vibration of piezoelectric nanowires including surface effects

in this paper, surface and piezoelectric effects on the vibration behavior of nanowires (nws) are investigated by using a timoshenko beam model. the electric field equations and the governing equations of motion for the piezoelectric nws are derived with the consideration of surface effects. by the exact solution of the governing equations, an expression for the natural frequencies of nws with simply-supported boundary conditions is obtained. the effects of piezoelectricity and surface effects on the vibrational behavior of timoshenko nws are graphically illustrated. a comparison is also made between the predictions of timoshenko beam model and those of its euler-bernoulli counterpart. additionally, the present results are validated through comparison with the available data in the literature.