The electro-mechanical coupling responses of functionally graded piezoelectric nanobeams with flexoelectric effect

The aim of this paper is to study the electro-mechanical coupling responses of functionally graded (FG) piezoelectric cantilever nanobeam under the concentrated load, and the material properties follow an exponential distribution in the thickness direction. The constitutive equations are derived from the electric Gibbs free energy density function. The governing equations and boundary conditions of the Euler-Bernoulli FG beam can be obtained by variational principle, and then, the analytical expressions for its deflection, polarization intensity, and induced potential are obtained. The results show that the flexoelectric effect has a significant impact on the deflection, polarization intensity, and induced potential of the FG cantilever nanobeam.