Analysis of piezoelectric bimorphs and plates with segmented actuators

Elastic plates with distributed or segmented piezoelectric layers have been analyzed using the classical laminated plate theory, the first-order shear deformation theory, and the results are compared with an analytical solution. The plate theories and the analytical solution take into account both the direct and the converse piezoelectric effects, and assume generalized plane strain deformations. The transverse displacements from both theories are in reasonable agreement. The classical lamination theory gives a discontinuous longitudinal stress at the edges of the segments whereas the analytical solution predicts a continuous curve with steep gradients. Piezoelectric bimorphs with the axis of transverse isotropy inclined at an angle to the thickness direction are also studied using the three formulations. The displacements and stresses obtained from the first-order shear deformation theory are in very good agreement with the analytical solution even for thick plates. It is advantageous to use shear bimorphs since the stresses induced in them are smaller than those in extension bimorphs.