Suppose the engine speed range (idle to max) is 600 to 6000 RPM, or 10 to 100 Hz. It's unlikely you can design a plate structure that has no vibration modes over the whole of that range, unless you make it ridiculously stiff (which probably means ridiculously heavy). So the problem then changes to "how to stop the engine vibrations getting into the plate", rather than worrying about the vibration frequencies of the plate.
You could think about doing that by fixing the plate on rubber mounts rather than metal-to-metal bolts or welds (possibly bolted joints with rubber washers, or something similar to rubber engine mounting blocks). Or think about ways to damp out the vibration of the plate, for example make a "sandwich" of two thin metal plates with a layer of rubber, polystyrene, etc, in between them.
(I'm assuming you are talking about a metal plate here - if not, wood will give more damping than metal for the same mass of material, if it satisfies your other design criteria.)
Choosing the best points to fix the plate to the frame will also make a difference. You want to fix it at the points where there is least vibration in the frame. (You may be able to judge that simply "by feel", if you don't have any vibration measuring equipment.)
Designing something like this entirely by calculations isn't very practical. As a starting point, you would probably want to measure the vibration levels in the frame without the plate at different engine RPMs (and probably different engine powers as well), rather than try to make a model of the engine and vehicle to predict them from first principles. Experimental "trial and error" is probably as good as way as any.