In piezoelectric materials and at the nano-scale, there is a coupling between electrical polarization and strain gradients fields, which is called flexoelectricity. The effects of this phenomenon seem to be negligible in micro/macro scales. The current study has attempted to have a cohesive concentration on the buckling behaviors of sandwich plates. To achieve the abovementioned aim with a higher accuracy, the flexoelectric effect assumes to be existing on the top and bottom face sheets and the core is a composite plate. Also, based on statistics, the first-order shear deformation theory seems to lead to more accurate results. Therefore, in the present research we follow this method to obtain results. The analytical method is applied to solve higher order governing equations. In addition, the critical buckling voltage is calculated considering the flexoelectricity, and it is found that the effects of flexoelectricity play significant roles in determining the critical buckling voltage. Moreover, it is revealed that the thickness of the flexoelectric face sheets and the aspect ratio of the sandwich plate play the same role in critical buckling load variations. It means that the critical buckling load decreases when the thickness of the flexoelectric face sheets or the aspect ratio of the sandwich plate increases and vice versa. The results of the present work can be used for the optimum design and control of similar systems such as micro-electro-mechanical and nano-electromechanical devices.

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In this research, semi-active control of sandwich plates with electro-rheological (ER) core and carbon nanotubes-reinforced composite facesheets using smart ER dampers is studied. Sandwich plate is subjected to the external electric field and rested on orthotropic visco-Pasternak foundation. The material properties of ER core and nanocomposite facesheets are obtained by Yalcintas model and Eshelby-Mori-Tanaka approach, respectively. The governing equations of motion are solved by a combination between finite element and Newmark methods for clamped and simply supported boundary condition. The effects of various parameters such as applied voltage, controlled electric field and initial gap of the electrodes on the vibration suppression time are discussed. The results show that the settling time of system introduced in this work is much less than previous researches in this field which is a very important advantage.