Torsional Dynamic Response of a Carbon Nanotube Embedded in Visco-Pasternak’s Medium

Abstract

The torsional dynamics of carbon nanotubes embedded in viscoelastic medium are presented by using the nonlocal elasticity theory. The medium is considered as a foundation model which characterized by the linear Winkler’s modulus, Pasternak’s (shear) foundation modulus and the damping coefficient. The governing torsional equation is obtained and solved for nanotubes subjected to various boundary conditions and stated under different loads. The effects of some parameters like nonlocal parameter, nanotube length, Winkler’s modulus, and damping coefficient on the angular displacement of the nanotube are investigated in detail. The angular displacements are very sensitive to all parameters, especially the inclusion of the viscous damping foundation. Present results can be useful in design of future nano composites, nano electromechanical systems like nano position sensors and linear servomotors. Sample angular displacements are tabulated and plotted for sensing the effect of all used parameters and to investigate the visco-Pasternak’s parameters for future comparisons.