Nice find Christian,
I did the algebra for the isotropic case and it came out to an aspect ratio of 5.07 to meet my proposed criteria of 1.3. LISA confirmed the same.
Luckily for me, my panels are not isotropic, so I don't need such an extreme aspect ratio. Also, clamped edges pushes the natural frequencies closer together than simple edges, so getting a little "clamping" action from the perimeter is not so bad in that respect.
I'll have to take a look at the orthotropic solution a little closer, and see if that can be converted to a relatively simple rule that applies for typical plywood properties.
Eric
I did the algebra for the isotropic case and it came out to an aspect ratio of 5.07 to meet my proposed criteria of 1.3. LISA confirmed the same.
Luckily for me, my panels are not isotropic, so I don't need such an extreme aspect ratio. Also, clamped edges pushes the natural frequencies closer together than simple edges, so getting a little "clamping" action from the perimeter is not so bad in that respect.
I'll have to take a look at the orthotropic solution a little closer, and see if that can be converted to a relatively simple rule that applies for typical plywood properties.
Eric
Parts-Express has a low-cost stand-alone option. Before anyone gets in a fit, I did not say it was the best, or the worst, but as DSP goes it's affordable.
Parts Express DSP
They also have some mini Class-D amps with built-in DSP that have plenty of power for home DMLs
Class-D with DSP
A lot of home receivers have a lot of the basic DSP functionality, and have for years, which means the used market is full of relatively low cost possibilities. For example I have an old Denon a friend gave me that has parametric EQ, active crossover, and time alignment. I also have a Yamaha I bought a long time ago (10 years?) that has DSP. From what I have seen here a unit with multiple parametric EQ per channel and active crossover would do most, maybe all that is needed for a DML; all of them have subwoofer out these days. The main thing IMO is that if you are looking for the nth degree of fidelity then you want one with a good ADC/DAC that samples at high bit resolution and frequency, higher than CD quality if you can find one.
FWIW In a car I use a MiniDSP C unit which granted is not cheap. That being said, there are multichannel amps with integrated DSP which include parametric EQ, active crossover, time alignment, etc. all integrated into the unit. Pioneer HUs, and now many others, also have integrated DSP.
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Deude,
Thanks yes I have seen those units and the minidsp.
Idk how much DSP affects the audible quality (suspect I would have difficulty hearing it) but if it does at all, I would think it best to avoid stand-alone dsp with analog in, where you end up having multiple DACS and ADCs.
I have a Denon amp now with dsp, and I have bought an after-market ipad app to configure it. Have not tried it much yet. But it’s not the latest model and cannot be controlled from laptop. Only the very recent ones allow you to control the curves properly afaik, and you pay a premium for that.
Paul
Thanks yes I have seen those units and the minidsp.
Idk how much DSP affects the audible quality (suspect I would have difficulty hearing it) but if it does at all, I would think it best to avoid stand-alone dsp with analog in, where you end up having multiple DACS and ADCs.
I have a Denon amp now with dsp, and I have bought an after-market ipad app to configure it. Have not tried it much yet. But it’s not the latest model and cannot be controlled from laptop. Only the very recent ones allow you to control the curves properly afaik, and you pay a premium for that.
Paul
Agreed.
PS: I meant to say DAC, not DSP in the prev message. "Idk how much the DAC affects the audible quality...
PS: I meant to say DAC, not DSP in the prev message. "Idk how much the DAC affects the audible quality...
@pway
Hello Paul,
After the difficulties with code aster, I had a look to other possibilities including tools to solve PDE. I understood with that the plate PDE (Kirchhoff) is not "FEM friendly". On the Elmer side, it is clear the orthotropic materials are not supported in the 2D simulations. So I came to the conclusion that the FDM (Finite Difference) is not a so bad way... Let me know if you see new possibilities.
Christian
Hello Paul,
After the difficulties with code aster, I had a look to other possibilities including tools to solve PDE. I understood with that the plate PDE (Kirchhoff) is not "FEM friendly". On the Elmer side, it is clear the orthotropic materials are not supported in the 2D simulations. So I came to the conclusion that the FDM (Finite Difference) is not a so bad way... Let me know if you see new possibilities.
Christian
@pway
Just to keep you inform : I have installed Fenics thanks to a docker container. Seems it runs just out of the box. I added on it Fenics shells which is a package dedicated to shells so plates... Seems also it runs. The tricky point is to understood the functionalities that are in PDE and FEM vocabulary... A bit obscure to me in first approach. Hopefully some examples are provided. Will see.
Christian
Just to keep you inform : I have installed Fenics thanks to a docker container. Seems it runs just out of the box. I added on it Fenics shells which is a package dedicated to shells so plates... Seems also it runs. The tricky point is to understood the functionalities that are in PDE and FEM vocabulary... A bit obscure to me in first approach. Hopefully some examples are provided. Will see.
Christian
Hi Christian
Sorry for the delay - Im finding it a bit hard lately to allocate time to this.
