How to build the perfect ported cabinet. ...

From this simple analysis, I found out that the best material is the one with the highest ratio of Youngs modulus to density.

Yes, it is sometimes called specific stiffness or specific modulus. When comparing materials specific modulus, low density wood (spruce, balsa, fir) compares quite well to other materials, but it is not significantly better than steel, aluminum, magnesium, and titanium. The very best woods have a specific modulus of about 24 (in units of 10^6 m^2/s^2), and most engineering grade metals are pretty consistently in the range of 23 to 26. Molybdenum and tungsten carbide are a little higher at around 32. Carbon fiber composite is about 110, Berylium is the unusual metal with a value of 155.

In short: metal speaker cones are not a good idea from an engineering point of view.

I disagree. There are some outstanding state of the art drivers which use metal diaphragms.
 
Absolutely. Metal, be it mono or an alloy as required by the design, can be an excellent material for loudspeaker cones. If they are designed and optimised for piston operation, then the objective is to select the material, its thickness and profile to maximise the practical BW and push the stopband modes as high as possible. The existence of stopband resonances (primarily bell) modes in such cases is neither here nor there as they are outside the intended operating range and you deal with them as required in the crossover. For drivers designed to use TL modes as part of their operation, it can be a good choice also; again, the material, its thickness and cone design (to say nothing of the suspension) are all fundamental to its operation, as many Jordan, MA, Bandor, some TB etc. units demonstrate. Which is not to make any blanket statement that metal cones are inherently superior to any other -there are good examples of all types.
 
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I thought that adding absorption to a BR cabinet was a trial-and-error exercise. Is there a way to accurately simulate or calculate this?

There is a good way to grasp what is happening to SPL of a woofer while altering the amount of absorption within a cabinet. Explanation is from a spreadsheet "Woofer Box And Circuit Designer". I have exported the total system SPL and loaded XSim to show the result. This is a simulation of a woofer with only difference being the Qa value.

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There's still more to it, I think. There's likely some non-linearity at play, because over-stuffing just sounds bad, and I just know intuitively that recovering a lost 1-2dB with EQ won't cut it.

One idea that comes to mind is some kind of hysteresis as mechanical energy gets converted into thermal.
As for the port itself, airflow reduces pressure, so 360° of a sine wave passing through should produce a 2nd harmonic because the pressure drops twice.
 
There is a good way to grasp what is happening to SPL of a woofer while altering the amount of absorption within a cabinet. Explanation is from a spreadsheet "Woofer Box And Circuit Designer". I have exported the total system SPL and loaded XSim to show the result. This is a simulation of a woofer with only difference being the Qa value.

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I presume the sim assumes that the stuffing is uniform within the enclosed volume.
 
It will do, assuming it's derived from a typical lumped-element modeller. Some more advanced types allow variable density & locations.

That apart: most vented boxes designed assuming Helmholtz operation should not require stuffing at all. Assuming they are not specifically designed to use it, which is a relatively narrow / specialised set of conditions, lagging the internal surfaces with an effective material like OC-703 bonded acoustic fibreglass board should be sufficient, and if the cabinet is of good proportions, non-opposing surfaces is generally adequate, with any additions to address excess ringing being determined by a basic click test (or you can measure if you prefer -the former is usually quicker). The exception tends to be with one dimension stretched sufficiently relative to the others that you get a longitudinal eigenmode, which will need more damping to suppress. Under those circumstances though, you really shouldn't be designing assuming basic Helmholtz conditions, since you already know in advance that there are going to be deviations unless you take considerable effort with the box internals to disrupt that longitudinal mode. Since that is inefficient design, you'd be better off accepting its existence and accounting for / incorporating it into the alignment from the outset.

As an aside: too much stuffing / too high a density of material in close proximity to a cone will start to act more like a solid, raising the potential for the higher pressure inadvertently mass-loading the diaphragm & suspension, preventing movement in the anticipated manner. This is something GM and I often point out; it's more commonly encountered with TL variations for obvious reasons, but if you're going to heavily stuff a vented or sealed box it can be something to watch out for there too.
 
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I looked up the formula for stiffness of a beam. You want high Young's Modulus of elasticity for a stiff beam.I then then plugged in the constraint that mass of the beam had to be fixed, allowing me to compare structures made with different materials, but all weighing the same, all intended to do the same job.

If you use a denser material, you have to make the beam cross sectional area smaller, to keep it from getting heavier. It turns out the penalty paid by doing this is heavy.

From this simple analysis, I found out that the best material is the one with the highest ratio of Youngs modulus to density.

This applies to loudspeaker cones just as well as to beams. A loudspeaker cone should be light and stiff. Again, when choosing a material from which to make the cone, you want a material that has a high ratio of Young's modulus of elasticity to density.
that is true, however the low frequency stiffness of a conical or spherical membrane is predominantly defined by it's geometry.
it's similar if you compare a monolithic beam to a truss beam.
for a monolitic beam you're best off with light and strong wood.
for a truss beam you will use steel or aluminium (bike frame).

however at higher frequencies when the membrane does not behave like a piston anymore paper has advantages over metal because of the propoerties you mentioned.
 
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I don't think it's all that hard to build a good reflex box. You can think anything to death in this hobby. The bottom line is the end result. I use 3/4 inch MDF, braced with lumber 2x3 and 2x4 and a "typical" amount of fiberglass stuffing. I use double flared ports to reduce turbulence. When all is said and done a high power sine sweep to listen for any audible vibration or resonances. Do an impedance sweep look for anomalies and see how closely matched the pair of cabinets are. Check Fb and it should be within about 1 Hz have actually measure within 1/2 Hz. Done!

Rob 🙂
 
Animal farm said "Instead I build the cabinet with angled reflectors at the top and bottom, with lots of non-symmetrical shelf-braces in between, to break up the standing waves without choking the driver/port."

Do you have any pictures or drawings. I have been experimenting with 3d printing as a speaker material building ( as a bafle faceplate to mount the speakers over the MDF/plywood) and i was thinking of design "wedges" to insert inside and break the corners and other surfaces. In addition, modern 3d printer allow to use tunable honeycomb cells that can help dampening the enclosure
 
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