Empty trailers bounce all over the place, and will really amplify tire imbalance. Try letting air out of the tires, down to 18-20 lb and see if it still shakes. I've hauled new trailers and have reduced air pressure down to about 12 lb just to keep them from shaking and bouncing when transporting for dealers. Do you still feel it with a good load on it?
Quick 32,36,& 44 Dually's
Ferris Evolution 27 Kaw 48"
DR Brush Mower
Toro Dingo 222
ISEKI Diesel Compact Tractor, attachments (bush hog, middle buster plow & land leveler
Steiner all wheel drive Tractor, attachments (stump grinder, rough cut mower, scrape blade & dual wheels)
5X10 open trailer
16' equipment trailer
1997 Ford F-350 7.3 4X4 SRW Crew Cab 8' bed