Thumping/grinding noise in hard right turn

The other day I made a hard right turn in a parking lot, and it sounded like a tire was rubbing against something -- made a thumping noise.  So today I checked the 1/2 shaft U-joints, and they all seem tight.  Then I took a hard right turn in the yard and it made a scraping noise -- sounded like the driveshaft rubbing on something.  No issues in a hard Left turn.

Lately when I start off, I can hear a faint whirring sound like a bad bearing or U-joint, and there is a slight vibration at speed.

I asked my mechanic this morning and he said it could be the diff clutches chattering.  He thought maybe a oil change with additive would help.

Anyone have and ideas about this? 

Posi clutches do not make noise if you are going straight....only when turning. The description sounds more like a bad bearing, or possibly the park brake shoes rubbing, or even the service brake pads. Noises drive me nuts...so many possibilities. I think I would jack the rear up, and see if there is any play in the hub bearings by grabbing a tire at 12 o'clock and 6 o'clock, push at 6/pull at 12 back & forth, and visa versa. In theory, there should be NO play. In the real world, there will be SLIGHT movement. If there is noticeable movement, you prolly have a hub bearing taking a doo-doo. If the bearings check out ok like that, then more sleuthing is needed.

Maybe a rear wheel bearing. 

I had the same problem.  First check to see if your tires are the correct size. Second have your alignment checked.  The car could have been in a wreck and not properly aligned. Mine needed front end work, the right tire was rubbing the frame and sounded just like what you described. Good Luck!

The car was aligned earlier this year after I had the Borgeson steering box put in.
I looked inside the front tire wells, and could no sign of tire rubbing.

Thanks for the suggestions!

I have a 69 that is having the same issue. After putting car on lift, there is play in the right rear tire.  Bearings are bad.  Having a tough time getting this issue fixed? Not many mechanics in my area that can work on older corvettes.