@Veleric , @pway
Following your post Eric with M Zenker's paper below a raw result of the FDM script. The case is easy as being a simply supported plate. Not written the mesh is 20mm. The red point is a proposal of driving point based on the idea of the paper (seems some indication are missing...) and for only the odd odd modes (a close position is obtained with all the modes). This remind me old posts saying "off center not too far". Encouraging. Don't be afraid by the execution time shown in the terminal view, my computer is old; much better on my son's one.
Following your post Eric with M Zenker's paper below a raw result of the FDM script. The case is easy as being a simply supported plate. Not written the mesh is 20mm. The red point is a proposal of driving point based on the idea of the paper (seems some indication are missing...) and for only the odd odd modes (a close position is obtained with all the modes). This remind me old posts saying "off center not too far". Encouraging. Don't be afraid by the execution time shown in the terminal view, my computer is old; much better on my son's one.
Christian,
Awesome, you are on your way! I don't see a poissons ratio (or Shear Modulus). Doesn't your FDM script require one or the other?
Eric
Thank you Eric
No Poisson's ratio for now as "only" clamped or simply supported conditions for isotropic material are implemented at this step. Next as the script gives encouraging results is free boundary condition which need it. The script is already prepared for orthotropic conditions which also requires it.
So coming next
Christian
Hi Christian
Well done!
Which paper are you referring to by Zenker? Is this Benjamin Zenker?
If I understand correctly, the image is a spatial average of the first several odd-odd modes shapes, correct? And you are inferring the best position by the maximum displacement?
Will your FDM technique allow non-square grids, curved edges, holes etc?
Paul
Hello Paul
The patent was reminded by Eric in the other thread #8285
https://www.researchgate.net/public...iated_Sound_Power_of_a_Flat_Panel_Loudspeaker
from Benjamin Zenker yes
Have a look fig4 to 6 where M Zenker proposes a method to find the best driving point. He first apply a transformation (norm) on each mode to "increase the contrast" and superpose them (here information are missing).
I just made a quick test first with all the first modes as in the paper and only with the odd odd (the snapshot posted).
This method can run with any method giving the mode shapes : FEM, FDM, direct mode shape calculation ie for SSSS.
In my script, it is FDM. I have the intention to explain more on it if the results are good enough.
In the examples of FDM method I know (far to be a specialist), the grids are mainly square or at least rectangular. I found one example of hexagonal grid. Curved edges or holes are additionnal difficulties. I found one paper pushing the method to object like guitar top. As all of that is new for me, it is in the "to see next...", by basic intention being to learn more about the calculation approach, having a basic tool able to deal with basic shapes, boundary conditions, form factor.
A tool chain lead by a Python script based on meshing tool and FEM that gives mode frequencies, mode shapes, able to simulate the behavior over the time (transitory) is probably a better way. The FDM script might be just a learning tool.
Read a little and seems pretty interesting, although I have little understanding of graphs, instrumentation, and spectrum analysis, but it raises a question if you could expand a sound stage by damping the rears and brightening the fronts thereby resonating according to the sound spectrum. Thanks for the fodder!
I was thinking about using a similar technique with the even modes to see if its possible to restore a few of the lowest of them as useful sources of far field sound. If you can imagine the same modal overlap of even modes, this could give the best location to make a hole or holes in the panel. If you have a hole, you cause preemptive cancellation of the antinode at (or near) that location with its opposite at the rear of the panel, so that it does NOT cancel with antinodes of opposite sign elsewhere on the panel.
Ideally you would get the driven mode shapes, which I suppose are not quite the same as the free response. Eg a drive point a one side of the centre will, I presume, give the largest response at the drive point and on the point symmetrically opposite.
If we had a simple and reliable way to estimate far field response from node shapes, frequencies, and the drive point, we could try to estimate a best panel with various parameters including holes, shape, aspect ratio etc. Could probably use genetic algorithm techniques to converge on optimum.
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Christian
I came across this book online. May be of interest, has chapter on acoustics.
https://eecs.wsu.edu/~schneidj/ufdtd/ufdtd.pdf
Thank you for the interest. DML are thin plates. I think we can assume that the displacement is the same for both sides. It is the resonance of the plate which is working not of the surfaces (bending waves : see below)... but my understanding of your idea might be wrong.
Christian
I think the FDM method (or a FEM if we are able to get the matrix of the displacement of each point) has this possibility. My idea is make a a simulation aver the time (transient) using a pulse (Dirac) at the driving point then integrate over the panel surface to get the response at distance. A FFT or any time to frequency transformation will give the frequency response. A prerequisite is to include in the FDM (or FEM) method a realistic model of damping (otherwise we'll get to sharp resonances).
