Axial vibration of the nanorods with the nonlocal continuum rod model

Nonlocal elastic rod model is developed and applied to investigate the small-scale effect on axial vibration of nanorods. Explicit expressions are derived for frequencies for clamped–clamped and clamped–free boundary conditions. It is concluded that the axial vibration frequencies are highly over estimated by the classical (local) rod model, which ignores the effect of small-length scale. Present results can be used for axial vibration of single-walled carbon nanotubes.