Something sounds loose but can't see what
One possibility is that a bolt through the bottom bracket shell is too long and is touching the spindle of your crankset. As the crank spindle rotates, it sets this bolt into vibration, and the frame along with it, at certain speeds. 

Check to see if you have a cable guide at the bottom of your bike. If you do, see if the bolt that attaches it to the frame is long enough to reach inside the bottom bracket shell.

Some other diagnostic things you could do:

Remove the chain and coast down a hill, pedaling at different speeds. Does it persist? If not, focus on the chain. 

If you have one available, swap the rear wheel. If this cures it, focus on the wheel and cogset. 

Take off one brake rotor. Pedal at various intensities somewhere safe. Sometimes various conditions will cause a subtly dragging rotor to start vibrating. Put it back on and try the other. 

If none of that is to blame, I would concentrate on the bottom bracket bearings and the crankset/chainrings. Take them all off, clean, inspect, regrease, tighten to specs.