On the size dependency of a dielectric partially covered laminated microbeam

A size-dependent model for a laminated microbeam with a partially covered flexoelectric layer is developed by using the isotropic flexoelectric theory. The static bending problem of the beam under the uniformly distributed load and the voltage with different boundary conditions is solved. The method of weighted residuals is applied to derive the analytical expressions of the charge, the potential, the polarization and the deflection. The size dependency of the charge, the potential, the polarization and the deflection is discussed. Results reveal that the charge, the potential, the polarization and the deflection is dependent on the ratio of beam thickness and material length-scale parameters. As the ratio increases, the charge, the potential, the polarization and the deflection gradually increase. In addition, the effects of length and thickness of flexoelectric layer on the induced charge and induced deflection are also studied. There is an optimum length and thickness of the flexoelectric layer to achieve the maximum induced charge and maximum induced deflection.