On the vibration of nanorods restrained by a linear spring in-span

• The axial vibration of nanorod with an attached spring is studied using nonlocal elasticity theory.
• The nonlocal constitutive equations of Eringen are employed in the formulation.
• The point of attachment of the spring has differing effect on the different modes of the vibration.
• The nonlocal elasticity should be considered for nanoscale rods.

The axial vibration of nanorod (carbon nanotube) with an attached spring is studied using nonlocal elasticity theory. The nonlocal constitutive equations of Eringen are employed in the formulation. The effect of various parameters like geometry of nanotube, position of spring and stiffness of the spring on the axial vibration of carbon nanotubes is discussed. It is shown that the point of attachment of the spring has differing effect on the different modes of the vibration. The present results can be used in the continuum modeling of nanoelectromechanical systems.