Voice Coil/ Solenoid driver
We have an application exactly like this we use to create a vibration for a motion test fixture, and we use an audio amplifier of the type used in automobiles to provide the bass boost.  You know the ones - they create the thumping that you hear from cars listening to loud music.  You can hook a function generator up to it and supply any waveform you want, and you can place a cap in series if you need to (we don't).  The one we have runs from 12 volts and cost about $80 new.