sound insulating - generator area

I posting this in the general are instred of electrical - generator, because it is not really about the generator, but sound insulating the cabin from the generator.

I have a torque ss - toyhauler 5th wheel - with an Onan RV-4KW generator mounted in a typical location right behind the kingpin area.
The generator is housed in a standard relatively thin sheet metal housing. The sheet metal easily flex, simply by pushing on it with my hand. To me it almost act as a resonator box (if there is such thing).

There is a good amount of noise is being transferred to the cabin.
Has anyone attempted to insulated the generator box.
There is plenty room to encase the outside of sheet metal box with dense Styrofoam- all around.
will it work reducing noise and viboration sound? Or I am wasting my time and money?

thanks