Inspiron 3521 fan noise

My Dell Inspiron 3521 is about two years old. For a while now the fan occasionally gets really noisy seemingly at random. Some things seem to set it off more than others, like when I move the laptop especially jerkily or when I'm running a game or something and move the computer. Usually the computer is warm when it happens, but not always; I can't find a specific trigger. Shutting the lid of the laptop ends the noise for a while, but it's annoying to constantly do that. What could possibly be causing the noise?

I've updated my video card drivers and attempted to clean the fan from the outside of the computer; I don't want to attempt to open the laptop to clean the fan from the inside. I just noticed that one of the screws in the case is missing, but the screw is next to the USB/HDMI/Ethernet ports, not the fan, so I'm not sure it's related. 

Thank you!