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This paper investigates the longitudinal vibration of a nanorod considering the lateral inertia effects. A micro-mechanical size dependent theory called as doublet mechanics is applied on vibration analysis of nanorods. The equations of motion and boundary conditions are derived using Hamilton Principle. Clamped-clamped and clamped-free boundary conditions are considered in the analysis. Doublet mechanics has a remarkable physical basis at the nano structures. Natural frequencies obtained by doublet mechanics give accurate results compared to classical elasticity results. The effects of length scale parameter, geometry of nanorods and lateral inertia are investigated in detail. It should be noted that doublet mechanics can be used for the design of nano-devices such as nano-motors, nano-transistors, nano-rotors etc.