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"?

 

[hacksaw]

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.

 

[WARose]

Thanks hacksaw. So it appears I was on the right track with question #1. To elaborate further: a lot of the texts I have read on wave propagation make the case that wave propagation becomes appropriate at the higher forcing frequencies because of the higher modes involved and also because the short duration/non-sinusoidal composition of the event.

With the latter, that's kind of out-of-date because most current software (like STADD for example) can handle non-sinusoidal forcing functions/impact loads (in a structural dynamics approach).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.

 

[hacksaw]

"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."

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.

 

[WARose]

Happy New Year to all.

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

 

[hacksaw]

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...

 

[WARose]

Thanks for the feedback hacksaw. So I guess the answer to my question is: "yes".

 

[WARose]

A couple of things I've picked up on since my last post: The SFEM (the Spectral Finite Element Method) appears to not be appropriate for large/complex structures. (This goes back to my question in the OP.)

This pretty much eliminates one question I still have regarding SFEM software: how does it account for frequency changes over distance? Even in soil, that happens only after several hundred feet. (For high frequencies.)

In any case, I appreciate the feedback and info I've gotten in this thread.