My horizontal stab on my .46 Extra 300L has a tendency to flutter so much it turns into a blur!! i used to put it down to slop in the elevator linkage so i mounted the servo at the rear side of the Fuz enabling a direct slop free linkage.

After a flight additional wobble of the tailplane can be felt by the hand on top of the natual flex of the structure. I ran cyano into the joint which prevented the wobble until the next flight.

i would appreciate it if anybody could give me any clues as to the cause and any methods of stopping the flutter.

Many thanks

I add tubing spupports to the bottom of the stabilizer on models that have shaky horizontals.
Flatten the ends and the middle.... bolted to the horizontal, screwed into a plywood plate on the fuselage.

If your Extra has a flat-plate stab, it probably is too flexible to get away without using the bracing wires used on most full-scale extras, I think. Mass balancers on the elevators might solve the problem, if you don't want to brace the stab.

The most common reason for a stabilizer flutter is the material is too soft.
The particular CAP ARF I show was notorious for throwing the horizontal clean off!
When I heard this, I added the braces before I flew it the first time.
I have a Somethin' Extra, which the kit instructions have the tail section wire braced, with only the bottom side of the horizontal braced... which I doubt it really needs, but with the SE, tail weight is needed anyway!
I have another plane which got into horizontal flutter when I went from a .65 to a .91. This one has wire bracing top and bottom.

Like TallPaul says, it is most likely to limber. If it is built up, you could sheet it top and bottom to stiffen it up.