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The flexoelectric effect is coupling of polarization and strain gradient,which exists in wide variety materials and presents strong size-dependent at the nanoscale.In recent,the flexoelectrie effect of the bending piezoelectric nanobeam and nanoplate has been investigated in open circuit electrical boundary and closed circuit electrical boundary.In their closed circuit electrical boundary,the electrodes fix the difference of electric potential at the top and bottom.However,the electrodes may undergo a difference of electric potential as a result of mechanical deformation due to the flexoelectric effect.Based on the Bernoulli-Euler beam model,this paper investigates the electromechanical coupling response of piezoelectric nanobeams with three electrical boundary conditions as well as the bulk flexoelectricity being considered.