Unless you place the trailer on concrete blocks you will almost always get a bit of movement or shaking in the trailer. It sits on tires and a suspension so you cannot get all movement out but the use of the
JT Strongarm stabilizer kit will stop most of it. Also use a good set of tire chocks (I use RotoChocks but they are not available anymore). There are other brands similar to the RotoChocks.
I also, when staying in one place for a long time, like snowbirding in the winter, will put another set of support stands under the frame just in front of the axles.(
Aluminum Jack supports)
We have found that the use of the chocks, built in four corner stabilizers, and the additional jack stand supports makes our 30 foot long trailer quite solid except for the occasional shake when someone starts dancing in the living room. ;)