I can only recall experiencing bicycle shimmy or head-shake one time. It was while riding a 56cm square Merckx SLX frame. This was a bike that I had put many, many miles on, and had never experienced it before. It was on a short, fast, bumpy downhill, also one ridden many times before. Never happened before. Never happened again. Same bike, same hill, same speed. I just chalked it up to the planets being out of alignment, not the bike!
I did experience severe head shake on a motorcycle once. It was in rural France, at 120+ miles per hour, and only when I tried to slow down! Very scary. I traced that problem to a loose motor-mount bolt. On most (if not all) motorcycles, the motor (when properly tightened down!) becomes an integral stress member of the frame.
Wayne "former motor(cycle)-head" Bingham Falls Church, VA