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