On the formulation of a piezoelectric plate model

In this paper, the formulation of a piezoelectric plate capable of describing the behavior of both the direct and converse piezoelectric effects is presented. The model of plate is meant as a bi-dimensional structured continuum with no limiting hypothesis kept about the thickness dimension. The constitutive relations and the equilibrium equations are obtained assigning a specific structure to the field of admissible displacement of a linear piezoelectric and transversely isotropic three-dimensional continuum within the hypotheses of linear constitutive relations and 'small' deformations from a stress-free placement. Based on the assumption that a linear distribution along the plate thickness direction of the electric potential is not sufficient for representing the potential electric energy, consequences are drawn for the assumptions to be made for the distributions along the thickness of the displacement field. The governing equations of the membrane and flexural behavior of the model are then obtained.