Hello Burnt
I think too that having the panel close to the floor may be good thing for the bass to have benefit of the floor reflection, limiting the front to rear cancellation. My point here was more transmission of the vibrations of a solid (the panel) to an other solid (the floor for example) as with the cantilever there is not the filter offered by the more traditional surrounding foam (or strings for other).
Hello Steve
I have no experience with ABH... does it imply the material thickness? At the moment my understanding is no. It is more a matter of how the thickness decreases from the membrane thickness to zero to slow down the waves. This is for homogeneous material. What about sandwich?
Hi Christian,
The transmission of panel energy to the floor is exactly what happens. It is a wooden floor though and you might need spikes for carpeted flooring.
On cancellation DML’s are Bipolar rather than Dipoles so cancellation doesn’t occur. As a long time developer of electrostatics and before that open baffles it took a long time for me to accept this but it seems to be the case. DMLs are fascinating beasts.
Burnt
Christian
Technically, I think you are correct that the acoustical black hole does not necessarily require a thick panel. But it does require a fairly precisely machined profile. So I was thinking that it would be easier to hit that profile with a thicker material than with a very thin material. Likewise, I’m sure it’s possible in theory to create an acoustical black hole with a sandwich construction. But I think it would take a much more complex profile and be much more difficult to achieve in reality.
As Paul wrote, an acrylic or a poly carbonate plate might not be too hard to use to create an acoustical black hole. But of course you have the efficiency penalty of those materials.
Eric
Thanks Paul now I see. When I hear the word cantilevered, I usually think of clamped at one end and free at the other end. But you mean it only in the sense of free at one end. I do think the idea is kind of cool. in a way you’re making two or more panels from one. And combining the natural frequencies of both. That’s not a route that ever occurred to me. The one thing that I wonder about with this configuration is how well it will work when the exciter is so close to the fixed points. I’m wondering if the area between all those fix points might be a node or near a node for most of the natural frequencies, and hence make it hard to drive them. It’ll be interesting to see how it models.
Eric
Hi Eric
No, not clamped, but with 4 pins holding the panel to the frame, it's more or less rigidly supported, hopefully allowing similar dynamics from the free end as fully clamped. This idea of independent movement for low-end support is behind my ellipses panel (four different sized regions), and ideas about various asymmetric blobby shapes.
I doubt the fixed points close to exciter will hurt too much, may even help, because a circular fixed point should act as a dispersive structure, spreading incident rays (billiards again, see Sinai billiard
). I would be more worried about the straight edges of the panel close to the exciter causing local resonances. For that reason it may be better to shift one pair of the pins directly across from the exciter rather than on 4 corners, or put a cusp, or waist the panel near the exciter. Position of pins is probably better asymmetric, so no three of them lie in a straight line.It could also be an issue that the exciter may drive the cantilever(s) too hard, because you have a sort of a double see-saw, with the pins as hinges. But a fixed pin also gives a 'model-able' and easily modified point for adjusting the design, if you know what I mean. Position can be changed, and various elastomeric or viscoelastic support materials (as washers) can be tried without having to start again, as is necessary with soft support all round.
The worry about local reflections has kept me away from the idea of narrow, high aspect ratio panels, even though I can see they should have advantages like less comb filtering, better stereo image. Your success with them, this new idea, and the fact I have a cheap chinese 4030 milling machine that will accept a width of ~35 cm may lead me to towards that. They are certainly more practical and attractive than other shapes.
Any idea how to assess how much noise is generated by the edge of a panel vibrating close (eg 2-3 mm) to a fixed baffle?
The low-end extension of the cantilever came as no surprise to me, but the better modal density did. It's likely that most of those nodes will turn out to be non-productive because a lot of them are from torsion of the panel, leading to opposite pressures on each side of a narrow panel, and zero effect in the far field. The whole idea may turn out to be a flash in the pan, as is usual...
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Aspect ratio
I did some tests of the spacing of eigenfrequencies of panels with various aspect ratios, again for frequencies 0->1000 Hz. All panels are normalised to 0.5 m^2, 30 mm XPS, E=20 MPa , Rho=30 kg.m^-3, Poisson 0.35, soft support.
| Aspect ratio | Mean | S.D. | min | max | Count < 1000 |
| Rect 1:1 | 33 | 29 | 0.3 | 103 | 29 |
| Rect 2:1 | 33 | 24 | 0.1 | 80 | 29 |
| Rect 3:1 | 34 | 21 | 1.6 | 80 | 28 |
| Rect 4:1 | 32 | 23 | 0.3 | 73 | 28 |
| Stadium, effective aspect ~1.8 | 34 | 24 | 0.1 | 74 | 29 |
The main factor is the panel area, with panels of the same area having very consistent mean spacing. I hoped for a larger effect with perimeter length.
