Dynamic analysis of Bernoulli-Euler piezoelectric nanobeam with electrostatic force

The effect of electrostatic force on the dynamic response of a Bernoulli-Euler piezoelectric nanobeam is analyzed in this paper. The governing equations with the electrostatic stress are derived based on a variational principle. Static bending problem of simply supported and cantilever beam is considered. The influence of the electrostatic force on the first four natural frequencies is discussed. It is shown that when the beam thickness is small, the effect of the electrostatic force is significant. When the beam thickness is large, the electrostatic force is insignificant and can be neglected. The results also indicate that one can adjust the natural frequency of a nanobeam by applying appropriate voltage.