No matter what the mass and stiffness there will be some frequency of fundamental resonance. At that frequency, if there is no damping then the transmission will be total (mass and stiffness reactances have cancelled and no loss was incorporated into the system). Of course, with a complex structure such as a cabinet there are multiple resonant modes (as well as the coincidence modes) for each side.
Not exciting the frequencies assumes you can push them up to the point of being out of band. If we are talking a subwoofer then I can believe that a concrete cabinet can have resonances pushed above 100 cycles or so and be totally nonresonant in band. For a 2 way you would need to get above 2 to 3 k. I'm not sure about concrete, but I know that wooden cabinets with crazy thickness and stiffness don't get the resonances above 2K.
Harwood showed two things of importance: resonances were more audible if moved up into the midrange (less audible if left low in frequency) and damping, required to get most cabinet resonances lower than the threshold he found in listening tests, became less effective as the cabinets got thicker/heavier/stiffer.
Finally, correct me if I'm wrong but the excitation of resonances is not related to excitation level. That is, you don't need a certain amount of energy to get the cabinet to vibrate.
David S.
+1 Dave, I agree with pretty much all of that.
The (perhaps random) thought of using 8mm thick granite tiles, was stiffness density, and a thick layer of felt for sure, maybe other measures to tame the 'ring', and probably more significantly, the reflective properties of harder, dense materials. I am undecided whether to attempt to decouple each panel at the corners, to further damp them. could work or could be disastrous!
Ive also heard thick Al plate boxed 7-10 litre speakers, and they didnt ring much. but the walls were 20mm thick....not very heavy really, and deader than I imagined.
The (perhaps random) thought of using 8mm thick granite tiles, was stiffness density, and a thick layer of felt for sure, maybe other measures to tame the 'ring', and probably more significantly, the reflective properties of harder, dense materials. I am undecided whether to attempt to decouple each panel at the corners, to further damp them. could work or could be disastrous!
Ive also heard thick Al plate boxed 7-10 litre speakers, and they didnt ring much. but the walls were 20mm thick....not very heavy really, and deader than I imagined.
I think you may be mistaken. *After re-reading, I may have misunderstood/or be mistaken myself...
My control theory is a little rough, but Im fairly certain that a system, when subjected to a Step input, then magnitude is indeed significant, to the resultant decay duration/time. If one assumes that we are in time domain, then we assume final steady state value ONLY then you are correct. Since unless it is of greater Q than critically damped it will not oscillate and steady state will rest at zero, or the K, gain value of the system Laplace function.
Hang on..
step input magnitude would effect the resonant decay time though, wouldnt it? In a heavily resonant system, this would 'swell'.
Maybe IM mistaken...not sure now lol
Also, perhaps stabbing in the dark here; I would GUESS that a panel resonance is a MCK mechanical system, and of 2nd order in nature. If this IS indeed the case, then it is perfectly possible to attempt to engineer a well damped 2nd order transfer function, (of a rolloff of between 1st and 2nd order), from which one could extrapolate the damping/stiffness ratio for a panel of known mass, until you get a good match?
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Like in designing a tweeter, the goal is to push the first few (strongest) modes as high as possible unless it interferes with our perception sensitivity. By any means neccessary 🙂 B&W Matrix? Many things changed since Harwood wrote his paper. You are missing the point of the paper, it is not a methodology of using thin damped panels, it is defining the critical bands. That's far more valuable information. He was right then as he is now. But that is only one way of doing things.
Heavier panels have more 'capacity' to store, so more damping has to be used. Thick and thin sould be used 'in relation to'.
Mondo has a point. Amount and duration of energy input is proportional to the stored energy and decay. Frictionless systems exist only on paper. There is a buildup and a release of energy.
I think that this conversation should be in a way of 'What are we trying to do?' not 'How?'. For every problem there is a solution.
if we have a given acceptable max panel resonance Q value, then SOMEONE out there, could calc the required transfer function. The damping co-eff of material, is the one factor or the TF. unless its a first order, which i doubt.(maybe odd only, not sure). If we form a plot of acceptable ring cycles, or time, against frequency, calc the fundamental or measure, ref the plot, find the Q. Im sure theres actually a lot more to it than that though, and its just my simplistic view lol.
Another aside: if we consider a step input, 1 by s input, then im not sure im correct. I think a sina input, perhaps more a ramp imput of short duration, sine could be the way to go in actuality. Doing that for many frequencies? Phew. That would be hard work
Another aside: if we consider a step input, 1 by s input, then im not sure im correct. I think a sina input, perhaps more a ramp imput of short duration, sine could be the way to go in actuality. Doing that for many frequencies? Phew. That would be hard work
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Pushing a tweeter resonance up makes sense. When I started my career there were still phenolic dome tweeters with resonances around 12 k. Moving those to 20k and beyond is a worthwhile improvement. It is not the same with cabinets. Realistic materials will not get resonance up beyond the crossover point of a 2 way system. As such you can't get them out of range. Harwood shows that they are more audible at higher frequencies than if left low (read the paper!)
