Vibration analysis of piezoelectric nanowires using the finite element method

ABSTRACT: A finite element model for free vibrations of piezoelectric nanowires (NWs) is developed based on the non-local Euler-Bernoulli beam theory and Galerkin method. The governing equation of motion for the piezoelectric NW with consideration of non-local effects and surface effect is obtained, and the approximate expressions for the natural frequencies and the fundamental buckling voltage are derived for simply supported boundary conditions. Also, an explicit relationship between the residual surface tension and the small scale parameter of the piezoelectric NW, based on the critical electric potential is offered at which the axial buckling occurs. Consequently, a method is given that may assist in experimental application of NW based instruments.