I can’t imagine that you would find any. However, you will find plenty of articles that advise against it, mainly for safety reasons. You could do an interval and getting people on and off the bike but then you break up the aerobic workout and get the heart rate down in between.
I have taken spin classes where they did incorporate some free weight exercises while still on the bike. I didn’t think it was unsafe, just uncomfortable. In my opinion it’s not wise to use heavy weights (dumbbells or weighted bars)while still on the bike. I’m not sure there are any studies that have been done on this subject (or at least I’m not aware of any). You just need to use common sense if you are going to use any type of free weights while still on the bike since not everyone is build the same and most likely they will have many imbalances. Also it’s difficult to maintain correct form while spinning at the same time.
As a higher level certified spinning instructor and certified exercise physiologist I can say with absolute certainty if you are taking a class where free weights are being used DURING the cycling portion of the class, it was NOT a spinning class. The overarching premise of the spinning program is that you do not do anything on the spin bike that you wouldn’t do on an outdoor bike, no exceptions.
Not only that — let’s talk about specifics to safety and appropriateness (not only an effectiveness issue — that’s a whole other story). Consider that an individual taking the class (as we see quite often) is more of a beginner to just under an intermediate exerciser – they will NOT have the body awareness nor the core control necessary to coordinate such a complex coordination of movement.
As certified professionals, it is essential to know the basics of kinesiology which would scream that this would be inappropriate at best and dangerous at worst. Please, I urge you to not consider doing such a thing even if it isn’t part of a spinning program! Inconsistencies and reckless attempts to increase intensity, especially without considering what is appropriate, is what undermines our industry as a whole.