Investigation of the vibration behavior of nano piezoelectric rod using surface effects and non-local elasticity theory

Due to the importance of the analysis of piezoelectric nanorods and the different conditions they are exposed to in engineering problems, in this research, for the first time, both nonlocal elasticity theory and surface energy theory have been used simultaneously to model a piezoelectric nanorod. The natural frequency values of the system have been extracted using the Galerkin weighted residual method. By applying an external excitation voltage, the forced vibrations of nonlocal nanorods with surface effects are presented. The results are reported for different vibrational modes, and the impact of different parameters such as dimensions, nonlocal parameters, and surface effects are investigated. The results of this study prove that the nonlocal elastic theory is more effective than the surface energy theory on the vibration behavior of piezoelectric nanorods. Also, the effect of piezoelectric properties is strengthened due to the nanoscale of the rods.