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The k31 mode - the original multilayer
Husain Shekhani • Jul 19, 2021
Some people think that the way to increase displacement in a piezoelectric transducer is add more layers or utilize an optimized resonator assembly. Don't limit your thinking.
The "original multilayer" aka displacement enhancer is actually the "k31" mode of a piezo.
When we apply voltage to a piezo, there is expansion or contraction in the polarization direction - that is the k33 mode. In this case, the displacement is equal to the d33 coefficient multiplied by the voltage.
However, the same piezo also exhibits transverse displacement (along the width) due to the Poisson's ratio - this is known as k31 operation. If we solve for the displacement in this direction, we will notice that the length (or width) will multiply the displacement. So, for a piezo bar with ratio 1mm thickness x 5 mm width x 20 mm length, the displacement will by multiplied by 20 - WOW!
Here is a complete derivation:
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