Radiator fan vibrating

loose/broke engine mount

There are several other things which can make a noise. The people you showed the car have the advantage of hearing or feeling the noise that we do not have a chance to do.

A catalytic noise can change with the engine RPM. You can rev up the engine in Park or Neutral and should be able to replicate the noise. If not, then you have a moving part making the noise.

Sometimes the Emergency brake material comes loose from the metal backing and jams inside the rear drum/rotors. It will cause vibration when pulling away from a stop, and eventually will grind into powder.

Rear axle differential clutches. There are friction disks inside some types of rear-ends. A special lube additive makes these work. Sometimes a refill of additive and lube can make marginally performing units more quiet.

U-joints can make noise and vibrate. Its another moving part noise.

The fan clutch can also make noise and vibration. The A/C compressor and compressor clutch bearing can make noise. The A/C clutch operates intermittently depending on pressure and temperature.temperature.

A vibration when accelerating is almost always related to drive train. Check the U-joints to make certain that the bolts are in place and snug. If so, then pull the axle and manipulate them, just don't let a caps fall off. If it does, you will probably have to replace the joint.

Are you sure your vibration is not drive line related, like u-joint,or wheel bearing?

Probably need to replace the fan. Like anything else they do were out. Just check the mounting points are tight 1st incase its just a loose bolt or clip.

Did you check to see if any debris was in fan box after removing fan. there could be something in it that the fan catches.

you may have one of the cv-axle goes bad. jack one side of a time, put parking brakes on.
start the car and put in drive run up to speed and feel the vibration, the side has more vibration is the one that goes bad

its prob the cooling fan its located in a housing along with the radiator fan at the front of your engine bay look down when you open the hood . and make sure the fan is spinning run the ac on high and wait ( do this while the car is running of course ) . do not run your ac if the fan isnt working . you will burn up the compressor . the noise and vibrations you feel are from the compressor turning on and off.
now if the fan is working its prob the compressor. if all else fails take it to a mech where they can test it ... its not pricey and its quick

replace blower motor and fan.

It could possibly be a bad motor mount.