To calculate this you assume that all the structure is inelastic. Ie not elastic! This leaves only the leaf springs to bend as the elastic part of the system.
Electro magnetic drives (Magnet-Schultz). Larger drives are usually either direct hydraulic or pneumatic but there are also a number of manufacturers of out of balance motors such as Vibrotechniques.
See http://www.heathcotes.com/ and go to products/springs also check out the spring manual in the downloads which explains how to design springs for vibrating machinery.
Hello Alex I have just seen this very old item and I wondered if you have ever looked into composite springs that have been specially made for vibratory machinery. This is not an AD but if interested I suggest that you check out www.heathcotes.com and others! Most vibrating conveyors and feeders...