Your GE Arctica fridge, like mine purchased around 2002, eventually starts making a howling noise which (as you will discover from google searching, and then taking the back of the freezer compartment apart, is caused by ice build up on the cowling surrounding the evaporator fan. The fan blades come into contact with the ice, making the noise. It is not a good noise.
Here is a exploded assembly diagram of the fridge with the offending parts noted in red:
You can temporarily fix the issue by defrosting the cowling, and some have had luck replacing the motherboard to prevent excessive frost generation. But my freezer compartment was not really frosting up that much, at least after I fixed the damper mechanism between the freezer and main compartments. I tried replacing the evaporator fan motor itself, thinking that the noise might come from worn out bearings. This did not work either, the noise was back within a month.
I have a solution that directly and reliably corrects the design flaw, which is that the cowling surfaces ices up in between system defrost cycles. I added some nichrome heating wire to the system which prevents ice build up at the expense of a few watts of electricity. The circuit consists of enough 38 gauge nichrome wire to circle the cowling twice, in series with a 50 ohm, 10W resistor. This draws power from a splice into the evaporator fan power supply. You can get the nichrome inexpensively from an ebay vendor for under $2.
Here is where I spliced into the power:
I wrapped the nichrome around the cowling twice, taped it in place and made it water-resistant with vinyl electrical tape, and then covered the cowling surface with metal heating tape to transfer heat evenly over the inner and outer surface of the cowling. Here is what it looks like after adding the metal tape:
Finally I soldered the 50 ohm power resistor into the circuit and taped it all down with metal tape onto the cowling surface.
This solution is working for me, no more howling and (at least for a few more years) I have avoided the expense of a new refrigerator.
(6 years later) The fix is still working, no issues or noise coming from the fan.