@pway
Now that you FEM capability, do you realize that you have a very simple way of determining the elastic constants of your plates? It has been discussed on this thread previously, but I'm not sure if you are aware. The method is based on this technique:
https://en.wikipedia.org/wiki/Impul...tion technique (IET,of a material of interest
I have my own variation of this method that requires only a single panel do evaluate E1, E2, and G12. Poisson's ratio is possible to get also, but requires a second panel size.
Eric
Now that you FEM capability, do you realize that you have a very simple way of determining the elastic constants of your plates? It has been discussed on this thread previously, but I'm not sure if you are aware. The method is based on this technique:
https://en.wikipedia.org/wiki/Impul...tion technique (IET,of a material of interest
I have my own variation of this method that requires only a single panel do evaluate E1, E2, and G12. Poisson's ratio is possible to get also, but requires a second panel size.
Eric
Hello Paul,
Elmer is now installed on my Manjaro laptop. I just tried to follow one tuto about elasticity in 2D. I got no bad message while running the project but I have to check about the visualization (I haven't spent much time on it...). I better understand now what is a .geo and .sif files... not the detail of the syntax of course!.
Thank you chdsl to remind us this thesis. It gathers all the equations we have shared here.
@Veleric : have a look page 24, 25 eq 3.4 (seen also in other paper) is the origin of the limitation in frequency I show in the material chart.
The idea behind the spike is interesting but the way it is shown a bit strange. We know it is possible to make DML by pushing on a diameter of 25 or even 32mm or more. This doesn't transform the panel in pistonic speaker. Where the idea of a spike becomes interesting (in my current opinion) is to avoid to have 2 regions : inner and outer the voice coil diameter; 2 regions that have a different behavior in high frequency. Here the DML was cut at 2k. Why? One hypothesis might be the low pass effect between the membrane mechanical impedance and the mobile mass. Is there a reference to the membrane material?
Indeed I am aware of your work in that area, which I thought was excellent. I have not read it all though, yet. I tried a simple test for E similar to the bending test - supporting panel between rollers and measuring the displacement for a known weight force. Difficult to get any usefully accurate results. I remember wondering how close you could get with a method like yours. An ‘accurate’ value for E also includes some fudge factors papering over the assumptions in the model like assumptions about the thickness, shear forces, inaccurate Poisson ratio etc.
You and Christian have done a lot to bring a scientific and systematic approach to the forum. And I find it amazing just how much physics is connected to the study of these things. Most recently I’ve been trying to wade through some of the acoustical implications of something called ‘quantum chaos’. Sounds like name-dropping or marketing hype I know, but it’s real.
Turns out the density and distribution of modes is related to the high frequency ray dynamics of the shape, otherwise known as a ‘billiard’, after the game. In particular, chaotic dynamics and a long ‘periodic orbits’ lead to high density and more even distribution. I believe I have observed this higher modal density with the only ‘complete’ speaker I’ve built so far - my ellipses, which you have seen.
See for example Nils Berglund channel on YouTube for pretty animations of dynamical billiards showing chaotic behaviour,
So anyhow, I am interested initially to use fem to do some statistical tests on the eigenfrequencies for different shapes.
Further to my last post about mode distribution, the guitar shape is interesting. The concave waist and hole are highly dispersive (in the sense of spreading out any incident rays), and the convex ends refocus and mix the rays. This shape is a highly chaotic billiard, and would have a very long periodic orbit I think. Also, I believe the hole and the taper may give you back some of the even modes.
I have worked out how to display and animate the modeshapes in Paraview for a 2D mesh from the elastic plate solver after a lot of Googling (note if you are using a 3D mesh I think it may me simpler as 3D is the standard case. I have not played with 3D meshes yet).
- Open the vtu file in Paraview
- Click on the "apply" button whenever it's green (don't ask why it doesn't happen automatically, IDK)
- You should see the shape of your model in the display
- Initially the display option is 'solid colour' - select on of 'Deflection eigenmode 1, 2, 3 etc' in the dropdown list.
- Then select the X coordinate in the next dropdown list - you should see the mode shape. I'm not sure what Y and Z represent, but it looks like they could be the first partial derivative in the X and Y direction respectively.
What you have here is just a 2D field displayed in some colour scheme. To display displacement in 3D, you need to convert it to 3D, and for that you need the 'warp scalar' function. Problem is that its not available by default because some sort of conversion is required.
Go to Edit/Settings and click on 'Auto convert properties'. Maybe click on 'Auto apply' too, while you're there.
When you reload the file, the warp scalar filter should be available. Choose warp scalar and check in the properties box that the slider shows the 3D displacement
After that you can choose View/animation view. Select "WarpByScalar" and "Scale Value" in the drop-downs. Click Add (+).
Double click the resulting item, and then double click the interpolation method - select sinusoidal.
For some reason, the max seems to have to come first. In the example below, I have 0.04 in the first box, 0 in the second box. Click apply/ok.
Then you should be able to press play, and see the animation.
Then you can do file/save animation.
Here is the 8th eigenmode for a cantilever rectangular plate.
Hello Paul
some time ago, I explored the math of the guitar contour. If it can help you...
Original file was openoffice calc (.ods).
The hole was to part of this but should be included. I should have another document for you... let see this evening (evening for me!)
Christian
@pway
Easier to find than I thought with a video in bonus!
Here is the link : Damping of structural vibrations in beams and elliptical plates using the acoustic black hole effect
And this video : Using Acoustic Black Holes to minimise reflections
Thanks Christian, that may be useful. Ill be using simple shapes to start.
@homeswinghome Please excuse a quick comment/question. Fascinating though acoustic black holes are their function is to absorb energy to damp vibration. I have looked at them in some detail in a tonearm design. I think that is the opposite of what is desired in a DML?
I'll but out and go back to simulating unipolar magnetic rings with bar magnets....
Burnt
Yes, thanks, I read about ABHs last year - another possibly useful technique. I searched on the forum and saw it had been mentioned previously.
However I thought you were going to send data on the position of the hole in the guitar, having just given me data on the outer shape?
ABH seems unrelated.
Sometime ago, I bought these transducers from China. They were just lying in the drawers since then, after the first try listening how they sound on tightened cloth, cardboard, EPS, ceramic tiles, table top etc. Since I saw that video, I'm looking for spikes to test them on framed picture that's done on cardboard (HDF). The image is fixed to the frame with small nails. The transducer is quite heavy, 275g, so won't hold by itself on glue.
Thanks - I linked this to the first post. Very nice work. I see you are a latex fan - you must be a mathematician?
Interesting that it’s not the modal vibrations that are chaotic, but the dynamics of the shape considered as a billiard, with balls or rays bouncing around. The modal patterns are still stable and predictable, but the fact of chaotic behavior in the billiard results in (or predicts) some favourable statistical properties in the modal frequencies and the spatial distribution of the mode shapes.
Hello Burnt
You remark is completely legitimate. The question is where to put the cursor between full reflection to no reflection. Some adjustment of the edges might help. At least it is a good thing to be aware of those black hole. I was really surprised with video. The aluminum barre is simply no more ringing. It is also the shape of the end of the bracing barre in guitar top no? When a panel is thinned in the voice coil area, is it that also?
Christian
Hello Paul,
Sorry, I was not clear... the connections in my neurons went to fast or more probably chaotic!
So about the guitar, I have only the contours. Reading your post, I thought I should have also taken notes of the hole characteristics (position, diameter) as it plays also a role in how the waves travel in the guitar top.
Then my brain jumps to the ABH and the paper linked : an ellipse with an ABH, thinking it might be something in your research area.
So, no more material from my side at the moment.
Christian