Three-Dimensional Thermal Stress Effects on Nonlinear Torsional Vibration of Carbon Nanotubes Embedded in an Elastic Medium

ABSTRACT Nonlinear torsional vibration of nanorods embedded in an elastic medium under three-dimensional thermal stresses is investigated in this study. The scale effect is introduced to the equation of motion using the nonlocal theory. The nanorods are under the effect of a three-dimensional thermal environment. The elastic medium is modeled by infinite rotational springs around the nanorod. Galerkin’s and He’s variational methods are used to solve the differential equation of motion and obtain torsional frequencies. An uncertainty analysis is done to show the effect of the uncertain parameters on the frequencies. The frequency sensitivities are obtained to demonstrate the frequency sensitivities to uncertain parameters. Effect of temperature changes, elastic medium stiffness, vibration amplitude, nonlocal scale coefficient, and nanorod length and diameter on the nonlinear torsional frequencies are investigated. The effect of temperature on the frequencies is dependent on the values of elastic medium stiffness, vibration amplitude, and nanorod length and diameter.