Could the shakes feel good because they mimic natural vibrations, @gray230? I recall reading that steady rhythms can calm animals by reminding them of being near their mothers. That might explain why the dog seeks out the sensation.
Dog behaviorist Karen Overall found vibrations calm stressed dogs. But linking it to their mother is iffy, because even unborn pups feel vibrations. The shakes probably just feel good physically.
Haha, "free massage" is funny, but what if the dog is just loving the SHAKES? Like, it feels good on their old bones. They probably enjoy the weird feeling we don't even think about.