A Study of DMLs as a Full Range Speaker

Eric,
This is a plywood answering to a MIL standard.
Have you considered the plywood coming in different thickness, species used in aircraft modelling? I found some interesting possibilities at french retailers (site only in french). Their plywood is said "aircraft" but with no certification for real aircraft use. I haven't search for more international retailers... This one in the US : https://shop.balsausa.com/category_s/1131.htm ? It is the kind of the kind of products I have seen in France.
I recorded also in my list of possibilities interesting store this one in Spain specialized in products for guitar making : https://www.madinter.com/en/ . No plywood but other products that might be interesting one day.
Christian

Christian,
It's a good idea but the ones I find on the aircraft modeling sites usually don't have panels more than 30 cm wide. Possibly that could be okay, but maybe on the too small side, I fear. The guitar soundboards are similarly small. I don't know exactly how to use them. Glue their edges to make larger panels and use like that, or add ribs to stiffen the cross direction? Added ribs are harder to model, so I'm not sure how how to design. But that doesn't mean they couldn't be good, just that they might require better tools, or more iterations, to design.
Eric
 
I read the first chapter of the piano soundboard paper (the only one in english). Very interesting how many concepts are common between musical instruments and our goals here. I split off the appendices and tried to translate, but the equations were mangled. Those appendices cover a lot of the important concepts for our purposes.

The factor that has been the subject of much discussion here (and forgive me, I havn't read all the correspondence on the matter!) appears early in the paper (p8) as 'radiation ratio' , 'acoustical constant' or 'Shelleng's vibration parameter

R=sqrt(E/rho^3)

I was about to refer to this paper https://sci-hub.se/https://doi.org/10.1121/1.4906186 which relates radiation efficiency for f<fc to damping factor eta. Then I read that the piano paper also draws a connection to damping. And indeed, with Eric's graph of acrylic vs plywood vs foam giving increasing SPL seems to suggest it could be damping playing a role.

I have to read these more carefully, as Im not sure I understand anyway. There are at least 3 sources of damping mentioned in papers, which is really just talking about energy losses - internal frictional damping, conductive damping (energy lost eg to the frame and surroundings) and radiation damping - the energy lost to radiated sound. If the relation is just between this factor and radiation damping, then it may be just another way of stating the same thing. And I cant see why the factor would have a relation to viscoelastic damping anyhow. OTOH the paper I cited above is talking about internal, viscoelastic/frictional damping related to greater efficiency at low f.

PS Inline html for greek characters doesn't seem to work. Have to use unicode entry I guess.
Hello Paul
Sorry no time right now to go deeply in your post. Just 2 points.
You can google the name of the author of the paper. Perhaps more things in English.
I will try to have a look on the most interesting parts, I might perhaps help in translation.
@Veleric : Eric, have you already found more in English around this thesis?
Christian
 
Christian,
It's a good idea but the ones I find on the aircraft modeling sites usually don't have panels more than 30 cm wide. Possibly that could be okay, but maybe on the too small side, I fear. The guitar soundboards are similarly small. I don't know exactly how to use them. Glue their edges to make larger panels and use like that, or add ribs to stiffen the cross direction? Added ribs are harder to model, so I'm not sure how how to design. But that doesn't mean they couldn't be good, just that they might require better tools, or more iterations, to design.
Eric
Hello Eric,
Same problem on my side. Most of the sources of plywood are 30cm... One in France offer wider one.
The other link is dedicated to the guitar building. If I remember from Youtube, guitar makers use board from the same tree glued by the edge so that they have a symmetric picture of the grain.
Yes ribs add a technical difficulty in a calculation approach... by the way, I don't think we (I at least) are very advanced on this way...
Christian
 
I recorded also in my list of possibilities interesting store this one in Spain specialized in products for guitar making : https://www.madinter.com/en/ . No plywood but other products that might be interesting one day.
Christian
Fascinating! Looking at the soundboards... I'm assuming two pieces get edge glued to form the board....I wonder how difficult that is for someone without specialized tools, to get a nice smooth bond. If I thought I could do it well without too much headache I might order some to try.
 
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Browsing aircraft plywood...

What do we think of very thin plywoods? I remember a few references to testing way back but has there been much exploration of plywoods down to 1mm and beyond? The varieties offered on the aircraft plywood have me entrigued.

If you were going to pick one to play with, what thickness would you start with?
 