I think the only thing that has changed since Harwood's time is that a generation of audiophiles have convinced themselves that heavier and stiffer is always better. What he showed was that the ratio of damping to stiffness is crucial and that conventional cabinets with wood products had little damping. He was interested in fiberglass as a potential future material.
Today wooden cabinets are still the norm for 90%+ of the market and it is clear that thinner walls and thicker damping material is the way to a higher performance cabinet.
I'm not sure what your point is. Cabinets are not frictinless but their resonances are quite high Q. The first half of the Harwood paper he is measuring material Q and finding numbers in double digits. At every resonance mass and stiffness reactances cancel and the only material parameter left (at that frequency) is frictional loss. Both Harwood's and Sowter's studies have examples showing that increasing wall thickness of a given material pushed resonances up a moderate amount (not out of band) and retained the same breakthrough level (same Q). But since mechanical impedance would be raised, even more damping would be required to lower the level of resonance.
If you want to reduce the level of breakthrough at resonance you need to add damping. The higher the mass and stiffness the greater the damping that will be required. Simple physics.
David S.
Ah. 🙂
It's not simply about the modal structure of the panel. While a panel with greater stiffness may have a grouping of modes higher in freq.., it doesn't mean that it will be higher in AMPLITUDE.
How much force? How is it applied?
Going back to your car panel analogy..
(conceptually):
1. Lightly tap a car panel (in it's real-world thickness)
2. Lightly tap a car panel that is an inch thick.
Which will display the higher amplitude?
Much confusion about what resonance means.
Mass is a positive reactance. Stiffness is a negative reactance. They are both imaginary values as in related to the square root of minus 1 or j. Because one is a positve reactance and the other negative you can picture them as being 90 degrees removed from the real valued component of resistance, 90 degrees in opposite directions (180 degrees apart from each other). They are vectors that point in opposite directions and vary in strength with frequency. Mass reactance doubles every Octave you go up and stiffness reactance halves every Octave you go up. That means that for any mass you can think of and any stiffness, there is some frequency where they would have exactly equal but opposite values. If they are coupled in a simple second order system that frequency would represent their frequency of resonance.
At that frequency it takes no effort at all to set them in motion and maintain that motion. So a child on a swing, a car on its springs (with no shocks), the Tacoma bridge (try u-tube), a swaying building, ocean waves, Big Ben the bell, in fact any structure, no matter how huge can be made to oscillate happily at its resonance because its considerable mass is just canceled out by its considerable stiffness.
We rebel at this intuitively, thinking that if we add mass to a structure we must be making it harder to move. For the most part that is true, but at resonance it is not true. At resonance the stiffness and mass are equal and opposite, one cancels the other and the massiveness becomes irrelevant.
All this is for the lossless case or a system of high Q. If we add shock absorbers to our car it takes great effort to bounce it at the resonance frequency. But all of that effort is going into frictional loss of the shock absorber alone. The mass of the car and the stiffness of the springs are still cancelling so the only impedance left is the shock absorber's resistance.
The same is true for cabinet walls. Every resonance is a special frequency where mass reactances and stiffness reactances are equal and have cancelled and the only thing preventing perpetual oscillation is the resistive loss of the material itself or that we might apply to its surface. Move away from the frequency and, yes, the heavy walls might be hard to displace, but not at resonance.
David S.
Mass is a positive reactance. Stiffness is a negative reactance. They are both imaginary values as in related to the square root of minus 1 or j. Because one is a positve reactance and the other negative you can picture them as being 90 degrees removed from the real valued component of resistance, 90 degrees in opposite directions (180 degrees apart from each other). They are vectors that point in opposite directions and vary in strength with frequency. Mass reactance doubles every Octave you go up and stiffness reactance halves every Octave you go up. That means that for any mass you can think of and any stiffness, there is some frequency where they would have exactly equal but opposite values. If they are coupled in a simple second order system that frequency would represent their frequency of resonance.
At that frequency it takes no effort at all to set them in motion and maintain that motion. So a child on a swing, a car on its springs (with no shocks), the Tacoma bridge (try u-tube), a swaying building, ocean waves, Big Ben the bell, in fact any structure, no matter how huge can be made to oscillate happily at its resonance because its considerable mass is just canceled out by its considerable stiffness.
We rebel at this intuitively, thinking that if we add mass to a structure we must be making it harder to move. For the most part that is true, but at resonance it is not true. At resonance the stiffness and mass are equal and opposite, one cancels the other and the massiveness becomes irrelevant.
