In this work, an electromechanically coupled finite element model for a piezolaminated beam was presented. For the mechanical model, classical sandwich theory (CST) was considered, where the core was modeled according to the third-order shear deformation theory (TSDT). On the contrary, the face sub-layers were modeled with the Euler-Bernoulli hypothesis. By means of the Von Karman's theory, the displacements-strains relations were developed. For complete satisfaction of the electrostatic equilibrium equation, for both shear and extensional piezoelectric layers, the longitudinal and transverse electrical fields were considered. In the next step, a variational formulation was written using the Hamilton's principle with extension to the piezoelectric media. Then, using the aforementioned assumptions, a finite element (FE) model was developed. Electrically, constant electric difference of potentials for core and face piezoelectric layers were assumed. Also, quadratic shape functions for the third-order variable of electric potential were considered for the core piezoelectric layers. For the mechanical variable interpolations, linear Lagrange, quadratic and cubic shape functions were considered for the axial displacement, bending rotation of the core and transverse displacement, respectively. For obtaining a faster and more reliable solution, the electrical and elemental variables were condensed out statically. Finally, by examining the governing equation for the sandwich beam, a new electromechanical effect for the extensional piezoelectric layers was shown up due to the consideration of the Von Karman's theory. for evaluation of natural frequencies, the first step is to linearize the governing equations of the system about a static equilibrium position. The validation of the proposed model is achieved by comparing it with the availableresults. After validation of the developed technique, a shear piezoelectric sandwiched beam with two extensional piezoelectric actuators is considered. It shows that by applying high voltage to the actuators, the percentage of changes in the natural flexural frequencies is considerable. The change is mainly due to the consideration of the Von Karman's theory. However, since there is no sensor in this configuration, the nonlinearity will not show it up noticeably. Therefore, to analyze the nonlinearity effect, another extensional piezoelectric layer is added to the previous model which acts as a sensor. It is shown that this nonlinearity effect could be important for higher applied forces and also have a considerable influence on the natural flexural frequencies. Key Words: Finite element method, Piezoelectric, Von Karman strain-displacement relations, Generalized Hamilton's principle, Third-order shear deformation theory.