The idea of holes to reduce the symmetry of odd modes is a possibility. To see how productive they will be. I am curious to see also the effect of local additional mass.
Some algorithm seems also possible. in B Zenker's paper there is a proposal to evaluate the FR smoothness. The limit is the computational time.
Christian
I apologize My orientation was way off topic and a much less precise extrapolation and embarrassing by comparison if I am understanding correctly. I was basically speaking of an imprecise room treatment around a speaker for a psuedo linear expansion of sound beyond a whole speaker. Sorry about that😊.
Thank you Paul
Going into it quickly :
- the type of sources for transient (derivative Gauss pulse that i already used as a substitute of the hearing gammatone function for spectrum analysis)
- the boundary conditions so that the energy is not reflected at the edge. I think that beyond the standard boundary conditions there is something to see with a different level of reflection (see the edge treatment by Gobel)
- the acoustics part for the propagation of an acoustic wave. I have another paper with that. Some 2D application (for simplification) should show what happen a panel or pistonic driver (ie in open baffle) is in a room.
OK understood. It was in my ideas some months after started with DML. Lower in priority now after I understood the main work is the panel itself probably not so much its surrounding.
Yeah, phasing a fuller range beyond what my Joseph's supply is well beyond my scope.
Christian,
I think your FDM is working very well.
Today I tried comparing my LISA results to the "exact" results for your exact dimensions and properties. Firstly, I realized that probably had never actually compared the two before! Why not I cannot even imagine!
In any event, my LISA model results were very similar to your FDM results, with the model predicting frequencies that were about 0.5% to 2.5% lower than the exact solution. I must admit I expected they would be a little better than that, but regardless I think it's good enough.
My "standard" model is 40x40 elements, 8 nodes each. I tried increasing the number of elements to 60x60, and also tried making the elements more square, but neither approach gave any better results than my original 40x40 model.
Eric
That's good for the FDM script.
If I was working with a software like Lisa, I wouldn't have tested that neither.
For a better view next time I will display the error with the decimal (few days ago error was above 1% because of mistake in the script... hopefully seeing the error was not reduced while increasing the cell number, I was able to find it).
I get better results when I double the cell number in each direction (so ratio 4 in surface). The computation time is the increasing then (my computer is slow). This information should be in a "report" at the end of this testing phase. I am currently trying to use approximation formulas I found in a paper (based on Mitchell Hazell formula) for additional test cases: Rocco Maso thesis
I’ve have Elmer working through python now. I didn’t use pyelmer in the end because it was not worth it. All config files were converted to yaml, which could be good, but there was no error checking and they were just dumped straight back into the sif file for processing. The only benefit really is convenience, and I can get that with a much smaller template based script.
I will do a few graphs of mode statistics vs shape change in the next few days.
Anyhow, interesting how we end up running into the same ideas. I have not gotten around to doing the impulse response, but I was thinking maybe the side lengths ought to be one of the parameters that are adjusted to get best fit, or some standard edge effect correction applied.
First run of Elmer in Python, investigating the effect of introducing asymmetries into a rectangular panel.
First slanting one of the panel sides, by decreasing top length and increasing bottom length.
100% slant turns the rectangle into a triangle
The plot has 100 points.
Aspect ratio is 2. Area 0.5 m^2
Plot shows mean, SD, and skewness. A gaussian distribution has a skewness of 0.
Looks like it's worthwhile going beyond 0.5, will post another graph.
Laptop has to work hard, being in a tight loop of meshing and FEM.
First slanting one of the panel sides, by decreasing top length and increasing bottom length.
100% slant turns the rectangle into a triangle
The plot has 100 points.
Aspect ratio is 2. Area 0.5 m^2
Plot shows mean, SD, and skewness. A gaussian distribution has a skewness of 0.
Looks like it's worthwhile going beyond 0.5, will post another graph.
Laptop has to work hard, being in a tight loop of meshing and FEM.
Graph below shows stats for side-slant from 0 to 0.9
The unlabeled red curve is a simple count of mode gaps < 5 Hz divided by 10, indicating that most of the SD variation is caused by the number of mode gaps near zero.
Interesting that the skewness is almost 0 at 0.6 slant. Unfortunately, zero skew does not imply Gaussian distribution:
A better histogram found at 0.28 slant where SD is minimum.
The unlabeled red curve is a simple count of mode gaps < 5 Hz divided by 10, indicating that most of the SD variation is caused by the number of mode gaps near zero.
Interesting that the skewness is almost 0 at 0.6 slant. Unfortunately, zero skew does not imply Gaussian distribution:
A better histogram found at 0.28 slant where SD is minimum.