perhaps this paper has been discussed before - if so, please remove. If not then it may be useful for some pro and boombox reflex / sealed cabinets. (folded horn tend to self brace and 15mm plywood can be sufficient)
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https://core.ac.uk/download/pdf/84005542.pdf
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https://core.ac.uk/download/pdf/84005542.pdf
I have not seen this paper before, so I think it is a good thread topic.
It is always nice when experimental data confirms theory. This paper (along with Augerpro's work) nicely demonstrates the difference between an empty box and one that has acoustical damping (i.e. stuffing). The strong acoustical modes are quite effectively damped out.
The structural resonance, however, is a puzzle. The first structural mode was at 170 Hz in the un braced box. The addition of a single brace LOWERED the frequency and reduced its magnitude... We would normally expect the frequency to go up. Furthermore, if the resonant frequency is lowered, typically we would expect a larger magnitude, not less...
I have not yet read the modelling portion of the paper, so I don't have any comments on that portion yet.
It is always nice when experimental data confirms theory. This paper (along with Augerpro's work) nicely demonstrates the difference between an empty box and one that has acoustical damping (i.e. stuffing). The strong acoustical modes are quite effectively damped out.
The structural resonance, however, is a puzzle. The first structural mode was at 170 Hz in the un braced box. The addition of a single brace LOWERED the frequency and reduced its magnitude... We would normally expect the frequency to go up. Furthermore, if the resonant frequency is lowered, typically we would expect a larger magnitude, not less...
I have not yet read the modelling portion of the paper, so I don't have any comments on that portion yet.
Alot of this is common sense IMO. I dont know anyone who is somewhat SQ minded that would build a portable bass cab without any bracing. Some cheap junk does without bracing to cut costs and artificially boost output, but most musicians wouldn't bother with something that sounds so bad. Ive lugged around an old Ampeg SVT with matching 8×10 cab because I was picky about my sound, but now that I'm older I don't want to deal with the weight or size, so I use a single 15 with a 2x10 cab most of the time. Any bigger venu will have a PA and adequate monitoring so there's no need for all that output anymore. My heavy all tube stuff stays home strictly used for recording.
Yes. Like a lot of research papers, this one sets up a simplistic problem, and then solves it, leaving the reader to wonder "So what? I could have told you that... "
It is a common problem in all branches of engineering and science. 95% of research is either pointless, or it is the intellectual equivalent of baby food.
I think the interesting part of the paper will be the modelling, which I have not had a chance to dig into yet. But even then, I wish they would have modelled a well built, well braced cabinet, and then compared the model results with experimental data. A single stick brace with some corner braces is hardly a "best practices" design. What the world really needs is for someone to build a really nice CLD cabinet, and then model it... and then instrument the cabinet and compare measured results to model results.
can I draw your attention to this example of a FEA optimized cab:
https://www.diyaudio.com/forums/pa-systems/366187-backpack-challenge-5.html#post6614014
I have been working on a compact 12" sub design and have the weight down to 22kg using 12mm ply but alas 12" sub drivers even with neo motors are heavy. There is some hope though you can now get high quality 10" drivers from B&C ~3kg so perhaps in the future there will be lighter 12" drivers....
https://www.diyaudio.com/forums/pa-systems/366187-backpack-challenge-5.html#post6614014
I have been working on a compact 12" sub design and have the weight down to 22kg using 12mm ply but alas 12" sub drivers even with neo motors are heavy. There is some hope though you can now get high quality 10" drivers from B&C ~3kg so perhaps in the future there will be lighter 12" drivers....
The measurements follow what would be expected from the physics. A brace between the centres of two opposite panels will add the mass of the brace but no stiffness to the motion of the two opposite panels moving together with the brace. More mass with the same stiffness means resonance at a lower frequency.
In general this form of bracing is not particularly wise because it introduces a new lowest frequency mode. However, if the forces driving the mode from the driver hammering on the baffle and the internal air pressure (at low frequencies where it is significant) is symmetrical then the mode will in practise only be weakly driven.
To brace effectively with struts one should triangulate. For example, connecting the centres of adjacent rather than opposite panels. Another alternative is an internal panel rather than a strut and to lighten it with wisely placed holes. Gluing struts to struts in other directions helps a bit.
