Size-dependent analysis of a three-layer microbeam including electromechanical coupling

Strain gradients can induce polarization even in centrosymmetric materials. A size-dependent model of a three-layer microbeam including a flexoelectric dielectric layer is proposed based on the theory presented by Hadjesfandiari. The governing equations, initial conditions and boundary conditions are derived by utilizing the Hamilton’s principle. Both the static bending and free vibration problems of cantilever and simply supported microbeams are solved. Numerical results reveal that for both cantilever beam and simply supported beam, the absolute values of voltages induced in the piezoelectric process and deflections generated in the inverse piezoelectric process decrease as the characteristic size decreases and increase with the increase of flexoelectric coefficient. The first order natural frequency increases negligibly as the flexoelectric coefficient increases while decreases significantly with the increase of the characteristic size. The first order natural frequency shows obvious size effect, but the size effect is almost diminishing as the thickness of the beam is far greater than the material length scale parameter.