Investigation of Torsional Static Behavior of Nano-rods Embedded in Elastic Medium Considering Surface Energy Effect

In this paper, the torsional static behavior of nano-rods under external torsional loads and embedded in elastic medium is investigated by considering the surface energy effect (the energy due to the surface shear modulus and the surface stress). For this purpose, surface stress components are obtained using the surface elasticity theory, and three types of external torsional loadings, uniform torque load, linear torque load, and sinusoidal torque load are considered. Then, the governing equation of motion of nano-rod is derived using the Hamilton’s principle. The governing equation of motion is analytically solved for clamped-clamped and clamped-free boundary conditions; and the surface energy effect on torsional static behavior of nano-rod (rotational displacements) is investigated for various values of nano-rod radius and length, and torsional torque. In order to complete the investigations, effects of value and sign of the surface energy components on torsional static behavior of nano-rod are also considered. The obtained results show that the effect of the surface energy can be dependent on the geometrical parameters and the value and sign of the surface energy components. Results of the present study can be useful in design of nano-electro-mechanical systems like nano--bearings and rotary servomotors.