There is a latch that the hood should catch on,it is in the center behind the battery,if it si missing it would rattle,and the grille also has the same latch,see if your has these,the hood and grille are usally tight.If the latch for the hood is there and not catching you will need to loosen the 4 bolts behind the grille and adjust to fit.
Is this a 316 with the Onan, or the older 316 with the single cylinder Kohler?
The Kohlers really shook unless at or near full throttle, and they were mounted on rubber isolation mounts. It's the nature of the old Kohlers, they shake and there really isn't much that can be done. The Onans are directly bolted to the frame and shake a lot less. Now, as mentioned above, the hood should have a metal spring clip that holds it down at the rear, right above the dash.