Surface and Magnetic Field Effects Analysis on the Primary and Superharmonic Resonance Frequency Response of Single Walled CNT

In this study, based on the nonlocal nonlinear Euler-Bernoulli beam model, the primary and superharmonic resonance of a single carbon nanotube (CNT) resting on a viscoelastic foundation under the magnetic axial loads and temperature as well as transverse harmonic forces was investigated. Using Galerkin approximation along with the trigonometric shape functions, the nonlinear partial differential governing equation is reduced to nonlinear ordinary differential equation. The frequency response of the single walled CNT is derived by implementing the multiple time scale method for the primary and superharmonic resonances. The effects of surface elasticity, change in temperature, magnetic field and the length-to-outer diameter aspect ratio on the frequency response of CNT in the cases of primary and superharmonic resonances were analyzed. The results show that the nonlinearity according to considered geometrical and mechanical parameters in this study, may cause unpleasant jumping phenomenon accompanied by unstable region in the frequency response. In addition to the surface elasticity, magnetic field, smaller temperature changes, as well as larger aspect ratio have positive effects on weakening the jumping phenomenon and extending the stability level of single walled CNT.