Recently, the SE method has been extensively used to investigate the wave propagation problems for the purpose of damage detection in structures [36,37]. However, according to the authors’ best knowledge, the SE method has not been previously used for accurately modeling of the through-the-thickness electric potentials for piezoelectric bimorphs.For the purpose of accurately representing the mechanical displacement and the electric potential, a reasonable choice is to use the ESL model for the mechanical variables and the layer-wise theory or the sublayer theory for the electric variables. In the present work, we attempt to combine the merits of the SE method and the sublayer model. More specifically, the mechanical variables, i.e., the displacements, are described based on FSDT.

The electrical variables, i.e., the potentials, are described using the sublayer model. SE method is then utilized to deduce the governing equations. Legendre orthogonal polynomials are adopted in the interpolation function to improve the accuracy. To validate the effectiveness and the capability of the present model, numerical simulations for a simply supported piezoelectric bimorph with two different load cases, i.e., a uniform pressure load applied to the top surface and a uniform potential applied to the top and bottom surfaces, are carried out. The results obtained by the present approach are then compared to those coming from the coupled 3-D FE simulations using ABAQUS. The comparisons show the good accuracy and efficiency of SE method for modeling of the through-the-thickness electric potentials of the piezoelectric bimorph.

2.?Mathematical Formulation2.1. Constitutive Relationships, Displacement and StrainA piezoelectric Batimastat bimorph made of two identical PZT-4 piezoelectric layers, which has been investigated by Fernandes [1], is considered here. The PZT-4 layer is assumed to behave in a linear orthotropic manner with small displacements and strains. As depicted in Figure 1, both piezoelectric layers have the same thickness 0.5 h and are poled in the same direction. The x-y plane of the coordinate system x-y-z coincides with the middle plane of the bimorph, and the z axis is defined normal to the middle plane following the right-hand rule. This work aims to investigate the problem of a simply supported piezoelectric bimorph under a uniform pressure load or an applied electric potential in the framework of linear theory of piezoelectricity. Assuming the PZT-4 layers work under isothermal conditions, the pyroelectric effects and thermomechanical couplings are not taken into account.