How do piezoeletric accelerometer sensors generate output voltage?
What makes a crystal a piezoelectric crystal is that it produces a voltage when deformed. This is the defining characteristic of a piezo electric crystal.

Are you sure you're asking about accelerometers and not gyroscopes? Gyros need a piezo because they need a resonator but I don't know why an accelerometer would need a resonator.  Almost every accelerometer from Analog Devices has this paragraph under "Theory of Operation" which does not mention any piezo crystals.



From ADXL1005 datasheet (an accelerometer)