There is a VERY loud vibrating kind of noise (brrrrrrr) when I abruptly take my foot off the gas pedal. It doesn't seem to matter at what speed I'm going and it instantly disappears as soon as I give it some gas. The sound seems to come from the engine compartment. I have checked the exhaust pipes to see if they might be loose but they're not. It seems to happen more when the car is warmed up. Any ideas what to check? Thanks

 

I would check for exhaust leaks next.

Here is a good video: