The first thing to do is remove the front panel of the air conditioner and check if the filter has gotten clogged with dust and debris. A clogged filter forces the fan to strain and creates vibration. At the same time, check whether the unit itself is loose on its fasteners - over a few years the fasteners could have come undone, and then even a working air conditioner will start to vibrate. Try gently shaking the panel when the device is off: if it rattles, tighten the screws.
If the panel and fasteners are fine and the filter is clean, the problem is most likely inside. A low humming often means the compressor has started working under overload - this could be due to the refrigerant lines getting dirty or a refrigerant leak, even if there are no visible leaks. Another possibility is wear on the fan bearings, which develops vibration with age.
At this point, I'd advise against trying to fix it yourself. Call a service center and ask for a diagnostic - the technician will listen to the sound, check the refrigerant pressure, and inspect the compressor. If it's contamination, the system needs flushing; if it's wear, parts need replacing. Don't put it off, because under load the compressor could fail completely, and that gets expensive.