Tech Vette man
Vettes are just a hobby and since I grew up around race cars the ability to understand and fix them sort of rubbed off
A "shimmy in the rear end" huh? I'm not going there! Ok, in all seriousness several things come to mind....
- loose lug nuts
- rear wheel bearings (total PIA btw)
- Suspension bushings
- Bad rear shocks
- fatigued rear spring
I'll assume you checked the lug nuts and made sure they were all tight
Generally a bearing will make a grinding or whirling noise. Soooo, that leaves bushings. If I had to guess, I'd look real hard at the trailing arm bushings and the camber rod bushings. Basically the car needs to be put on jackstands and then you check for excessive play. If the bushings are bad, it'll be really obvious. You can look at the rear shocks for signs of fluid leakage and frankly if you're in doubt regarding the age of them, I'd replace them. If the spring is bad, generally the car will sit really low in the rear, it may sit higher on one side vs the other, and it'll bounce a lot over bumps.
Without being able to look at the parts in person, this is a problem that is tough to trouble-shoot via the 'net.
Keep me posted, let me know what you check/find out and we can probably work thru it.
Jim