...at high enough frequencies and thick enough plates, I should have said.
I confirmed this just now for LISA. The results for a 4 mm plate are only very slightly affected by a large change in G13 and G23 and mainly at high frequency, But for a 32 mm plate, the same change in G13 and G23 made a huge impact, especially at high frequency but large even at low frequency.
I just never modelled plates that thick before.
Eric
Eric, would you give me the values for some material that you have used (presumably a plywood) and have eigenmode results for, so I can check whether the Elmer plate model works with orthotropic materials, and if so whether it gives the same results? I will also need the other data for the model and mesh of course.
Yes, I noticed the matrix was symmetric. Apparently I need to input the inverse of the compliance (aka stiffness ?) matrix for input into the Elmer SIF file, as mentioned in the post I linked. I can calculate that on my old HP15C with a bit of revision
, or in Python.
Also, did you measure all 4 values yourself with impulse technique, is that possible - thought it was just the E values and Poisson? (Sorry still have not gotten around to doing that myself & reading closely your procedure - will get to it probably next week.)
Yes, I noticed the matrix was symmetric. Apparently I need to input the inverse of the compliance (aka stiffness ?) matrix for input into the Elmer SIF file, as mentioned in the post I linked. I can calculate that on my old HP15C with a bit of revision
, or in Python.Also, did you measure all 4 values yourself with impulse technique, is that possible - thought it was just the E values and Poisson? (Sorry still have not gotten around to doing that myself & reading closely your procedure - will get to it probably next week.)
Paul,
Yes, I will do that. Let me see what I can find in my notes, they are often indecipherable, so I may have to generate a new dataset!
The values for E11, E22, and G12 are the easiest to get, practically any size panel will do. To get nu12 you have to use a plate that is cut with an aspect ratio of (E11/E22)^0.25. Such a plate is called a poisson plate. With such a plate, some of the eigenfrequencies become pretty sensitive to the value of nu12, which is not the case for a plate with arbitrary dimensions.
One good thing to know also is that the aspect ratio of your poisson plate does not have to be exactly right, just close. The first time I tried cutting such a plate I thought it had to be perfect. But it turns out that it doesn't.
Eric
Paul,
There's good reading here about the impulse method:
https://resonalyser.com/abouttheory/
https://resonalyser.com/wood/
https://resonalyser.com/aboutarticles/
The knowledge articles are just abstracts as I recall, but (if you can't find them yourself) they will email you the full articles. I was too lazy to look myself and let them email them to me.
This one was good as I recall.
https://www.researchgate.net/public..._the_Poisson's_Ratio_of_Orthotropic_Materials
Eric
There's good reading here about the impulse method:
https://resonalyser.com/abouttheory/
https://resonalyser.com/wood/
https://resonalyser.com/aboutarticles/
The knowledge articles are just abstracts as I recall, but (if you can't find them yourself) they will email you the full articles. I was too lazy to look myself and let them email them to me.
This one was good as I recall.
https://www.researchgate.net/public..._the_Poisson's_Ratio_of_Orthotropic_Materials
Eric
Ah yes. I remember you discussing whether Christian had happened upon a Poisson plate geometry by accident.
Paul,
Here's some data for you on a fiberglass balsa sandwich panel. The balsa grain is running in the long direction of the panel, so it's stiffer in that direction. Here are the panel details:
0.457 m x 0.606 m
rho = 247 kg/m3
h=3.51 mm
The images below shows the eigenfrequencies (Hz) along with a schematic of each mode. The lines inside the rectangle represent the nodal lines for the mode. With the above parameters and the first three frequencies below you should be able to estimate G, E1, and E2. The remaining frequencies provide a check on the model. If you get those three parameters right, the model should predict the remaining modes decently.
Since this is not a poisson plate, it won't give you the best possibility to estimate nu accurately, but I did find that the upper frequencies did change a bit with changes in estimated nu,
With this data and LISA I was able to come up with estimates of G, E1, E2, and nu that predicted all but three of the 14 listed frequencies within 1%. The others were off by about 2%. I can share my values if you want, but I thought you'd probably want to try it on your own first.
