Vibration analysis of piezoelectric nanowires with surface and small scale effects

An analytical model for predicting surface effects on the free transverse vibrations of piezoelectric nanowires (NWs) is developed based on the non-local Euler-Bernoulli beam theory. The governing equation of motion for the piezoelectric NW with consideration of both surface and non-local effects is initially obtained, and the exact expressions for the natural frequencies and the fundamental buckling voltage are derived for simple support conditions. In addition, an explicit relationship between the residual surface tension and the small scale parameter of the piezoelectric NW, in terms of the critical electric potential at which the axial buckling occurs, is offered. Accordingly, a design chart is presented which may assist in experimental characterization of the mechanical properties of piezoelectric NW-based devices.