If a cabinet is (actually!) stiffened it will raise the frequency of the resonance but the magnitude of the sound radiated by the lowest frequency resonances will normally be roughly the same. You can see this in the BBC measurements, KEF LS50 white paper and the wall thickness simulation section of this paper. The reason for this is because although the deflection of the cabinet has reduced in magnitude due to the increased stiffness it requires less deflection at higher frequencies for equal loudness (e.g. size and deflection of woofer vs tweeter). The two effects roughly cancel although other factors like radiation patterns and how effectively the modes are driven can influence the result because it isn't strictly an apples to apples comparison.
The reason the weakly driven lowest frequency mode is present in the measurements and not the simulations is almost certainly because the driving forces introduced in the simulation are perfectly symmetric and hence the lowest mode is not driven at all rather than weakly driven as in the experiment. Had the students (this reads like an undergraduate project) shown the lowest few mode shapes and their frequencies this would be clear.
Anyway, it is an interesting paper and what is presented is repeatable by keen DIYers using less easy to use but free software for those that don't have access to expensive commercial FE packages like comsol. However, to measure the sound radiation from the cabinet around the audibility threshold of -20 to -40 dB (it is frequency dependent) or so below that from the drivers requires a more sophisticated measurement approach which is typically achieved by measuring the vibration over the whole of the cabinet surface. Similarly the magnitude of the cabinet resonances in the presence of the effective and strongly frequency dependent levels of damping required for an inaudible cabinet will require a more sophisticated approach to modal analysis than is present in most simulation codes if a Frequency Response Functions is to be viable with home computers.
" A brace between the centres of two opposite panels will add the mass of the brace but no stiffness to the motion of the two opposite panels moving together with the brace."
This would seem to lead to pre-tensioning. Conventional construction methods probably won't like it, especially at all the joints/edges. But pulling the panels together, perhaps from centroid, could create some interesting options. Probably best suited to a high strength material with special attention to the edge design.
This would seem to lead to pre-tensioning. Conventional construction methods probably won't like it, especially at all the joints/edges. But pulling the panels together, perhaps from centroid, could create some interesting options. Probably best suited to a high strength material with special attention to the edge design.
Not significantly if the struts are cut to something close to the distance between the panels given that the centre of large panels are far from stiff (which is of course why they are trying to be stiffened with struts!).
That wouldn't really count as pre-stressed/pre-tensioned. You pull the panels inward, towards the upper end of panel yield strength.
I think you might have got hold of the wrong end of the stick. If you place a weight at the centre of single vibrating panel it will then vibrate at a lower frequency because of the increased moving mass and the same stiffness from stretching the panel. I think this is fairly intuitive. If you now add another panel at the other of a strut you have pretty much the same setup with the two panels moving together.
Of course if the two panels try to move in opposite directions the stiffness is increased greatly. This is what people placing struts like this are seeking to achieve but they often don't appreciate that a new potentially problematic lower frequency mode has been introduced.
"I think you might have got hold of the wrong end of the stick."
What stick, the dark art of bracing? The example of placing a weight on the panel is not all convincing. Even within that example, it's implicit that the panel is effectively more stiff, i.e. physically displaces less. Otherwise how would you explain the lowering of frequency mode? So if you weigh down your panel at say 100kg and it rings at an undesirable frequency, my response is that a tensioned panel can be tuned to whatever arbitrary "weight" is desirable. Crank it up to 1000kg.
I would think that if you cut down on a panel's physical displacement you will have effectively reduced the amount of energy dissipation, whatever the frequency.
How else can I interpret the message; either you mean that a tensioned panel will not move less, or it will move less and that's bad?
What stick, the dark art of bracing? The example of placing a weight on the panel is not all convincing. Even within that example, it's implicit that the panel is effectively more stiff, i.e. physically displaces less. Otherwise how would you explain the lowering of frequency mode? So if you weigh down your panel at say 100kg and it rings at an undesirable frequency, my response is that a tensioned panel can be tuned to whatever arbitrary "weight" is desirable. Crank it up to 1000kg.
I would think that if you cut down on a panel's physical displacement you will have effectively reduced the amount of energy dissipation, whatever the frequency.
How else can I interpret the message; either you mean that a tensioned panel will not move less, or it will move less and that's bad?