Of course you still missed the part that's the most fun, that is, sorting out which frequency is associated with which mode.
Eric
Hi Eric
I think we have a misunderstanding. I’ve not yet used the Elmer orthotropic plate matrix, so what I was asking for was the resolved Elasticity matrix values, etc so I can make a first trial run, to compare with your eigenvalues, much like we did previously for the homogeneous plate. I have first to check whether it works at all, and the correct format for the matrix.
After that I guess I can go forward to use the impulse trial and error technique (via Python bc I think I have a matrix inversion in between E values and the matrix Elmer expects).
Paul
I think we have a misunderstanding. I’ve not yet used the Elmer orthotropic plate matrix, so what I was asking for was the resolved Elasticity matrix values, etc so I can make a first trial run, to compare with your eigenvalues, much like we did previously for the homogeneous plate. I have first to check whether it works at all, and the correct format for the matrix.
After that I guess I can go forward to use the impulse trial and error technique (via Python bc I think I have a matrix inversion in between E values and the matrix Elmer expects).
Paul
For who has an interest in the FDM (Finite Difference Method) I have just uploaded 3 files in the github AudioDIY_DML page.
Those papers have no direct application for now to DML... the next step should be more applicative (if it works!). The current steps shown the technique performances and were the technique appropriation.
All feedback, corrections welcome.
Tell me if you want the sources "as they are"... I have to ask some help from my son for a better page structure!
Christian
Those papers have no direct application for now to DML... the next step should be more applicative (if it works!). The current steps shown the technique performances and were the technique appropriation.
- part 1 : introduction to DML. Interesting for who wants an introduction to FDM
- part 2a : check of the system matrix construction. Not of interest but for me in testing the script
- part 2b : 5 simple test cases made from simply supported and clamped conditions compare to Elmer results
All feedback, corrections welcome.
Tell me if you want the sources "as they are"... I have to ask some help from my son for a better page structure!
Christian
Haha. Sorry,
So what you actually want is the part I didn't tell you, right?!
If I give you my inputs for the elastic properties (for the plate above), and the eigenfrequencies LISA calculated, is that what you would like? Is that correct? I assume you will calculate the compliance (or stiffness) matrix yourself, correct?
Eric
Yes that's what I am after.
I will try this tomorrow hopefully.
Wait...are you also having to calculate the final matrix for input into Lisa? I assumed you were just plugging in the raw E values, but if you need to massage them (I think its an matrix inversion, correct?) than by all means give me that too!!
I will try this tomorrow hopefully.
Ive been trying to run the Elmer Harmonic analysis.
First I needed to learn how to mesh a sub-area of the panel to represent the exciter area, upon which I can apply a pressure force from Elmer. I think I have done that bit.
I also managed to get the harmonic model to run on the plate with a force applied, but the results look like they came from a static force (ie no trace of eigenmodes, just a localised displacement around the exciter).
Elmer it seems is very powerful, but It's woefully undocumented. Its like all these boffins going about their business, improving the solvers and models, and never updating the documentation. I actually sort of complained about it in this post: https://www.elmerfem.org/forum/viewtopic.php?t=7895
Lets hope I have not got them offside, because Ill be asking more questions today about HarmonicMode!
First I needed to learn how to mesh a sub-area of the panel to represent the exciter area, upon which I can apply a pressure force from Elmer. I think I have done that bit.
I also managed to get the harmonic model to run on the plate with a force applied, but the results look like they came from a static force (ie no trace of eigenmodes, just a localised displacement around the exciter).
Elmer it seems is very powerful, but It's woefully undocumented. Its like all these boffins going about their business, improving the solvers and models, and never updating the documentation. I actually sort of complained about it in this post: https://www.elmerfem.org/forum/viewtopic.php?t=7895
Lets hope I have not got them offside, because Ill be asking more questions today about HarmonicMode!