Fascinating! Looking at the soundboards... I'm assuming two pieces get edge glued to form the board....I wonder how difficult that is for someone without specialized tools, to get a nice smooth bond. If I thought I could do it well without too much headache I might order some to try.
If the question is how to glue edge to edge... this is not the most difficult. There are video on Youtube showing that (sorry I don't have the link). Basically, put the 2 pieces side to side, put a tape on the junction, open like a book, put the glue on both edges, close and add tape on the second side. String instrument makers use ropes to keep the 2 pieces under pressure and flat. Not tested for now but seems accessible.
Christian
 
Fascinating! Looking at the soundboards... I'm assuming two pieces get edge glued to form the board....I wonder how difficult that is for someone without specialized tools, to get a nice smooth bond. If I thought I could do it well without too much headache I might order some to try.
I don't know how you are "supposed" to do it, but I've edge glued pieces of 1/8" (and 1/16") balsa together pretty successfully. I applied PVA glue to the edges, then used strips of masking tape every 3 or 4 inches, and then laid it on a smooth flat surface. After the glue dried I sanded both sides gently with a palm sander. It looked pretty good, however, I was using it as a core for a carbon fiber sandwich, so it didn't really matter what it looked like.
Eric
 
If the question is how to glue edge to edge... this is not the most difficult. There are video on Youtube showing that (sorry I don't have the link). Basically, put the 2 pieces side to side, put a tape on the junction, open like a book, put the glue on both edges, close and add tape on the second side. String instrument makers use ropes to keep the 2 pieces under pressure and flat. Not tested for now but seems accessible.
Christian
Yeah, that's similar to what I did.
Eric
 
Browsing aircraft plywood...

What do we think of very thin plywoods? I remember a few references to testing way back but has there been much exploration of plywoods down to 1mm and beyond? The varieties offered on the aircraft plywood have me entrigued.

If you were going to pick one to play with, what thickness would you start with?
NaRenaud,
What source(s) are you looking at for the aircraft plywood? For myself, I'd be looking for (1) the thinnest 5 ply structure and (2) the lowest density species.
Concerning the number of plies, a 3 ply structure might be okay, but the strategy I'm working on really only works well if the difference in stiffness between the two directions is not too great. The three ply structures often are close to 10 times stiffer in the direction of the grain on the surface plies, so don't interest me at the moment.
Eric
 
Browsing aircraft plywood...

What do we think of very thin plywoods? I remember a few references to testing way back but has there been much exploration of plywoods down to 1mm and beyond? The varieties offered on the aircraft plywood have me entrigued.

If you were going to pick one to play with, what thickness would you start with?
This question is still open for me... I don't know how are those plywood. If the efficiency is related to E/rho³, the thickness reduction won't increase the efficiency. Then the question is why to go to such plywood? One answer is to reduce the panel dimensions for a given 1st mode or reach lower 1st mode in similar dimensions. We might think there is a limit in the thickness reduction. Is there a condition that will stop the bending wave? Is there a condition that will make the modes disappear? So the best way should be to find some samples to make tests.
In M Azima's paper NXT Where a little chaos is good for you , one characteristic of DML listed is they are scalable. That means that you can test on a small panel. When going to a larger one with the same proportions, the bandwidth will be extended to the low frequencies. There are probably some restriction in that like the role of the suspension and nothing says if there is a limit in the increase of the dimension. At the moment, I am in favor of mock up in the dimensions 20cm width.
Christian
 
I read the first chapter of the piano soundboard paper (the only one in english). Very interesting how many concepts are common between musical instruments and our goals here. I split off the appendices and tried to translate, but the equations were mangled. Those appendices cover a lot of the important concepts for our purposes.

The factor that has been the subject of much discussion here (and forgive me, I havn't read all the correspondence on the matter!) appears early in the paper (p8) as 'radiation ratio' , 'acoustical constant' or 'Shelleng's vibration parameter

R=sqrt(E/rho^3)

I was about to refer to this paper https://sci-hub.se/https://doi.org/10.1121/1.4906186 which relates radiation efficiency for f<fc to damping factor eta. Then I read that the piano paper also draws a connection to damping. And indeed, with Eric's graph of acrylic vs plywood vs foam giving increasing SPL seems to suggest it could be damping playing a role.

I have to read these more carefully, as Im not sure I understand anyway. There are at least 3 sources of damping mentioned in papers, which is really just talking about energy losses - internal frictional damping, conductive damping (energy lost eg to the frame and surroundings) and radiation damping - the energy lost to radiated sound. If the relation is just between this factor and radiation damping, then it may be just another way of stating the same thing. And I cant see why the factor would have a relation to viscoelastic damping anyhow. OTOH the paper I cited above is talking about internal, viscoelastic/frictional damping related to greater efficiency at low f.

