Simulation of Free Vibrations of Multi-Walled Carbon Nanotube Based on Non-Local Theory of Thin Elastic Orthotropic Shells

Abstract

The mathematical model of multi-walled carbon nanotube embedded in an elastic matrix is proposed. The effect of the surrounding elastic medium are considered using the Winkler-type spring constant. The tube may be prestressed by external forces. The Flugge type equations for orthotropic cylindrical shells, including the initial membrane hoop and axial stresses, are used as the governing ones. The constitutive equations are formulated by considering the small-scale effects. The dependence of natural frequencies upon a number of waves in the longitudinal direction, tube length and the motion directions of walls as well is studied.

Keywords

• multi-walled carbon nanotube
• nonlocal theory of elasticity
• van der waals forces
• equations of motion
• free vibrations