content_image/360752.jpg
and at z = ± h/ 2 

<img src='content_image/360752.jpg'>

If the flexoelectric coefficients are equal to zero, the equations (23) coincide with the equa- tions for plates presented in [7]. 

Numerical solution to the system (23) with the boundary conditions (24) - (26) allow us to find the deflection of the nano-switch, the strains, the stresses, and the electric potential accumulated in the cantilever. 

## VI. CONCLUSIONS 

In the present work, the nonlocal properties of the dielectric materials at nanoscale have been taken into account through the flexoelectric effect. Based on the Hamilton’s principle and the electric enthalpy density with additional term describing the coupling between the polarization and the strain gradient, the equations of motion for Euler-Bernoulli and Timoshenko beam models as well as 2-D plate model have been derived. These equations, may be used to analyse the static and dynamic behavior of cantilever nano-switch. The formula connected the flexoelectric coefficient and the maximum deflection of the cantilever has been presented. 

Two dimensional model allows us to analyse the electric potential accumulated in the nano-switch due to the flexoelectric effect. 

