My car is making this wierd vibrating noise.   It isn't a rattle, but like a deep vibration coming from somewhere in the center consol, foreward of the transmission.   It happens when braking fast, turning hard, or turning at high speed.   The mechanic couldn't really find the problem but he thought it micht be a loose heat shield.   He tightened it down but that only lasted a couple of hours.   Any ideas what it is?

It is also squeaking when I go down hill (sounds like a belt) and the steering column squeaks when turning.