Multilayered Piezoelectric Refined Plate Theory

Abstract

A two-dimensional theory for the analysis of multilayered piezoelectric plates is presented. The theory is based on a hybrid approach in which the continuity conditions for both mechanical and electric unknowns at layer interfaces, as well as the imposed conditions on the bounding surfaces and at the interfaces, are independently satiss ed. Then, the piezoelectric boundary-valueproblem is stated usingmechanicaldisplacementsand electrostatic potential, in conjunction with the coupled piezoelectric constitutive law. The proposed model is simple to use, incorporatingonlyy ve independent generalized displacementsand oneor two independentgeneralized electrostatic potentials as unknowns. The number of electric unknowns depends on the number of layers and electric prescribed conditions. The accuracy of the proposed theory is assessed through investigation of signii cant problems, for which an exact three-dimensional solution is known from Heyliger: rst, in dynamics, the free vibrations of ve-layered piezoelectric plates and second, in statics, for three-layered plates with an imposed force density. Results obtained with our model compare very well with the exact three-dimensional theory.