All this is for the lossless case or a system of high Q. If we add shock absorbers to our car it takes great effort to bounce it at the resonance frequency. But all of that effort is going into frictional loss of the shock absorber alone. The mass of the car and the stiffness of the springs are still cancelling so the only impedance left is the shock absorber's resistance.
The same is true for cabinet walls. Every resonance is a special frequency where mass reactances and stiffness reactances are equal and have cancelled and the only thing preventing perpetual oscillation is the resistive loss of the material itself or that we might apply to its surface. Move away from the frequency and, yes, the heavy walls might be hard to displace, but not at resonance.
David S.
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I am happy to accept there is more than one solution but they need to be quantifiable. Solution X or Y will have a given set of properties that allow for minimal cabinet resonance. It is measureable and quantifiable, yet the research and data is painfully lacking.
The BBC paper is the only one that analyses the problem and comes up with soultions backed up by measurements. It proves that rigid heavy + braced wood enclosure materials are inferior to light damped ones. Ive seen no research from the "rigid and heavy" gang suggesting the opposite and yet the "inferior" techinique is employed in most of cases. It makes no sense whatsoever.
concrete used for extreme vibration control -
very Extreme -
Japanese aircraft carrier Shinano - Wikipedia, the free encyclopedia
sometimes people get carried away, by whatever gets their attention.
much like small childern , dave/mini-dave have a new game,
hopefully they will realize what this is,
and stop before they get into too much trouble.
(or seriously hurt anyone)
basically this is what is happening -
its ok to go the wrong way for a while,
as most people will grow out of that sort of thing.
``````````````````````````````````````````````````````
so what happens should they not get some maturity?
(and this isn't about religion, this is about Reality)
what happens when someone gos way too far the wrong way
very Extreme -
Japanese aircraft carrier Shinano - Wikipedia, the free encyclopedia
sometimes people get carried away, by whatever gets their attention.
much like small childern , dave/mini-dave have a new game,
hopefully they will realize what this is,
and stop before they get into too much trouble.
(or seriously hurt anyone)
basically this is what is happening -
An externally hosted image should be here but it was not working when we last tested it.
its ok to go the wrong way for a while,
as most people will grow out of that sort of thing.
``````````````````````````````````````````````````````
so what happens should they not get some maturity?
(and this isn't about religion, this is about Reality)
what happens when someone gos way too far the wrong way
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It is not my intention to "seriously hurt anyone":
By teaching a little physics.
By questioning mistaken beliefs.
By highlighting important research.
Apologies if I've distressed anyone previously comfortable in their views.
David
By teaching a little physics.
By questioning mistaken beliefs.
By highlighting important research.
Apologies if I've distressed anyone previously comfortable in their views.
David
Ok, all of you nerds break out your glasses. It's going to get tough. I'll try to teleport Dave to the present. And I'm probably going to make mistakes.
Due to Hooke's law of elasticity stiffness up to proportionality can be written as:
restoring force = -stiffness x travel or
F=-sx
Due to Newton's law we have an expression:
mass x acceleration = restoring force or
ma=-sx or
ma + sx = 0
If we introduce damping it looks like:
ma + sx + rx' = 0
Considering that we do not want to solve a simple problem we have to introduce 3D space. By implementing it in a multiple degrees of freedom system we can calculate displacement for each consecutive node of spatial matrix. In matrix form we can write it as:
[M]{u''}+[C]{u'}+[K]{u}={F}
where M stands for mass, C for damping, K for restoring force and F for force that displaces the node. M,C & K matrices are constant with time, but node displacement isn't. So, performing modal analysis for a given no of mode shapes we get natural frequencies. We can do it in two ways: 1. stimulate the model with ie. sinus tones (which is more likely to happen in the loudspeaker) or 2. using transient analysis (similar like ringing a bell). This is actually a huge subject so I'm going to stop now.
So, using a set of circumstances, we can determine pretty much what is going to happen inside the material if we use proper boundary conditions (restraint, force etc) and material coefficients. There might get loud if we go past proportionality limit of the material and that calls for correction with real measured Hooke's diagram.
Another way would be intentionally subjecting a structure to vibrate and then concentrating the damping in the most suitable place. Whatever rocks your boat.
I understod your comment, Dave, on 90% of box material usage. It's all about economy and extra profit 🙂 zero technology and science.
Due to Hooke's law of elasticity stiffness up to proportionality can be written as:
restoring force = -stiffness x travel or
F=-sx
Due to Newton's law we have an expression:
mass x acceleration = restoring force or
ma=-sx or
ma + sx = 0
If we introduce damping it looks like:
ma + sx + rx' = 0
Considering that we do not want to solve a simple problem we have to introduce 3D space. By implementing it in a multiple degrees of freedom system we can calculate displacement for each consecutive node of spatial matrix. In matrix form we can write it as:
[M]{u''}+[C]{u'}+[K]{u}={F}
where M stands for mass, C for damping, K for restoring force and F for force that displaces the node. M,C & K matrices are constant with time, but node displacement isn't. So, performing modal analysis for a given no of mode shapes we get natural frequencies. We can do it in two ways: 1. stimulate the model with ie. sinus tones (which is more likely to happen in the loudspeaker) or 2. using transient analysis (similar like ringing a bell). This is actually a huge subject so I'm going to stop now.
