Exact Solution for Rectangular Sandwich Plates with Embedded Piezoelectric Shear Actuators

An exact solution is obtained for the three-dimensional deformations of simply supported laminated rectangular thick plates with embedded shear mode piezoelectric actuators, subjected to mechanical and electrical loading on the upper and lower surfaces. Each layer of the laminate is made of either an orthotropic elastic material or a piezoelectric material whose poling direction lies in the plane of the plate, with perfect bonding between the adjoining layers. The exact displacements and stresses for a homogeneous piezoelectric plate for various lengthto-thickness ratios are compared with those obtained by the Ž rst-order shear deformation theory. Results are also presented for a sandwich plate consisting of a shearmode piezoelectric core sandwiched between two elastic layers. A comparison of the stresses with those in the corresponding surface-mounted extension actuation conŽ guration shows that for the same transverse de ection of the plate centroid, the maximum longitudinal stress within the actuator is signiŽ cantly smaller for the shear actuation mechanism. The exact results presented here can be used to assess the accuracy of different plate theories and/or for validating Ž nite element codes.