that even relatively simple structures have such complex moding in 3 dimensions, that depending on the meshing and time/frequency range considered, you will find that mother nature is more complex than we might realize and degeneracy is a but reflection of the fineness of resolution being considered.

 

[WARose]

The simple answer to the question you've raised is "no",

I asked 3....and I'm not sure which one you are saying "no" to.

 

[hacksaw]

"But that comes back to my original question: does a "wave propagation" model transfer these vibrations better?"

The simple answer is no, to the original question. That said the discrepancies to which you refer, often involve modal complexity that can only be resolved with proper meshing and all of the "actual details" of the structure. Such details are rarely explored in design environments and the details so complex as to rarely discussed in text books and research publications.

To answer the question beyond that, you'll need a chair with full-tilt software, and lots of computing resources. Lots of fun for sure...

 

[WARose]

Thanks hacksaw....but if you noticed, later on I asked these three questions:

1. It would seem to me that at the right forcing frequency, this method (i.e. wave propagation analysis) would predict higher displacements, stress, etc than a normal modal analysis (with stiffness not modified by the wave number). Ergo this method becomes appropriate at certain cut-off frequencies. Do you agree with that?

I ask because a lot of FEA programs allow you to put in non-sinusoidal dynamic loads.

2. Is there a ceiling for that response? In impact loads, the max. response (the Dynamic Load Factor, or DLF) is about 2. However in vibration analysis, with sufficiently low damping, you can get values well in excess of that.

3. In mode conversion (i.e. converting axial waves to flexural waves at changes in geometry, etc)......is there a lot of energy loss in this process? Or is it minimal (depending on the level of damping)?

Those are the questions I was referring to. Greg has already took a shot at #2.