PS Inline html for greek characters doesn't seem to work. Have to use unicode entry I guess.
Paul
I think you are referring to the graph of my post #4664. This graph was made after some tests where I measured the SPL (Umik mic with REW with a limited bandwidth pinknoise) at distance. Those tests are probably far from to be very precise. It shows me the low (even no) influence of the thickness and a not to bad alignment of SPL=f(sqrt(E/rho³)). I don't understand the link you propose with damping in this graph.
I am pretty sure the damping as a role but until now I have no idea how to approach it. In the paper you linked, I am a bit lost when the authors use the radiation efficiency. My skills in acoustics are too low... I am lost at the first line : the radiation efficiency is the ratio of the sound power radiated from a structure (ok I understand that...) to that of a piston of the same size moving with the same average velocity (??? I can't imagine such source as a reference, what would be its FR???).
I propose this link for the paper : Radiation efficiency of damped plates (free access).
Christian
 
Christian,
It's a good idea but the ones I find on the aircraft modeling sites usually don't have panels more than 30 cm wide. Possibly that could be okay, but maybe on the too small side, I fear. The guitar soundboards are similarly small. I don't know exactly how to use them. Glue their edges to make larger panels and use like that, or add ribs to stiffen the cross direction? Added ribs are harder to model, so I'm not sure how how to design. But that doesn't mean they couldn't be good, just that they might require better tools, or more iterations, to design.
Eric
Eric,
I am not sure that instrument soundboard will do the job has we expect. M Ege who wrote the thesis mentions in another paper (Synthetic description of the piano soundboard mechanical mobility) that above 1.1kHz in his case, there is a change in behavior. It is when the distance between the ribs are equal to one half wave length (don't come to the conclusion I have read and understood all the paper, very far of that, just pick that element).
If there were not so many things to test, I think I'd glue some boards together and then add ribs. It is to early for me to add new parameters. I will stay on a structure where we can assume the geometry doesn't create a change within the bandwidth (thin enough, cells small enough if composite and so on...).
Christian
 
low quality 3 ply from an old veg crate .
i will post a picture of the two panels playing.
on the right is the old art panel i cut up to insert the new 185 x 175cm panel.
on the left is the naked panel with only the exciter attached .
both panels are running full range , the art panel goes down to 40hz but the naked panel only goes down to about 140hz so i added a couple of weights to bring down the response to 100hz.
no sub used.
recorded at 1m as usual.
m4a.
a very detailed sound with plenty of ambiance .
steve.
 

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Pictures of low quality 3mm ply panels.
The second picture is of the weights attached in the corners to increase the output down to 100hz.
This is a very basic panel without me even doing anything to improve the sound ,yet !
Not that it needs much doing to it.
It is a very flexible panel and bends easily.
Steve.
 

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Paul
I think you are referring to the graph of my post #4664. This graph was made after some tests where I measured the SPL (Umik mic with REW with a limited bandwidth pinknoise) at distance. Those tests are probably far from to be very precise. It shows me the low (even no) influence of the thickness and a not to bad alignment of SPL=f(sqrt(E/rho³)). I don't understand the link you propose with damping in this graph.
I am pretty sure the damping as a role but until now I have no idea how to approach it. In the paper you linked, I am a bit lost when the authors use the radiation efficiency. My skills in acoustics are too low... I am lost at the first line : the radiation efficiency is the ratio of the sound power radiated from a structure (ok I understand that...) to that of a piston of the same size moving with the same average velocity (??? I can't imagine such source as a reference, what would be its FR???).
I propose this link for the paper : Radiation efficiency of damped plates (free access).
Christian
Sorry it was your graph, not Eric's. I only meant this seems to support a relation to damping because I would expect the damping factors to be in that order: acrylic < ply < foam.

Im learning too, piece by piece as time permits (unfortunately you need ALL the pieces for a proper understanding - these phonomena are complex). The basic idea for efficiency is to describe how well a moving (vibrating) object transfers kinetic energy of a body (mean-square velocity) into sound waves. The piston is used as a reference because its a simple model whose theoretical behaviour is well characterised. Efficiency is not really the right word, because it can be >100% (ie more efficient than the piston reference).

Im trying to understand the relation of the Scheleng parameter R to damping. They say:

Screen Shot 2022-04-17 at 12.45.40 pm.jpg


This damping factor is radiative damping - not energy lost in the material, but energy lost to sound. In other words, they are talking about radiative efficiency, as you said in the beginning. Note also the factor A which confirms that longer panels are better radiators at low frequency.

