Metarinka has pointed out the principle supporting both thermal and vibrational stress relief. You deliver energy to the iron atoms (sorry, Metarinka, metals are made up of atoms, not molecules) to make them vibrate at a higher energy level. This energy can be delivered by heating up the welded steel, and in this case you have PWHT, or by attaching a vibrator to it, and in this case you have VSR. 
For those who are interested in knowing it, VSR was developed in Iron Curtain countries back in the 50's. The frequentors of this site who are under 30 don't know it, but in those days what happened in Iron Curtain countries was a deep mistery for us in the Western world, and for this reason we didn't know that VSR existed. 
After the end of Communism and the opening of former Communist countries, VSR become known in Western world but in the beginning it was regarded with some inconfidence. Later on this inconfidence was forgotten in European countries, but not in the USA. That's why VSR is widely accepted in Europe nowadays but not in the USA, where the applicable standards (ASME I, VIII and B 31, for example) still consider mandatory the thermal stress relief.
Giovanni S. Crisi