Equations for Elastic Plates with Partially Electroded Piezoelectric Actuators in Flexure with Shear Deformation and Rotatory Inertia

A system of two-dimensional equations for the flexural motion of an elastic plate with both electroded and unelectroded portions of piezoelectric actuators attached to the top and bottom surfaces are derived from existing equations of thin elastic and piezoelectric plates by satisfying the actuator-plate interface conditions. In the derivation, the piezoelectric actuators are assumed to be very thin compared to the elastic plate and are treated as films which are in extensional motion but do not resist bending. The unelectroded portions of the piezoelectric actuators have the effect of reducing the shear stress concentration near the edges of the actuators. These equations are generalizations of an earlier system of equations in the literature in that the elastic plate is governed by the Reissner Mindlin theory of flexure with shear deformation and rotatory inertia. Therefore they can be used in cases when the elastic plate is not very thin. The equations obtained are of second order and are suitable for finite element implementation.