There does seem to be a beneficial effect of decreasing maximum spacing, and the stadium apparently achieves a reduction at 1.8 aspect ratio that only occurs for rectangles at 4:1. But there is little effect upon forcing apart the very close eigenfrequencies.
I looked at one of the high order eigenmodes for the stadium, hoping it would look relatively random, as is predicted by the quantum chaos stuff. It still looked highly symmetrical :-(.
I really don't even know whether these FEM tools can even be expected to show subtle effects like this anyway. It may be a case of GIGO.
Here's a link to the website (in Japanese, but most probably gets translated to English).
Hello Burnt
You might find the paper in this post 4313 interesting (I hope...). It shows the FR, the phase of the front and the rear wave (on the axis) of a DML (Canvas) and of an OB of the same size.
Yes DML are fascinating... Put one panel of moderate size on a furniture to get a wide range speaker with a wide dispersion. No box effect.
Christian
PS : the measurements and the conclusion about the phase is correct, I am no so sure for the conclusion about the reflections.
Hello PaulHi Eric
No, not clamped, but with 4 pins holding the panel to the frame, it's more or less rigidly supported, hopefully allowing similar dynamics from the free end as fully clamped. This idea of independent movement for low-end support is behind my ellipses panel (four different sized regions), and ideas about various asymmetric blobby shapes.
I doubt the fixed points close to exciter will hurt too much, may even help, because a circular fixed point should act as a dispersive structure, spreading incident rays (billiards again, see Sinai billiard
It could also be an issue that the exciter may drive the cantilever(s) too hard, because you have a sort of a double see-saw, with the pins as hinges. But a fixed pin also gives a 'model-able' and easily modified point for adjusting the design, if you know what I mean. Position can be changed, and various elastomeric or viscoelastic support materials (as washers) can be tried without having to start again, as is necessary with soft support all round.
The worry about local reflections has kept me away from the idea of narrow, high aspect ratio panels, even though I can see they should have advantages like less comb filtering, better stereo image. Your success with them, this new idea, and the fact I have a cheap chinese 4030 milling machine that will accept a width of ~35 cm may lead me to towards that. They are certainly more practical and attractive than other shapes.
Any idea how to assess how much noise is generated by the edge of a panel vibrating close (eg 2-3 mm) to a fixed baffle?
The low-end extension of the cantilever came as no surprise to me, but the better modal density did. It's likely that most of those nodes will turn out to be non-productive because a lot of them are from torsion of the panel, leading to opposite pressures on each side of a narrow panel, and zero effect in the far field. The whole idea may turn out to be a flash in the pan, as is usual...
I see, I think like Eric, that I was not in the right understanding of your idea making a direct connection between cantilever and clamp. In the literature about plate vibration, the cantilever plate seems to be a "classic" to describe a plate with 3 free edges and the fourth clamped. In your idea, the word "cantilever" describes each lobe starting from the points. Correct? A four point with free edges suspended plate?
By the way, I think I saw somewhere a cantilever DML (asymetric one with the lower side clamped as in the standard cantiler plate) but can't remember where...
Hi Christian
Yes a classic cantilever in architecture or in plates is to have one side fixed. I just name this cantilever to identify the intention or hope that the free ends would have relatively similar dynamics to a cantilever, and relatively independent of each other, giving higher ,oral density at LF. Maybe let’s call it the “centre pinned panel”.? I’m open to suggestions
I tried to model it last night with 2 pins to start, but the simple plate solver is giving me mode shapes like a free plate. Either I have not defines the edges of the mesh correctly, or the algorithm cannot deal with internal boundary conditions.
I think I've sorted the issue with boundaries. Looks like Elmer grid renumbers the boundaries. By opening in ElmerGui you can see the new numbers.
Looks like the idea of relatively independence of the two ends is borne out in the data, even with just 2 pins. The modes seem to be nicely interleaved too. But some are pretty clearly unproductive, and I think there may be fewer modes overall that if the ends were completely independent cantilevers).
Mode1 (7 Hz)
Mode 2 (21Hz)
Mode3 (26 Hz)
Mode 4 (45 Hz)
Mode 5( 59 Hz)
Mode 6 (81 Hz)
Here is an image of what I think is the first partial derivative of the displacement in y direction for the first mode, clearly showing the involvement of the pins:
Looks like the idea of relatively independence of the two ends is borne out in the data, even with just 2 pins. The modes seem to be nicely interleaved too. But some are pretty clearly unproductive, and I think there may be fewer modes overall that if the ends were completely independent cantilevers).
