You will need a suitable AC amplifier (driver) for the voice coil. Contact the manufacturer for recommendations. Also see the note in the data sheet, that for maximum power, the actuator has to be mounted on a massive heat sink, and it will get hot enough to boil water.
The Arduino cannot directly generate AC voltages, so you will need a bipolar DAC and power supply.
For a fully controllable AC signal, some fairly sophisticated software is required. Google "Arduino DDS" for some ideas.