Over a six month period we experienced severe nosewheel shimmy in two of our B737-200's equipped with the gravel-protect sledge adjacent to the nosewheel. I saw one 737 touch down and the severe shimmy fractured both nosewheel tyres with the landing run completed on the rims.
My event started shortly after opening the thrust levers for take off when a really bad shimmy started at 30 knots, then a big bang in the vicinity of the nosewheel with loss of directional control and various hydraulic caution lights. Stopped on the runway and found that the hydraulic lines had fractured and the scissors link broken. Another company had experienced similar problems with nosewheel shimmy in the -200 and it was discovered that if you gave the noswheel steering a quick "tweak" as soon as the shimmy occurred, you could stop the shimmy for a few seconds. It was a long time ago and I don't recall the final rectification that fixed the problem although I vaguely remember something to do withy faulty batch of re-treaded nosewheel tyres.