Bart B.
The string is a useful analogy. All analogies convey an idea about what it happening, not the ultimate truth about what it happening. That is why people keep bringing up musical instruments.
In a rifle barrel the barrel will vibrate with a fixed point at the receiver and another fixed point at some position in the barrel towards the muzzle, as measured by Bill Calfee here:
http://ozfclass.com/articles/1/psm_2005_03.html
But I will try to explain pressure bedding using only a rifle barrel as an example.
By putting a dampener on the barrel with stock pressure, the barrel is going to vibrate less simply due to energy absorption by the stock, but also shift the remaining "free" portion of the barrel into a higher frequency which has a dead spot closwer to the muzzle. You would need do do some Fourier Transform math to calculate the frequency based on measurements, but it could be done (to separate the fundamental frequency that was dampened from the resultant higher pitch frequency).
As the metal heats up, the effects of pressure will change as the barrel steel changes plasticity so accuracy over the long range will suffer. Free floating barrels are isolated from outside influences, so as long as everything is mechanically true, there won't be a loss of accuracy even with a hot barrel. Group size may open up slightly (mainly due to friction), but the group statistical center should remain the same.
Jimro