What could be causing vibration in my furnace?
I'd suspect the new inducer (exhaust) motor if this sound begins to occur just before ignition; before the HSI ( hot surface ignitor) gets hot. A gas flame makes more of a roar than a hum. I've had less than stellar inducer motors in the past, with questionable bearings making it sound like rum-rum-rum-rum... 

I've also had duct work vibrate at the unit; go around putting pressure on things until the sound changes. I still believe the sound is caused by the inducer; though it's not necessarily the source of the sound. 

Take the furnace's top-section of the faceplate off, and try grabbing stuff; beware the 120v wiring. Tighten down the clamps that lead from inducer motor to the plastic pipe. Also try putting little pieces of insulation where piping might be resting on things.

It's not unheard of that replacement parts be less than spectacular. Encountering this exact problem, I've lived with a (now a little less) noisy replacement inducer for 10 years now.