It's insightful to state it this way, because a higher radiative damping means both higher SPL, and a tighter impulse response, because the panel is losing energy to the air, not resonating too much.

This is a simple relation because it relates only to one frequency - the fundamental resonance. But I guess we can assume that a higher R value increases efficiency for all f < fc.
 
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View attachment 1045404

This damping factor is radiative damping - not energy lost in the material, but energy lost to sound. In other words, they are talking about radiative efficiency, as you said in the beginning. Note also the factor A which confirms that longer panels are better radiators at low frequency.

Hi pway - I'd like to think that, as I prefer panels about 3:1 but for low Fo you need low A in that formula -> @1:1 the fractional part = 2, and @ 4:1 it equals 4.25. So worse not better.

Makes sense to me for isotropic plates as the skinny side stiffness predominates (depending on support conditions). However, in real life, natural timber and plywood are anisotropic which is of fundamental importance to the behaviour/performance of rectangular panels. Balancing lateral and longitudinal stiffnesses with aspect ratios is a goal for me.

Eucy
 
Eucy,
Revply is a US thing, so Christian has not tried it. But the 5 ply construction with thin outer layers is actually pretty common in the US for "underlayment" plywoods. These plywoods commonly use quite light core layers, which are surprisingly free of voids and such (for their cost). And curiously, they use an attractive reconstituted veneer face later. This construction leads to a pretty light and stiff panel, with similar stiffness in both directions and prettier face than most plywoods. So overall they make decent inexpensive panels.
I'm not sure what photo suggested "excessive" flexibility, but generally they are much stiffer in the "cross" direction than most any three layer plywood having roughly equal thickness layers.
Sadly, of late, the supply and quality of these plywoods has diminished considerably, in my area at least.
Eric
Thanks Eric

Would be interesting to try

Eucy
 
Sorry it was your graph, not Eric's. I only meant this seems to support a relation to damping because I would expect the damping factors to be in that order: acrylic < ply < foam.

Im learning too, piece by piece as time permits (unfortunately you need ALL the pieces for a proper understanding - these phonomena are complex). The basic idea for efficiency is to describe how well a moving (vibrating) object transfers kinetic energy of a body (mean-square velocity) into sound waves. The piston is used as a reference because its a simple model whose theoretical behaviour is well characterised. Efficiency is not really the right word, because it can be >100% (ie more efficient than the piston reference).

Im trying to understand the relation of the Scheleng parameter R to damping. They say:

View attachment 1045404

This damping factor is radiative damping - not energy lost in the material, but energy lost to sound. In other words, they are talking about radiative efficiency, as you said in the beginning. Note also the factor A which confirms that longer panels are better radiators at low frequency.

It's insightful to state it this way, because a higher radiative damping means both higher SPL, and a tighter impulse response, because the panel is losing energy to the air, not resonating too much.

This is a simple relation because it relates only to one frequency - the fundamental resonance. But I guess we can assume that a higher R value increases efficiency for all f < fc.
I see the difference in the vocabulary. 2nd order response being in my "standard tools", automatically I relate "damping" word to the energy absorption! OK got it.
You are pointing an interesting factor with the form factor A. I don't know if I have all the data, probably yes, to input this correction in the graph. It might be quite easy to compare the SPL of 2 panels of the same material with a different form factor.
For now, I won't link this radiative damping (or efficiency) to the impulse response. The impulse response is build from the response at each frequency and then the damping (energy loss according the time) at each frequency which in my current understanding is link to some properties of the material not in the relations above. If we refer to simple 2nd order system, the damping is not in the mass (density), in the stiffness (Young module) but in a third parameter (loss, internal friction).
I agree on the last assumption. It seems the behavior changes near fc.
Christian
 
Hi pway - I'd like to think that, as I prefer panels about 3:1 but for low Fo you need low A in that formula -> @1:1 the fractional part = 2, and @ 4:1 it equals 4.25. So worse not better.

Makes sense to me for isotropic plates as the skinny side stiffness predominates (depending on support conditions). However, in real life, natural timber and plywood are anisotropic which is of fundamental importance to the behaviour/performance of rectangular panels. Balancing lateral and longitudinal stiffnesses with aspect ratios is a goal for me.

Eucy
Hello Eucy
This is a relation about efficiency. The highest A or R in this relation, the highest SPL. This relation doesn't give the F0 which is related to an other "A" which is the panel area and also the form factor... so additional math needed to have a better picture including what about the SPL and F0 following the choice of a and b.
Christian
 
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