A modified first-order plate theory of laminated piezoelectric plate actuators

Piezoelectric actuators with large output and high reliability are widely applied in electron device. In this paper, a modified first-order plate theory of laminated piezoelectric plates with upper and lower electrodes is presented. Then, based on the Mindlin first-order shear deformation theory, a quadratic function of electric potential across the thickness is used to describe the inverse piezoelectric effect. The laminated plate governing equations are derived in terms of the resultant force, moment and electric displacement. Further, supplementary equations are introduced through the continuity of electrical potential and the normal electric displacement across interface of each lamina, which are applied to solve the unknown electric functions in each lamina. The numerical results of displacement, deflection and electric potential are consistent with those obtained by the three-dimensional finite element method. Finally, with such a modified plate theory, regulation mechanisms of polarization direction and layer numbers are investigated on actuation properties of laminated piezoelectric actuators. It is shown that the polarization direction can change the driving displacement by an order of magnitude. It is expected that the modified theory can provide a more efficient and accurate approach for analysis of multilayer piezoelectric composite actuators.