For Pete's sake. I used to try all the suggestions made here. Spent money on new torque link bushings. Spent time and money--lots of it--on shimmy dampeners. Fooled with bearing preload. Tried all sorts of techniques when landing to try to prevent it. Did static balances endlessly.
All of it was a waste of time in most cases, since it was, as I said before, treating symptoms instead of the root cause, which was a dynamically imbalanced wheel. Aircraft tires are notoriously poorly balanced when manufactured (Goodyears are better than most) and they still use tubes, which introduce another factor and which are often not installed well and can be bunched up some in the tire and throw everything off.
It wasn't until I balanced a wheel dynamically that I finally had spectacular success stopping shimmy. I did it by cleaning the grease off the bearings and putting them in the wheel and holding the axle and spacers so that I could use a bench grinder with a wire wheel to spin the thing, and found that it wobbled something fierce. I fooled with stick-on weights in various places in the wheel, held in temporarily by cubes of foam rubber, and was able to get the wheel spinning as smoothly as silk. Regreased the bearings, put it all back together, and the shimmy was absolutely gone. Did nothing at all to the rest of the nosegear machinery. Whenever I replaced a nosewheel tire I redid the balance, or if anyone complained of the least bit of shimmy, which can happen as the tire wears.
I modified an old dynamic balancer to fit the nosewheel and was able to do it much faster. Now I work elsewhere and am back to the manual method and can't find an old balancer. Might have to build one. Some motorcycle shops have dynamic balancers that could fit a nosewheel, since bikes have the same steering geometry and shimmy issues.
Dynamic balancing makes all those expensive nosegear components last way, way longer, and stops shaking the daylights out of the radios and instruments and lights and airframe. Saves big bucks.
Goodyear sells stick-on weights for aviation. Parts number 9900 or something like that. Aviall. Don't use them on nosewheels that retract up under the engine where the sticky stuff gets hot and lets go.
Dan