I MAY HAVE A BETTER OPTION!!!!!!!!!!
High density foam. I don’t know why I didn’t think of this before. I think it’s because, for decoupling large areas in a recording studio it’s just horribly cost prohibitive so we don’t use it for that kind of task. But we do use it to decouple smaller things all the time. And you should be able to find it at a local fabric store or maybe even a craft store. It’s used for couch cushions, mattresses, etc. I don’t know how popular that kind of furniture is in Japan, but I would imagine you should be able to find it. Here’s a link of what I’m talking about
https://www.joann.com/airtex-3-96-oz...m/2162279.html. It’s expensive, but way cheaper than having to import rigid fiberglass. Rigid fiberglass is mainly used as insulation in commercial buildings so for a non-contractor to get it you need to buy it from an acoustics dealer. I know that in Europe it is very hard to get and studios there use something called mineral wool or rock wool. It’s a kind of floppy for your application and I don’t think it would work well. It’s possible that’s what they use in Japan instead of rigid fiberglass.
From a decoupling standpoint, high density foam would work even BETTER. I would go with 3” high density foam which, in the U.S., runs about $50 per yard. If all you can find is 2”, then use that, but thicker is better! You can find it at a fabric/craft store. In the U.S. it’s usually green, but it does come in different colors. Use the exact same application as I described with the rigid fiberglass. It is not so great of an acoustic material for airborne sound, but it is amazing at decoupling. Even better than rigid fiberglass. In recording studios we often use this stuff (not in green color, because it isn’t cool) to decouple studio speakers from their stands or the meter bridge of the recording console (where many studios mount their speakers). This helps prevent the vibrations from the speaker (from the cone moving back and forth violently to create sound) from transmitting into the floor and going from there to another room and up microphone stands and vibrating the microphone. As an additional upside, you won’t need to wrap it in fabric to keep the fibers from coming loose.
Here’s a pic of HD foam in my studio. It has a heavy steel plate on top of it, and then the speaker on top of that. In your case, the speaker is your bench. The steel plate is there for mass and has to do with the ability of the speaker to reproduce sound accurately so ignore that. Although you still need the sheet of MDF or plywood to distribute the load evenly over the foam. MDF would actually be better because of its greater density and mass. The greater the density and mass the lower the resonant frequency (you want as low as possible) and the hard it is to vibrate acting like a speaker. You want as little vibration as possible because that will become airborne sound. You can kill vibrations if necessary with a sandbag or two. My speakers are also on heavy sand filled stands which further decouples them from the floor (basically, there is ZERO vibration at my floor!). Sand is awesome, but I’ve racked my brain on a way to use it for your purpose and can’t come up with a reasonable way to do it.
speaker.jpg
Here’s another shot where I had to keep hard drives on a shelf that is coupled to a wall. To keep the wall from sounding like an amplifier, I threw some HD foam under them. This is the green color stuff you are likely to encounter. The 2” I have here is likely overkill, but I had it so it was free. I will say though, that a 1” piece of medium density foam was not enough decoupling.
harddrives.jpg
Decoupling is a tricky business if you are really trying to silence something. You will NOT be able to silence your bench from your downstairs neighbor as the amount of energy generated from say, chopping a mortise, is insane. But I suspect you could seriously reduce it massively. And I think heavy sawing vibrations could be completely eliminated.