Finite Element Modeling of the Piezolaminated Beam Using Von Karman Nonlinear Strain- Displacement Relation

A refined sandwich beam model is proposed in the present work. The facing layers respect Euler-Bernoulli assumptions and the core is modeled with the thirdorder shear deformation theory (TSDT). In the Von Karman sense, the geometrically nonlinear relations between displacement fields and strains are developed. In what follows, a theoretical variational formulation of the problem is presented and then used to develop the electromechanically coupled finite element model of multilayer sandwich beam with considering mechanical DoFs as well as the electric ones. Finally, the nonlinear system of equations is linearized. It is shown that natural frequencies can change considerably for higher applied voltage to extensional piezoelectric layers.