I also want to say something more about the other forum and chdsl. As I reported before to you guys, I think there is something very fishy going on. No normal person spams a forum for months on end, regardless of whether or not responses are forthcoming, or positive.
Remember before I said here that I believed him to be cooperating with that russian guy who was on the forum a few months ago? The one who ALSO had crazy theories about transverse waves in air? Well recently chdsl posted the SAME paper that the Russian guy posted, a completely obscure paper about transverse waves in air generated with metamaterials.
I'm telling you that there is more to chdsl than anyone suspects. I still believe him to be either the same person as the russian guy, or a close collaborator.
And I believe chdsl is not a fool. Everything he does on that forum is very carefully calculated to disrupt. His presence on that forum is not his hobby, its his job. And he does it very well.
Again I dont know why this would be. Maybe the Russian bot farms have selected some of the most obcure unsuspecting forums for their social disruption experiments? Maybe the Russian manufacturers of DML panels dont want people to be able to make their own. I know how crazy this sounds, and I dont know what's going on. But something fishy is going on.
Remember before I said here that I believed him to be cooperating with that russian guy who was on the forum a few months ago? The one who ALSO had crazy theories about transverse waves in air? Well recently chdsl posted the SAME paper that the Russian guy posted, a completely obscure paper about transverse waves in air generated with metamaterials.
I'm telling you that there is more to chdsl than anyone suspects. I still believe him to be either the same person as the russian guy, or a close collaborator.
And I believe chdsl is not a fool. Everything he does on that forum is very carefully calculated to disrupt. His presence on that forum is not his hobby, its his job. And he does it very well.
Again I dont know why this would be. Maybe the Russian bot farms have selected some of the most obcure unsuspecting forums for their social disruption experiments? Maybe the Russian manufacturers of DML panels dont want people to be able to make their own. I know how crazy this sounds, and I dont know what's going on. But something fishy is going on.
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Looks like I have some promising results (or at least 'sanity checks') from the harmonic analysis, after playing with the linear solver and preconditioner options to get it to converge.
Mesh and sif files attached.
- With the frequency set to an eigenfrequency, it gives that mode shape
- Smaller amplitude the further that the "exciter" is from the antinode, as expected.
- Frequencies below the fundamental, give a static deflection of the panel under the exciter - makes sense.
- For frequencies between resonances, you get some sort of hybrid (see below)
- I have not set any damping yet, so I was surprised to have it spit out results in between. It did have trouble converging between eigenfrequencies though, until I used ILUT preconditioner. And it had more trouble with higher frequencies. ILUT made a huge difference - now converges essentially instantly whereas before it was not converging sometimes after 3000 iterations.
- The displacements seem too small. I'm using an exciter area of 30mm diameter (about 7cm^2). Im applying a pressure of 10^4 (I presume this is Pa or N/m^2), which is 1 N/cm^2, so 7N force overall which is about 0.8 kg force, and I only have a small deflections - see bottom image, I get 1.7 mm.
- Oh wait, that could be 1.7 metres deflection!! Never mind, it's early days yet and results are promising.
- Probably if I can enter realistic values for Raleigh damping (research required!) and a more realistic value for exciter force, we should get much closer to real results.
Mesh and sif files attached.
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Ive set up the mesh and SIF file to run this but am stuck on the structure of the elasticity tensor.
It seems I need to start from a 4 x 4 compliance matrix (not 3x3), and invert the matrix with other software before entry into Elmer sif file.
Presumably its very similar to the 3x3 matrix, with extra column & row contain the 'axisymmetric' terms (I think that's what they're called) G13 and G23.
Ive asked on Elmer forum, but maybe you know the structure?
Paul
Hi Paul
Just found the example below of anisotropic material. From Elmer non-GUI Tutorials page 6
The order of magnitude are similar to Young modulus (was 100E9 in the beginning of the example), not inverse.
Christian