Look for the BBC paper
I'm too lazy to look it up, but you may wish to look for the BBC paper from 1970 (-ish) that led to the design of their famous LS3 or LS5 (?) speakers. Its design goals included lightweight, well braced box. It has been discussed on this board.
I'm too lazy to look it up, but you may wish to look for the BBC paper from 1970 (-ish) that led to the design of their famous LS3 or LS5 (?) speakers. Its design goals included lightweight, well braced box. It has been discussed on this board.
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Try gluing with a rigid non flexible glue rings of heavy walled cardboard tubing cut to 1.5” lengths. These rings make the panels appear to be much thicker raising resonances while taking very little volume and breaking up standing waves with their curve shape. To test this take two identical panels and glue a few four inch dia rings on one. Knock on them and compare the sound. It’s as if the wood was doubled in thickness.
Thanks for the response on what you do and do not find intuitive. I had thought that most here would expect heavy weak structures to have their main resonances at lower frequencies and lighter stiffer ones to have theirs at higher frequencies. If this is not the case then it must follow that the physics of what causes resonances and hence the roles of mass, stiffness and damping in a cabinet structure cannot be known in even a vague but reasonably correct manner. Obviously I don't mean everyone reading the forum but it is informative about how someone discussing the sound radiation from cabinets would need to present things in order to reach a majority of readers.
To answer your question, the frequency of a particular mode/resonance of a structure is proportional to the square root of the stiffness involved divided by the mass involved. (I am being slightly vague because the mass and stiffness is distributed over a structure rather than being a single lump which requires calculus and integration for precision.) Adding mass at the centre of the panel is increasing the inertia of the motion signficantly without changing the bending stiffness of the panel. Hence the resonant frequency will be lower. This is what the paper is showing, what an engineer would expect but perhaps isn't what non-engineers would expect?
Effective pre-stressing will involve forces many orders of magnitude larger but can be relevant for some metal cabinets (e.g. the Nordic Tone) but not wooden ones. It is irrelevant to a discussion about how to effectively brace a large reasonably light wooden woofer cabinet of the kind in the paper.
But at higher frequencies the sound is moving the air faster compared to lower frequencies. Does that involve more energy, less energy or the same?
I clearly have little understanding of how you have interpreted what I posted which is interesting.
Andy your explanation is very plausible. I agree. However, it is not what I would normally expect. For most boxes, the first mode resonance is usually the two largest panels flexing in opposition, and adding a single stick brace has some stiffening effect. As you point out, a stick brace is not the ideal form of bracing.
Yes it is clear that since the resonance frequency was lowered, the attempt at stiffening was not effective. All that was achieved is added mass.
I was mildly surprised by the model simplifying assumptions made by the researchers (1) two opposing walls were modelled, the other 4 walls were rigid and sound proof, and (2) they used a clamped wall boundary condition for the two walls being modelled. Frankly I would have thought this would have created a lot more error than it did. Their model results were not any worse than most vibration-FEA I have seen.
j.
@andy19191
You can safely assume I'm a level 1 beginner. If the paper in the OP is being called out as pedestrian, then what is the threshold for how you address the audience, grad. level minimum?
I don't need to know physics to notice consistency. So far you've said a tensioned brace will have no impact, have negative impact, or have desired impact given the correct material. If this all came out in one response it would be a little easier to onboard.
The original suggestion for tensioned bracing had the key proviso baked in; that a suitable material is required.
I love the physics lessons though, keep em coming
You can safely assume I'm a level 1 beginner. If the paper in the OP is being called out as pedestrian, then what is the threshold for how you address the audience, grad. level minimum?
I don't need to know physics to notice consistency. So far you've said a tensioned brace will have no impact, have negative impact, or have desired impact given the correct material. If this all came out in one response it would be a little easier to onboard.
The original suggestion for tensioned bracing had the key proviso baked in; that a suitable material is required.
I love the physics lessons though, keep em coming
Usually the lowest frequency mode and the most troublesome (it radiates strongly in the direction of the listener) is the low frequency driver bouncing on the baffle. The rest of the cabinet will move in sympathy but the frequency primarily follows from the mass of the driver and the stiffness of the baffle. It is why studying the vibration of panels and boxes without the drivers present is likely to be as misleading as it is helpful without a familiarity with how speakers vibrate.
