A consistent theory of thin piezoelectric plates

In this paper a theory of thin piezoelectric plates is obtained through a rational derivation from the three-dimensional linear theory of piezoelectricity. The coupling between the electric and mechanical fields is taken into account, leading to a consistent definition of the bending and stretching stiffnesses. In particular, it is shown that a piezoelectric plate has a different stretching stiffness when it is used as an actuator or as a sensor. The procedure used to derive the field equations governing the piezoelectric plate problem is based on the initial functions method, in conjunction with a rescaling of the applied loads. The field equations are then rewritten in a variational form, according to a generalized statement of the virtual work principle, in order to deduce the compatible boundary conditions. The theory established here is used to find closed-form expressions of the solutions of some technical problems, involving piezoelectric plates used as sensors or actuators.