My PG349Q is about a year old and started making weird rattling noises both when the monitor is on and off(!). Please take a short listen:
https://youtu.be/fAN7UQKUiCY
(and no it's not vibrating because of background music) it's been doing this 24/7 for the last 2 days at least. Gave the back a gentle 'slap' but that didn't do anything.

Does the 349Q have a hidden fan? Certainly sounds like it.