Structural Foam for chassis stiffening

I think it would reduce road noise and vibration some, but I'm not sure what you'd get out of it as far as chassis stiffening.

Reason being the adhesion to the chassis. To get a significant improvement in stiffness you need to have really good adhesion to the metal, and I'm not sure you'll get that adding structural foam to 40+ year old cars. There wasn't a lot of rust prevention going on with these cars, the inside of the structures usually have some surface flash rust even on really clean cars, not to mention dirt and debris that accumulates because not all the spaces you're talking about are fully sealed to the exterior of the car. If you've replaced crossmembers and things on these cars you know what I'm talking about, it's amazing how much dirt and rocks can get into the frame and crossmembers.

So, even with a high adhesion structural foam I'm not sure you'd get a good enough adhesion to the base metal and not just say, the surface rust. And then of course those interior structures aren't fully hollow either. Rockers, crossmembers, frame rails etc have stiffening plates located inside of them in certain locations (attachment points etc). Most have holes in them, but they might impede the foam from reaching certain areas inside the structures, and it might be difficult to check if you've gotten everything filled with foam.

Only other thing I would worry about is how the foam might trap moisture in some sections of the chassis. Especially if you didn't get great adhesion everywhere, it could tend to localize rust damage in areas that didn't get fully filled or adhered to the metal. You could get pockets of dirt/debris/moisture that could speed up localized rust damage.

Not a bad idea at all though. It definitely makes a big difference in new cars. Not sure retrofitting it would have all the same benefits though. Just thinking out loud, I read the papers and have seen its use in that engineering world but I'm no expert.