In the States they manufacture a product named ‘Mortite’ it is used for ceiling windows they call it caulking. You can find it on eBay but it is very expensive, it’s the postage costs. It is a very good dense damping material that is moulded and pressed into place. I have used it many times but I have not been able to find a product in the uk, that’s not to say there isn’t one, I’m sure there is I’m probably not looking in the right place. Any way it’s very good at dampening. I’ve used it dampening the inside of cases etc to stop them ringing. The best of it is it’s easy removable and leaves no marks
Hope this helps