Dimensional reduction study of piezoelectric ceramics constitutive equationsfrom 3-D to 2-D and 1-D

摘要

The accurate performance evaluation is crucial to the design and development ofmacro/micro sized piezoelectric devices, and key to this is the proper use ofthe stiffness/compliance and piezoelectric coefficients of the piezoelectricceramics involved. Although the literature points out effective piezoelectriccoefficients: and for thin film materials, and reduced dimensionality ofequations for bulk material, the elastic and piezoelectric coefficients remainunchanged from the 3D equations in most of the reported macro/micro sizeddevice’s 1D and 2D analyses involving the e form of the constitutive equations.This leads to variations between numerically predicted and experimental resultsin most devices. In order to understand effects of the dimensional reductionfrom 3D to 2D and 1D on stiffness/compliance and piezoelectric coefficients,this paper derives the 2D and 1D constitutive equations from the 3D equationswith focus upon the discussion of often required device configurations forsensor and actuator design and analysis. Two modified coefficients are proposed,termed reduced and enhanced and these enable better understanding of effects ofthe dimensional reduction and also effects on the design and analysis of sensorsand actuator