There is a very simple formula to calculate the variation in outer diameter OD of a PZT disc:

Δ OD = (d31 * OD * V )/t

where t is the thickness of the disc and V the voltage.

Unfortunately, this formula is deemed valid only for a free piezo and at low frequency (1 kHz).

Can this formula be adapted to obtain the Δ OD hat higher frequencies (specifically at or above radial resonance frequency)?

Furthermore, can assumptions be made as how this translates to the Δ OD of a piezo which is bonded to a surface or is a FE-model the only way to go?

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