Mode1 (7 Hz)
Mode 2 (21Hz)
Mode3 (26 Hz)
Mode 4 (45 Hz)
Mode 5( 59 Hz)
Mode 6 (81 Hz)
Here is an image of what I think is the first partial derivative of the displacement in y direction for the first mode, clearly showing the involvement of the pins:
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Christian,
Here are the geo, msh and sif files for the above case. This sif file shows how eigenvalues are saved. Elmersolver saves the vtu file to the mesh folder for some reason, even though I have set "Results directory = "."
Commands:
elmergrid 14 2 cantilever.msh -autoclean -out mesh
elmersolver
I still haven't started using a proper workflow, being too caught up in little experiments. Without a workflow its easy to make mistakes about file versions, where things are being saved etc.
Paul
Here are the geo, msh and sif files for the above case. This sif file shows how eigenvalues are saved. Elmersolver saves the vtu file to the mesh folder for some reason, even though I have set "Results directory = "."
Commands:
elmergrid 14 2 cantilever.msh -autoclean -out mesh
elmersolver
I still haven't started using a proper workflow, being too caught up in little experiments. Without a workflow its easy to make mistakes about file versions, where things are being saved etc.
Paul
Hi Christian,
Thank you for sharing. Have you ever measured the phase of a rigid panel?
Burnt
Hello Burnt
Unfortunately no. At the time I did that, the canvas was the only available. The canvas offers to me the possibility to make an OB of about same dimension quite easily (some wood board avalable in close dimensions). If it is of first interest, I can think to do additional tests with my plywood panels but it will be not before 3 weeks from now (need the time at the right place). As there is no doubt in my mind that front and rear waves are out of phase (when the pressure increases in front, it decreases in the rear as the membrane keeps its constant thickness), I haven't given a follow to that test.
When I search for this post, I had the same thought than you : the weak point in the demo is canvas, not a more standard DML. Nevertheless, you can see the small difference between the bass at distance and at proximity. What is missing is the OB at proximity. This is something I could add even if the installation won't be exactly the same.
By the way, in the hypothesis of out of phase waves, there is for me a missing element which is how they combines and what is the difference with an OB. A very low frequency (1st mode) the membrane of the DML moves entirely in the same way... Some mystery remains... My knowledge in that is too low.
Christian
Hi Christian, for something so simple they have a very complex behavior.
I can well believe that the canvas version is dipolar, I have built one myself and panel displacement at low frequency and high volume was visible to the eye. At some time in the future it would be interesting to measure a rigid panel to see if there are any differences but in the end I don't really think is that important. My belief, rather than measurement, really stems from an article presented by Farad Azima back in 1999. If you are interested here is a link to a copy.
http://www.soundright.org.uk/NXTchaos.pdf
In the paper he explains that the front and rear radiation is uncorrelated and they sum constructively unlike a conventional panel speaker. He actually cautions against describing this as a bipole, or a statistical bipole, so my memory is obviously at fault here or I just abbreviated the description to bipolar as a lot of people have. It is the uncorrelated phases of the panel that allows both back and front radiation to sum constructively rather than cancel. Please don't go to any special effort on this on my behalf, your measurements are very clear, a canvas based DML has a dipole like radiation at the distance measured, there is no doubt about that.
Burnt
I can well believe that the canvas version is dipolar, I have built one myself and panel displacement at low frequency and high volume was visible to the eye. At some time in the future it would be interesting to measure a rigid panel to see if there are any differences but in the end I don't really think is that important. My belief, rather than measurement, really stems from an article presented by Farad Azima back in 1999. If you are interested here is a link to a copy.
http://www.soundright.org.uk/NXTchaos.pdf
In the paper he explains that the front and rear radiation is uncorrelated and they sum constructively unlike a conventional panel speaker. He actually cautions against describing this as a bipole, or a statistical bipole, so my memory is obviously at fault here or I just abbreviated the description to bipolar as a lot of people have. It is the uncorrelated phases of the panel that allows both back and front radiation to sum constructively rather than cancel. Please don't go to any special effort on this on my behalf, your measurements are very clear, a canvas based DML has a dipole like radiation at the distance measured, there is no doubt about that.
Burnt
That would indeed be nice. One of the reasons I've avoided irregular shapes is simply because there is no real way to guess at how productive each mode might be. With symmetric shapes it's much more obvious (or at least seems to be). But I have little doubt that with some irregular shapes a higher fraction of modes could be productive.
Eric
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Paul,
I thought degenerate meant this:
Okay, serious now: I never heard the concept of degenerate modes before but I think I have seen it in modelling, especially, with very symmetric dimensions.
Playing with ellipses the other day I got these two modes, at nearly the same frequency (of course).
I've seen similar things before with square or nearly square plates. I always assumed it was a modelling artifact. Is this what you are referring to?
Eric
