Not just cheap fretsaws that vibrate, many years ago I bought a quite expensive British built Fretsaw (Diamond) Vibration was awful, after contact with the makers I was advised to bolt it to a worktop or stand (100% essential) and bolt the work table to the floor, I was also advised to remove a balancing weight that the factory fitted as when bolted down the saw was smoother without it.
Another factor to take into account is that although I use mine on a wooden stand a metal one is better (much less vibration) it has something to do with the frequency of the vibration, this is why many better scroll saw makers offer an expensive metal stand for their saws!
FWIW I also have a Hegner multicut with variable speed, they are expensive but a fantastic machine, very smooth, extremely quiet and a real joy to use, it is my favourite workshop machine TBH!