So, using a set of circumstances, we can determine pretty much what is going to happen inside the material if we use proper boundary conditions (restraint, force etc) and material coefficients. There might get loud if we go past proportionality limit of the material and that calls for correction with real measured Hooke's diagram.
Another way would be intentionally subjecting a structure to vibrate and then concentrating the damping in the most suitable place. Whatever rocks your boat.
I understod your comment, Dave, on 90% of box material usage. It's all about economy and extra profit 🙂 zero technology and science.
All this is very nice, but it still comes down to the OP wondering if concrete is a better option for a mid-size Mission rebuild. I am still suggesting that although MDF, Plywood, and timber may be inexpensive, they are actually quite good materials for building speaker cabinets. I might like to try a few modern materials, but I have not exhausted what can be done with basically paper. I only know of one company who has pushed these limits with custom specified materials ( different for each size cabinet) and I am not convinced the results are audibly better, or just what they have to do to justify their price. I go back to a really simple question: So, you want to build a better cabinet, what are you going to do better? (Yes, I do have a list in mind, but have at me if you wish 😀)
What you don't see in the picture is slight pre-tension on the sides.
What you don't see in the picture is slight pre-tension on the sides.
Attachments
interesting. I once pondered the feasability of running multiple steel truss rods through a panel of 2 laminations, in much the same way as a guitar neck. Using the bending created to increase the tensile load on each panel. My reasoning being that it would stiffen the most flaccid of materials. Downside being the panel is moved closer to the materials plastic deformation range. Depends on material i guess. Maybe plastic operation is preferable to elastic? I dont know for sure, but then if so the right plastic polymer material could be very well behaved. Other than that woodfibre is fine with me, metal plate and stone are more rigid, but i figure what you gain in one quarter, you lose in another.
the next question i would have is: at resonance, where the reactive parts cancel and we are left with the resistive loss, the excitation amplitude still has to exceed the loss, for a resonance to exist. Loss to excitation threshold is then clearly the relevant factor. I do not know everything (clearly), but id imagine there is near zero chance that this can occur. Increasing loss is then the only route left to minimising resonance. Ive read harwood thoroughly, but there are more modern papers which explore the real life excitation spectra, and throws a small amount of doubt into the fray. Doubt may be the wrong word, lets just say it 'moves the goalposts' a ways.
as for the OP, I wouldnt waste time with concrete, unless damping precautions are tatjen. Maybe concrete and 50% by volume of rubber chips would have better characteristics?
I'm not following this notion. Resonance of a structure exists and has no threshold. Bells don't fail to ring if lightly tapped. Tuning forks don't decay away to a point and then abruptly stop because they have reached a threshold. There may be nonlinearities at very high levels but there are no nonlinearities to make the resonances drop out at low levels.
Regarding excitation spectra, iIn a previous thread a poster tried to cast doubt on real music exciting resonances, stating that he could tune a system for the resonances to miss the music. This ignores the fact that there are many parts of music outside of any exact 12 tone spectrum. Also cabinet resonance series are too complex to simply fall on mathematically harmonic frequencies. We also don't perfectly stick to a precise scale when singing or playing music (outside of autotune!). If you have papers to the contrary of this then please list them.
The classic tests feed the speaker in the normal way and measure the output of the various cabinet walls. Flat spectral input (sweep, or noise or impulse, it makes no difference) tend to show a series of resonant outputs starting in the middle hundreds, with fairly equal peak outputs. Qs are high but not so high that music wouldn't easily excite them.
Another poster questioned what we were trying to achieve? I think we want our acoustic output to be exclusively from the woofer, rather than from the walls of the cabinet. We want a generally low level from the cabinet, but much more than that, we don't want the output to be bunched at any frequencies or resonant in nature. That would allow the output to lag over time and be much more evident (no longer masked by the music). What we hear in the end is the contribution from all surfaces, both the cone and the cabinet.
There have been some tests where the cabinet was made fully sealed (no drivers) with a second speaker and cabinet buried inside. In that case obviously the only sound would be that which escaped through the cabinet walls. By reports (I haven't done it) the cabinet output was colored and resonant rather than smooth. This is what we would expect based on any accelerometer or near microphone measurements that I have seen.
You can also try face to face out-of-phase tests where, if you get the balance or nulling pretty good, you can probably begin to hear what the cabinet contribution is. Certainly, stethescope tests (which I have done) give a good sense of the resonant nature of cabinet contributions.
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