Cary SLI-80HS Integrated

Most likely capacitors.  most likely what is twisting is a dust cover.  I see 3 screws that probably fasten everything in place.  I wouldn't rotate it.  Rotating ta cap could cause the leads to short, although not likely.  

If it were mine, I'd just take the bottom off and tighten it and go back to listening.  Most people don't like to look inside.

Jerry

Sounds like caps (have not see a photo). 
 

go in from under and tighten them 

Seems like an excellent question to pose to Cary.  

Yes, those are caps. Unplug the amp, remove the tubes, turn the amp over or on it’s side and remove the base plate (several screws). There should be 3 or 4 screws with washers & nuts on each cap mount, one might have come loose or is missing. Should be an easy fix.