A CONSISTENT THEORY OF THIN PIEZOELECTRIC PLATES

In this paper a theory of thin piezoelectric plates is obtained throug h a rational derivation from the three-dimensional linear theory of pi ezoelectricity. The coupling between the electric and mechanical field s is taken into account, leading to a consistent definition of the ben ding and stretching stiffnesses. In particular, it is shown that a pie zoelectric 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 in itial 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 establ ished here is used to find closed-form expressions of the solutions of some technical problems, involving piezoelectric plates used as senso rs or actuators.