Adding the single brace at the panel centres will eliminate the mode where the strongest motion was the centres of the largest panels moving in opposite directions. This won't be one of the lowest modes which generally involves the whole speaker deforming but it is likely to be a significant one which needs addressing. That isn't the problem. The problem is that it has introduced a new lower frequency mode that would be loud if it was driven which it usually isn't except possibly weakly. Nonetheless introducing potentially problematic low frequency modes even if largely undriven is not something an experienced engineer would tend to do given it is easy enough to stiffen in other ways without creating this type of potential problem.
Perhaps it may be wise to state that generalising too much is unwise. Large and small speakers have different issues. 2 ways and 3 ways with separate bass boxes like this paper have different issues.
I must confess I did not read the words but only glanced at the pictures being familiar with the type of simulation and (incorrectly!) assuming they had performed a modal analysis of the cabinet and drivers using a simple model for damping which is unimportant if the objective is to push the frequency of the lowest resonance above the passband. Then used the motion of the cabinet with the BEM module in COMSOL to determine the radiated sound.
Having now scanned section 4.1 for the modelling I agree it looks a bit odd. DTU are capable in this area and assuming a supervisor was in the loop it suggests the project might have had other objectives apart from the study of cabinet vibration. The high computational cost of discretising the internal and external air would appear to bring only small benefits. Perhaps the sound from the port, playing with 3D distributions of the stuffing within the cabinet, or something else pushed things in that direction.
Whatever, it is interesting stuff and it's good to see people have a go at this type of thing.
Pedestrian? The paper reads like a decent student project. Nothing wrong with decent student projects.
Most speaker DIYers are not engineering graduates but will have been taught science and physics at school. How much of it has stuck and what else has picked up from an interest in speaker DIY is the question. I am aware that little that I have posted in the past seems to have been picked up and I am wondering to what extent it has been understood or wanted.
That is news to me since I wasn't aware of talking about tensioned braces (apart from the Nordic Tone reference) just standard ones as used in the paper and a fair few wooden DIY speaker cabinets.
^?????
Um....., I suggest using the center brace under tension and you flat out say it won't have an effect. You took my suggestion and neutered it by implying a scenario where the panel would be under a minimal tensile load. I clarify that the panels are to be loaded to a high degree of tension. You then claim that the effective outcome will be negative because, physics. I try to intuit your explanation as to why and you insinuate that it takes a big brain understanding of physics to weigh in on cab design. My erroneous intuition is pointed out by you as you then go on to affirm that a panel under tension can be effective given the correct material application. A proviso I had already established from the very first mention of putting a tensile load on the brace.
Doesn't ring a bell?
Not trying to be all agro, but you shot the suggestion down, apparently under the assumption that I would simply take your word for it. Having given you more information to work with, you then chose to unleash the snark by telling me I have the short end of the stick. Meaning what; I don't know physics, case closed? Not leaving me a lot of choice here other than to call out that you have changed your position three times while holding science over my head like I'm not qualified to weigh in. I can deal with snark. I can deal with rejected ideas. I can deal with both at the same time. But if you're gonna take me on a tour, rub my nose in physics, waffle on your original statement.... AND overlook basic detail written in a very concise couple of sentences given in the original suggestion... yeah, NO
Um....., I suggest using the center brace under tension and you flat out say it won't have an effect. You took my suggestion and neutered it by implying a scenario where the panel would be under a minimal tensile load. I clarify that the panels are to be loaded to a high degree of tension. You then claim that the effective outcome will be negative because, physics. I try to intuit your explanation as to why and you insinuate that it takes a big brain understanding of physics to weigh in on cab design. My erroneous intuition is pointed out by you as you then go on to affirm that a panel under tension can be effective given the correct material application. A proviso I had already established from the very first mention of putting a tensile load on the brace.
Doesn't ring a bell?
Not trying to be all agro, but you shot the suggestion down, apparently under the assumption that I would simply take your word for it. Having given you more information to work with, you then chose to unleash the snark by telling me I have the short end of the stick. Meaning what; I don't know physics, case closed? Not leaving me a lot of choice here other than to call out that you have changed your position three times while holding science over my head like I'm not qualified to weigh in. I can deal with snark. I can deal with rejected ideas. I can deal with both at the same time. But if you're gonna take me on a tour, rub my nose in physics, waffle on your original statement.... AND overlook basic detail written in a very concise couple of sentences given in the original suggestion... yeah, NO
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