Rattle from underneath w/out a tunnel brace
 

I have a 2011 SS with Headers, Hi-flow cats, and Borla Atak exhaust. The noise occurs at take off mainly in first, when shifting into 2nd/3rd gear at low RPMs (parking lots/neighbor hood rd). At first I thought it may have been the Brace suggested on other post. I tried using "spacers" still occurred recently took off the brace completely and the sound is still there! Any suggestions? TIA

May be hitting the heat shield, check to see how close your exhaust pipes are from front to back as far as clearance goes. May just need a slight adjustment

Are the headers touching the steering shaft when you let the clutch out under acceleration ?

Something similar and maybe even the same thing happened to me when installed a set of ARH 1-7/8 LTs. Mines a 2011 as well and it made this rattling noise upon takeoff just like you're talking about and it turned out to be this stud that sticks out from the passenger side fender that was hitting one of the header tubes. You might want to take a look. It's easy to see the stud by just looking under the hood. All I did was just saw a bit of it off and that did the trick.

I had the same thing happen as CamaroFan22 just cut the stud off.

Take it to a muffler shop and have them diagnose it for you. Could be a hanger, defective muffler or cat. At the very least they can weed the exhaust out, but imo its within the exhaust's cat back.