Big BenD Bass Horn: Belts and Braces part 1
The horn, especially the spire and mouth sections, have large flat panels, and these must be braced. Panel vibrations will act like notch filters in parallel to the horn path, and will suck energy from the sound transmitted through the horn. And not just that, the panel resonances may have high Q values, re-radiating the absorbed vibrations at the wrong time, with ringing. We clearly don't want any of this, but it may be hard to elimiate.
There are two papers that cover the basics of enclosure bracing: Loudspeaker Enclosure Walls by Peter W. Tappan  and The Theory of Loudspeaker Cabinet Resonances by James K. Iverson . These papers give both theoretical and experimental data on the effectiveness of wall construction and bracing, and should be studied by anyone making speaker enclosures.
Both wall absorption and resonant frequencies affect how much the wall will vibrate. Absorption is more effective the higher the resonant frequency, so raising the resonant frequencies is effective in several ways. Below the first resonant frequency (mode), it is the stiffness of the wall that limits vibrations, higher up the mass dominates.
If the first wall resonance could be moved out of the passband of the horn, this would massively reduce the contribution from the horn walls. Increasing the wall stiffnes can be done by using thicker material, adding tension, changing the shape, or bracing. The material is already 18mm birch ply and relatively stiff, and the whole structure could easily become difficult to handle if it was made thicker. The shape is given by the horn, and can't be changed (but it is possible to increase the tension in the panels by adding a slight curvature). Bracing is the most suitable approach, and tension is also automatically added in the curved section of the horn.
The most effective bracing method is braces along the long direction of a panel. Tappan recommends to place the braces so that the circles that can be inscribed in the unbraced parts of the panels are as small as possible. It is also important that the braces add enough stiffness to make a difference. If the brace isn't stiff enough, it will just add a bit of mass to the wall and may actually lower the resonant frequency.
At high frequencies the wall radiation is very directional, and for most enclousures this means that the parasittic radiation is directed away from the listening area and can be more readily absorbed. But in this horn, the front of the spire, although partially covered by the midrange horn, is a large radiating surface pointing towards the listening area. It is therefore critical to reduce radiation from this wall.
Comparing Bracing Methods
Usually one would put braces internally and externally on the horn based on experience, gut feel and what "looks right". But this may result in a lot of unnecessary braces, adding weight, and unneccessary work. Below are data for a 12" by 18" (305 by 457mm) steel panel, 0.02" (0.63mm) thick, clamped at the edges, and braced in different ways .
It is clear that the quite common perpendicular brace is not very effective in raising the resonance frequency, and that the perhaps less intuitive lengthwise brace is the most effective.
My first thoughts about reducing panel vibrations was to drive the horn with a signal generator and feel around for areas of excessive vibrations. My second thought was that maybe a knuckle test using the spectrum analyzer in Arta together with a measuring microphone could provide some more useful data, and allow me to move resonances out of the passband. Then I remembered I had an ACH-01 accelerometer. I built a phantom powered preamp for it, allowing me to use a normal sound card with microphone input. Then I could make repeatable, quantifiable measurements of bracing performance.
The first measurements were done on a rear chamber, throat bend and middle section (spire).
The rear chamber is a square box of about 65 liters. There is no bracing apart from a frame with T-nuts to bolt on the rear cover.
The panels will be left unbraced until the end. The back wall provides a reference measurement to check that the system is run at the same levels throughout the tests.
The throat bend has a lot of built-in stiffness from the bending. The main vibrations seem to be above about 800Hz, so there doesn't appear to be a great need for extra bracing here.
The next article will cover the bracing of the spire.
 Tappan, Peter W.: "Loudspeaker Enclosure Walls"; JAES Volume 10 Issue 3 pp. 224-231; July 1962
 Iverson, James K.: "The Theory of Loudspeaker Cabinet Resonances"; JAES Volume 21 Issue 3 pp. 177-180; April 1973