Not sure what you mean that plate PDE is not FEM friendly. I remember Elmer used the smitc technique to prevent 'locking', is that what you mean?. I think I read that code aster uses some other techniques to prevent the same phenomenon of convergence failure. But I doubt plate PDE is any more subject to this than other PDEs.
I think you've made great progress with the FDM, but I would prefer to stick with techniques which have been validated, and can accomodate any shape or support condition.
Elmer almost supports orthotropic, it just requires a bit more code to be added, which they won't do unless its attached to a project or funding. One response I had from Kevin Arden on the Elmer forum had him adding that extra code by another mechanism. He said it worked, but I didn't pursue it because I didn't want to open yet another can of worms:
I have not been back to Code Aster, are you convinced it is a non-starter for you? If so, there is no point in me pursuing it further.
Paul
There are examples of using Fenics here https://computational-acoustics.gitlab.io/website/
I think it may be made by the same people as bempp.
I read through the first couple of tutorials, it seems mathematical grounding is needed (but the same is true of bempp, and I managed to get results from that).
At this point, I have a bunch of half-finished bits and pieces I want to get back to, so I may just go my own way with isoptropic Elmer + bempp. I'm in danger of losing the threads if I try anything else I think. I just need to find some time, I need to be more focused...
I would be happy to try Fenics if you make progress on that 🙂.
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Hello Paul
Don't worry. We have all our lives and priorities to manage. This is a DIY so leisure time topic
I read in different documents (Scikit-fem, Fenics?) that the PDE of plate being of the 4th order (biharmonic), their transformation by the FEM approach (trial function + integral) leads to discontinuity. It can be solved by specific finite elements and some advanced transformation of the standard initial PDE. My knowledge in FEM is too weak to make a precise synthesis.
I understand and I have in mind what you want to do with non rectangular shape. You're right to highlight the validation question. We saw some posts ago the interest to compare results. I continue to search for an FEM alternative.
Yes, I saw the answer you get in the Elmer forum. Let's keep an eye on it.
I was really disappointed with Code Aster. As I don't want to have at the top of the questions "how to make the tool working on my computer?", it is a no go for me.
Thank you to remind us this source!
This is the difficulty! Solid physics and mathematical basis are needed. My hope for starting is to find examples close enough to what we search just to have to make some variations in the way the results are used. Second hope is to find some documents that will demystify the mathematical form.
I will inform on the progress or... the non progress!
The following is an update on this earlier post, where I described how to determine the elastic constants of an orthotropic plate. The post referenced above details how do extract the constants E1, E2 and G12 from "tap tests" that identify the natural frequencies of a free plate, in combination with an FEA (or FDM) model. This new post is intended to provide help for extracting also the poisson's ratio (nu), and the other two shear moduli. These additional constants are most important (I think) for accurate modelling of skin/core/skin composites which have relatively light (and compliant) cores. Examples include things like panels with carbon fibers skins over a balsa core, or aluminum skins on a Nomex core, and even plywoods.
In the following I am using the notation used by my LISA FEA program (sorry), where the constants are given as: Eu, Ev, Guv, Gvw, Gwu, and nu-uv. I think you can assume that u=1=x, v=2=y, and w=3=z, if you prefer an alternate notation.
What follows is simply a table I generated for a hypothetical plate, where I simply varied each of the six elastic constants to see which modal frequencies are most strongly affected by each of the constants. For me, the value of this table (I hope) is too make my crude manual "trial and error" method a little more efficient, by helping me decide which constants to adjust in order to better fit natural frequencies identified by tap testing. But this information might also be useful for developing a fully automated method, as Christian has been working on.
The plate I chose as the base case has the following characteristics. These represent no actual panel, but are in the ballpark for a plywood panel. Hopefully some of the generalizations from these results will apply to some real composite panels.
length=585 mm
height=407 mm
thick=6.0 mm
density=600 kg/m3
Eu=6.0 GPa
Ev=6.0 GPa
Guv=0.6 GPa
Gvw=0.6 GPa
Gwu=0.6 GPa
nu-uv=0.25
Below is the table of results. The highlighted cell are modes most affected by changing each of the elastic constants. The lower table shows which constant is changed. One thing to note is that the predicted natural frequencies are much, much more sensitive to the first three moduli than the other two. For the first three moduli, a 50% increase in each (from 6 GPa to 9 GPa) created a big shift in two or more modal frequencies. On the other hand, to produce significant effects from the other two moduli, I decreased them by a factor of 20!
I'd like to believe that the following generalizations may hold pretty well:
- Guv can be inferred from the 1,1 mode.
- Eu can be inferred from the 0,2 mode, along with the other modes where the second index is higher than the first.
- Ev can be inferred from the 2,0 mode, along with the other modes where the first index is higher than the second.
- The other constants mainly influence the higher frequency modes,
- Gvw can be inferred from the high frequency modes where the second index is higher than the first.
- Gwu can be inferred from the high frequency modes where the first index is higher than the second.
- Nu-uv has to be inferred (maybe??) from the high frequency modes where both indices are high.
Eric