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

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