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O.K. Basic design principles:1) A container without sharp corners for things to pile up in. Quick and dirty design would be to take an inner tube, inflate it to the needed size, and cast in plaster or concrete. You could use anything from dolly wheels up to find the right size.
2) Line the cast with fiberglass to make a shell light enough but still the right half-doughnut shape. (Now is the time to add mounts for the springs from (3) below and the motor.) While you're about it -- consider taking the original inner tube and gluing it to the inside of the shell, so your abrasive media won't be generating fiberglass dust as it works.3) Mount the shell on some stiff springs -- perhaps a bunch of old valve springs from a dead engine. The number of springs will vary with the size and the vibration speed, but I would guess that three or four should do.
4) Mount an electric motor to the bottom of the center of the shell, with an off-center weight mounted to the shaft. A DC/universal motor would allow you to easily vary the speed to optimize the vibration, for a given weight and set of springs. You can also adjust the vibration by being able to adjust how far off-center the weight is.5) Oh yes -- figure some way to mount a lid over it while it is in use, to keep the dust form the media and the workpiece from winding up in your lungs.
So -- these are the basics of the design. Anything else is to adapt to your own materials and junk motors, parts, and such.
These aren't rocket science, after all.