A lot of owners suffer from this and in most cases it is difficult to solve.
Some planes have a torsionally attached gas strut which controls this (assuming there is no play elsewhere) but many have no apparent adjustment.
The Socata TB series has nothing, apart from a subtle adjustment in the nose gear mechanism.
One 145 company guy told me years ago his normal solution is to let some air out of the tyre before giving the plane back to the customer 
He said it is standard procedure on turboprops too. However this doesn’t always work…
It is probably also affected by the general amount of play (i.e. wear) in the steering linkage – for nosewheel steered types.
Peter wrote:
Some planes have a torsionally attached gas strut which controls this (assuming there is no play elsewhere) but many have no apparent adjustment.
I haven’t seen that particular type but what’s curious to me that some of these units contain springs acting to center the nosewheel steering (e.g. steel wire springs) and others are apparently hydraulic or friction dampers with no springs either gas or mechanical. Mine has the spring type with no damping but there is a fair amount of mechanical friction in the system and it has never shimmied. I wonder if the spring type units are intended to have any effect on reducing shimmy.
Lower tire air pressure increases the damping provided by the contact patch scrubbing on the ground. Since the radius of the increased area is large relative to the steering axis, I believe it doesn’t take a drastic reduction in tire air pressure to increase damping.
Tail wheels tend to have the same issue, some types have the reputation more than others.
Peter wrote:
He said it is standard procedure on turboprops too.
I don’t believe that. Our mechanics are very keen on keeping the wheels at the correct pressure – and this was no different when our company still had KingAirs on the fleet. But I guess every mechanic has his own secret recipe to treat shimmy and I know for sure that none of these recipes works. I don’t think that I ever flew anything that did not have nosewheel shimmy at some combination of speed and loading.
Sorry – by “gas strut” I meant a fluid filled damper.
Neither my nose wheel or tailwheel plane (since installing Scott 2000 T/W) has ever shimmied the steerable wheel. The Cessnas I flew for a while had lots of shimmy, I think in that case because the dampers needed to be overhaulled. Lord sells STC’d units that last longer without service – maybe somebody here has experience with those.
I remembered there is another design to increase tire damping, used on ‘anti-shimmy’ tail wheel tires. These typically have a wide groove down the middle, so that the contact patch is at a larger radius regarldess of inflation pressure. I understand Zlins have them.
Retractable Cessnas are notoriously bad for nosewheel shimmy. On two occasions this got so bad that I aborted the takeoff, as it really felt as if something had broken.
Owning two Cessna 152’s I have had quite a bit of trouble with shimmy and have by & large got it under control, the big issues are as follows.
Cheap tyres, yes those very cheap round profile things, buy a square profile tyre.
Poorly services shimmy damper, service it each maintenance check or better buy a Lord damper.
Play in wheel bearings, poor adjustment or worn bearings.
Play in torque links, this has to be quite bad to cause shimmy unless one of the above factors is present.
On our 172s we had recurring problems with nose wheel shimmy.
i think one of the problems is than when it first start it will soon wear the bushing in a way that even if the primary reason for the shimmy is sorted out, it will continue.
Our solution was in one operation to overhaul the bushings and then change to original damper to the LORD rubber type. Since then we have not had any shimmy.
IMO the number ONE cause for nose wheel shimmy : not enough nose Up elevator input .
