You know, there are many things in audio which defy full and complete comprehension.

Let me explain......
I suggest mu metal shields, Glen proves it ain't necessary, and rather it is wire routing which is important. I suggest mounting the modules at the rear of the case so input leads can be short, and countless builders, all protesting a hum free zone, prove such precautions are unnecessary.
Then I suggest Star Earth of the amps should be connected to chassis and mains earth. Someone does it, voila!! HUM!!! So we disconnect Star Earth, and on some amps hum intrudes and on others goes away.
I think this demonstrates that building an amp is a bit like a recipe; add to taste! An informed tinkerer can always eliminate the hum; but it is a common problem and always the last frontier.
Now, another can of worms. Damping.
I have had one hour telephone calls from people extolling the virtues of wrapping the pcb in plastic bags full of sand, mounting it on pitch, using various composites of rubber and neoprene and balsa to support the various structures. My eyes have at times rolled completely out of sight....
There is no doubt that many electronic components are microphonic. The obvious ones are tubes (though NEVER in my designs!), but also caps, and arguably, semiconductors, particularly the small ones which weigh little and stand on their leads. Furthermore, there is not yet any storage medium which does not move; so here, microphonics could reasonably be expected to have profound influence. The obvious example is a turntable, but CD players are highly susceptible to vibration transmission, with the laser assembly in particular very tetchy.
That said, there are countless examples of materials which 'improve' the sound when added to audiophile components. Let's explore the electronic side of this observation.
Vibration is primarily dependent on two things; stiffness, and mass. If the excitation comes from the music, which is music, replete with a wide range of different frequencies, it's reasonable to assume it will affect small, light parts, which are a little 'floppy', not overly 'stiff'.
On the AKSA amplifiers, the parts most likely to be affected are the electros, the diff pair, and the voltage amp to a lesser extent. The outputs and drivers are securely attached, and pretty heavy, so they may not vibrate much, although their excitation currents are high to compensate. Nonetheless you get the point; any vibrations will affect the electrical characteristics to a small extent, and may even be manifest in the sonics.
On the GK-1, however, we have a very light assembly, with a long, floppy pcb, and a tube. There is definitely an issue with attachment here; we might well mount it on some sort of elastic, compressive medium which will prevent vibrations from persisting.
So, in general, I support mounting on damping materials. There is not sufficient known about this phenomenon to dismiss it out of hand. Correspondingly, there is not much literature on this vexed topic, so, we must keep an open mind and admit there might be some sense to it. We need to understand that complex systems are very difficult to analyse; music, and the long chain of electronic amplification in all our stereos, is a complex system, and this defies mathematical modelling. Hence the dearth of information on the topic; but that's not to say it should ever be dismissed. It's fair to say that the human ear is extraordinarily sensitive - far more than test instruments - and if 10 people in a group of 15 hear something, it's probable that there's something in it.
Cheers,
Hugh