I've noticed that if my car idles too long it starts to get this really heavy vibration that shakes the whole car for a bit then it'll stop, then start again every 10 min or so. I've discovered it's the fans. Any advice? I don't know if that's something I should be concerned with.

 

the fans? what fans? replace them...

 

Your fans turning on creates vibrations in the car? That's a new one to me. They cycle on and off to keep the car from overheating.