Most refrigerator noise is due to problems with a fan, according to PartsSelect. Bad fan blades, motors, and motor grommets all cause vibrations that cause the noise.
Most refrigerators have a fan that cools the condenser coils, as of 2015. Manufacturers place this fan near the condenser in most models. This location helps also helps to evaporate water from the drain pan so it does not leak on the floor. Inspection requires unplugging the refrigerator and removing the back access panel. Debris collecting on the fan blade sometimes causes it to vibrate. Other issues to check include a damaged blade and a visibly worn or seized motor.
The evaporator fan motor is in the freezer compartment. It pulls air over the evaporator coils to cool the freezer. If it is not working correctly, it causes noise, and ice and frozen food sometimes melt in the refrigerator. Inspecting this fan requires disconnecting the refrigerator from the power source and removing the fan cover. If the motor shaft does not move, the fan motor likely needs replacing. The evaporator motor also uses a fan grommet to reduce vibration noise. The grommet is subject to wear and sometimes detaches from the mounting bracket. Replacing a worn grommet stops the noise.