Describing pzt planes and corresponding coefficients

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The discussion centers on understanding the d31 and d33 strain coefficients in the context of PZT actuated membranes. The numbers refer to specific geometric directions related to elongation and shear in piezoelectric materials. The piezo tensor is complex, but the coefficients are not arbitrary; they correspond to preset directions that are crucial for applying the coefficients in equations. Clarification is sought on these specific directions to facilitate further understanding and application in a project. Understanding these coefficients is essential for effectively working with PZT actuators.
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I have to understand some papers concerning pzt actuated membranes for a project and I keep stumbling upon d31 or d33 strain coefficients. Can someone please explain to me what do the 31 and 33 numbers refer to, regarding the geometry?

I'm not sure I'm getting this so please feel free to ask for clarifications.
Thank you all in advance.
 
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Because the piezo tensor is impractically huge but hollow and repetitive, the indices are re-numbered, with 1 and 3 meaning things like elongation and shear.
 
Thank you for you time Enthalpy. I understand that the numbers are something like what you described, however it seems that, as far as pzt actuators are concerned, the d31 and so on coefficients have been specified and my understanding is this is not arbitrary. I am trying to figure out what these preset "directions" are so that I can carry on applying the numbers to the equations :)
 

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