How to damp bookshelf enclosure resonance?

It looks to me like the original crossover had three parts in it, a resistor, a capacitor and a coil. I could be wrong, but It seems the guy bought three parts of identical values to the original crossover and just wired them exactly the same. If it were me I would have just swapped the parts directly on the existing circuit board one at a time and the job would be done. No rewiring required. Pull the resistor, put the new one in its place. Same for the coil and cap. I don't actually believe there will be any audible or measurable difference from these boutique parts if they are of the same value as the originals as the original parts were of high quality. Of course it's fun to do a project anyway. Hope that helps.
Thanks it does help a lot.
Cheers
TD
 
Identify the resonant wall.
Brace it at it's center either to the opposing wall or to two oposing corners of the enclosure. To connect the brace to the resonant wall, instead of glue, use a generous layer of butyl caulk. The points of connection depend on the source of the vibration. It can be the the speaker magnet moving the baffle or it can be the box inflating and deflating.
Similar method was described in KEF LS50 whitepaper to stop the front baffle from vibrating. They pressed the magnet to the rear with damping rubber. The results surpassed bitumen layer on the walls, suggested above.
It's more effective if the panel is already braced with stiff connection. But in that case, you need two damping braces, one for each section.
 
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Here is an image of the original crossover design. Notice the reverse polarity on the tweeter.

Kef Q350 Crossover.jpg
 
It looks to me like the original crossover had three parts in it, a resistor, a capacitor and a coil. I could be wrong, but It seems the guy bought three parts of identical values to the original crossover and just wired them exactly the same. If it were me I would have just swapped the parts directly on the existing circuit board one at a time and the job would be done. No rewiring required. Pull the resistor, put the new one in its place. Same for the coil and cap. I don't actually believe there will be any audible or measurable difference from these boutique parts if they are of the same value as the originals as the original parts were of high quality. Of course it's fun to do a project anyway. Hope that helps.

The parts were hot glued onto the circuit board, they weren't going anywhere.