I have a yt3600 and when I shut it off it shakes like crazy. This is my second one and I don't really remember if my first one did that. My first one broke the crank.
It runs perfect but when I turn down the throttle it doesn't quite go down to the rpm's that it was when I first start it. When I turn the key off the whole tractor shakes.
I have a couple YT3600 and have had one for years...both shake when you turn the engine off.....If the PTO is on it is the torque off the pto and deck causing an imbalance...if the PTO is off should not shake much.....Try decelerating idle down turn off PTO and see if it still shakes...if so previous post had good ideas....