Effect of electrostatic force on a piezoelectric nanobeam

This paper deals with the bending of Bernoulli-Euler piezoelectric nanobeams. Unlike in the classical theory, the effect of electrostatic force is taken into account. A variational principle is employed to derive the governing equations, and the electrostatic force moment is defined. The electrostatic force moment depends on the piezoelectricity. A cantilever beam problem is solved. It is shown that the effect of the electrostatic force on the deflection of the beam is significant when the beam thickness is small, and decreases with increase of the beam thickness. The results indicate that the deflection of a nanobeam can be modified through the electrostatic force by adjusting the voltage.