Hi Max - You seem to be fixated on a slab for some reason. Buy damped machine feet and that's money well spent. This slab/plinth thing is going in the wrong direction? If its a test case for machine parts maybe a good idea but in terms of machining benefit you won't get any. Re: inability to predict. With all of these materials nearly everyone is unable to predict. I do dynamic analysis for a couple of companies and I'm always telling them this is fuzzy stuff unless they commit to a serious materials testing program (elastic and sonic). Which they don't do due to $$$... so even us pros are guessing at some stuff... If you have simulation that does modal analysis it will calculate the critical (natural) vibration modes of your structure & parts. The next step is to add damping and unless you have real data on that for the material you/everyone is guessing...

If you ran the monolithic slab you will see that its modes are well away from any of the machine modes. So the plinth is not doing anything to "absorb" vibes in regard to helping the machine quality of cut... The dampest solution is to make a box and fill it with sand. Any "solid" has quite a low damping ratio. This is explained in the Topic 14 article. But the load does not travel through your plinth. The machine loadpath is between the tool and the part (ie the machine) that's the path you need to investigate.

So 1) define exactly what you are trying to achieve here? 2) if your doing something right the forum is very quiet, if your doing something wrong the noise is very load! Peter

In regard to machine mounting there are two camps:
1) The machine is mounted free on its own feet. This camp relies on the machine mass for dynamic stability. The machine does not accelerate fast enough (generate high enough inertia loads) to move the machine mass. The bigger the machine the more it moves into this territory. There are some mill makers for instance that expressly forbid machines to be connected to the floor, probably for thermal reasons. But there are other makers that recommend the machine is bolted to the floor for better stiffness and stability. My 300kg router if I ramp up the accles will dance easily...
2) Bolt the machine to the earth. This effectively makes your machine infinite mass. Some makers recommend this and provide machine feet that allow this. This solves the dancing machine issue if the machine is light and has high accel potential. This is particular to fast small/medium machines and most robots are screwed to the planet as they move very fast and are very light... Keep at it. Peter