Sensitivity Analysis of Thickness Assumptions for Piezoelectric Plate Models

This article compares different axiomatic 2D theories for linear homogeneous piezoelectric plates. Simple actuator and sensor configurations are considered of thin and thick piezoelectric ceramics working either in transverse extension (31 mode) or in shear mode (15 mode). By generalizing a previously established unified formulation, a large number of different through-thickness approximations for the in-plane displacement, the transverse displacement and the electrostatic potential are introduced. Additionally, either full 3D constitutive law or reduced constitutive equations accounting for a vanishing transverse normal stress are employed in these plate theories. By referring to an analytical Naviertype closed-form solution, a systematic assessment of various 2D models is performed. The proposed sensitivity analysis of plate theories with respect to their electromechanical response can serve as a useful guide for choosing appropriate models depending on the piezoelectric polarization scheme, the use as sensor or actuator, and the plate thickness.