Some of the commercial units I have seen have coil springs.
I like the idea of an eccentric disc/pulley mounted to the shaker tray.
Or, if not eccentric, weighted so that it creates vibration. The good thing about a weight (Like a bolt and bunch of washers) is that it can be dialed in, by using a smaller bolt, and/or adding or subtracting washers.
Speed can be adjusted via RPM, as well as pulley diameters, but i think you want it running above 1/2 the rated RPMs of the motor, because that is where the power is.
What you need to adjust for is proper harmonics. Each and every thing has a frequency at which it will resonate and feedback causing harmonic vibration.
The trick is to find that spot, where the entire tray assembly is acting like a tuning fork.