## Vibration vs. Wave Propagation Analysis

## Vibration vs. Wave Propagation Analysis

(OP)

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"?

## RE: Vibration vs. Wave Propagation Analysis

## RE: Vibration vs. Wave Propagation Analysis

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.

## RE: Vibration vs. Wave Propagation Analysis

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

## RE: Vibration vs. Wave Propagation Analysis

## RE: Vibration vs. Wave Propagation Analysis

## RE: Vibration vs. Wave Propagation Analysis

Is this directed at me or Greg?

## RE: Vibration vs. Wave Propagation Analysis

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

## RE: Vibration vs. Wave Propagation Analysis

## RE: Vibration vs. Wave Propagation Analysis

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.

## RE: Vibration vs. Wave Propagation Analysis

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)?

## RE: Vibration vs. Wave Propagation Analysis

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.

## RE: Vibration vs. Wave Propagation Analysis

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)' ?

## RE: Vibration vs. Wave Propagation Analysis

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

## RE: Vibration vs. Wave Propagation Analysis

## RE: Vibration vs. Wave Propagation Analysis

Also I don't know the answers.

Cheers

Greg Locock

## RE: Vibration vs. Wave Propagation Analysis

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.

## RE: Vibration vs. Wave Propagation Analysis

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

## RE: Vibration vs. Wave Propagation Analysis

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...

## RE: Vibration vs. Wave Propagation Analysis

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.

## RE: Vibration vs. Wave Propagation Analysis

3. Losses are losses, many kinds of loss to consider, many kinds and dependent on your design specifics.

2. Greg has already addressed

1. The amplitudes of the structural dynamics are driven by the excitation. When you get right to it, the entire dynamics at all frequencies are govered by the solutions to the equation of motion and in the form of waves at all frequencies!

You'll have to explore the last comment in the texts you've consulted, for why that's the case.

## RE: Vibration vs. Wave Propagation Analysis

With the latter, that's kind of out-of-date because most current software (like STADD for example) can handle non-sinusoidal forcing functions/impact loads (in a structural dynamics approach). With the former, that can resolved by just a matter of meshing (to get the necessary d.o.f. to get to the higher modes).

So that left me wondering:

well, if those 2 obstacles can be overcome.....why is this needed?The answer in my mind had to be the stiffness matrices I was seeing in these texts: they are modified by the wave number. (Unlike the structural dynamics approach.) Ergo, at the right combination of forcing frequency and natural frequency (predicted by a wave number modified stiffness matrix) the wave propagation approach would yield higher displacements, stress, etc than a normal modal/structural dynamics analysis (with stiffness not modified by the wave number).So that is where that question (i.e. #1) came from.

## RE: Vibration vs. Wave Propagation Analysis

The response depends on your excitation, the structure and its modes. The question as first posed dealt with structural dynamics, but then prospect of accoustic or wave propagation is thrown into the mix.

Such matters are resolved before you begin the model building, and governed by the excitation source, its characteristics, and the degree of coupling to your structure. Beyond just a general comment, you must consult the published research literature.

For engineered structures, the simple answer is that the structural dynamics control.

## RE: Vibration vs. Wave Propagation Analysis

Another question: Further reading on this subject shows that the dynamic stiffness for elements in a wave propagation analysis is different than elements derived by the traditional formulations (i.e. not modified by the (forcing frequency dependent) wave number). By definition, that would result in different natural frequencies for something formulated in a wave propagation analysis vs. a conventional [structural dynamics] analysis.

However, one text I have says this: "Thus the apparently odd behavior of Figure 5.6 [a plot of dynamic stiffness vs. wave number] is also implied in the conventional formulation- if a significant number of elements are used. The spectral approach is equivalent to an infinite number of conventional elements."

^{[1]}So does that mean a FEA approach to determining the natural modes/frequencies would yield the same results as the elements used in a wave propagation analysis IF the former were meshed enough?

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[1] 'Wave Propagation in Structures: an FFT-Based Spectral Analysis Methodology', by: James F. Doyle (paperback re-print of 1989 (hardcover) edition), p.143

## RE: Vibration vs. Wave Propagation Analysis

Don't forget, you can have wave propagation defined by your materials of construction and by the structure. If you have FEA capable of dynamic analysis with proper meshing, and enough time on you hands and with first rate computational resources you can do anything...

Pick a simple structure, like a thin walled cylinder, and get busy...you will also need to include a complex modulus of elasticity...and a spare computer to check the eng-tips postings...

## RE: Vibration vs. Wave Propagation Analysis