Running AC solenoid vibration pump with DC voltage
I would say that you could use a DC square wave, but I would be careful about using PWM because they were designed to produce a specific amount of output at a rated power.
An insufficient (too short) duty cycle could make them either inoperational or less than properly operational.
A duty cycle of more than 50% or 10ms could overload and overheat the coil.
Some models have a maximum running time specified in minutes, followed by a specified minimum OFF time in minutes, so you have to be careful if using those (best not to get those models).