Vibration and static buckling behavior of variable thickness flexoelectric nanoplates

The nanoplates have been used extensively in electronic devices, during the working process they can be affected by external forces. To enhance the working performance of mechanical systems, flexoelectric effects are usually added, therefore, it is necessary to study the mechanical behavior of these material structures under the effect of these effects. This is the first research to examine the vibration response and static buckling of variable flexoelectric nanoplates using the FEM and novel shear deformation theory type hyperbolic sine functions, where the thickness is adjusted by linear and nonlinear rules. This is a simple theory, which does not need any shear correction factors, while the mechanical responses of the structures are still described exactly. The numerical results of this work are compared with those of the analytical approach and other methods. Then, the influences of geometrical and material parameters on the free vibration and static bucking of the structure are explored. The data shows that the flexoelectric effect has a strong effect on the free vibration and static bucking behavior as well as the vibration mode shapes of the nanoplates. The working performance is increased when taking into account the effect of flexoelectricity. This work also shows that for each changing rule of plate thickness, the flexoelectric effect also significantly changes the mechanical response of the plate. This is an important suggestion in the design and use of plate structures in engineering practice.