content_image/362056.jpg content_image/362055.jpg content_image/362052.jpg content_image/362053.jpg content_image/362054.jpg
case, the Euler-Bernoulli beam model provides overestimated frequencies. Two-dimensional model allows us to evaluate the electric potential accumulated in the nano-switch due to induced nonuniform strain. 

## II. GOVERNING EQUATIONS 

Electromechanical nano-switch may be simulated as a dielectric cantilever nanobeam (Fig. 1). The material of the beam may have tetragonal or cubic symmetry or in another words it may be piezo- or nonpiezoelectric. 

First, let us consider flexoelectric properties of the beam. In [1]-[4] the fourth-order flexoelectric tensor is introduced in two different ways: as µ$_{ijkl}$u$_{j,kl}$ 

or as f$_{ijkl}$ in the additional term in the thermodynamic potential [4]: 

<img src='content_image/362056.jpg'>

<img src='content_image/362055.jpg'>

Here, S$_{ij}$ , e$_{ijk}$ , η$_{lm}$ , are the components of the strain, dielectric, and relative permittivity tensors, respectively, P$_{i}$ , u$_{i}$ , E$_{m}$ , are the components of polarization, displacement, and electric field vectors, respectively, ε$_{o}$ is the permittivity of vacuum. 

In [5] there is a structure of the flexoelectric coefficients for a cubic material (in matrix notation): 

According to [1] and [6], the electric enthalpy may be presented in the form 

<img src='content_image/362052.jpg'>

<img src='content_image/362053.jpg'>

<img src='content_image/362054.jpg'>

