Analysis of nonlinear dynamic stability of single-walled carbon nanotubes in thermal environments

Based on the non-local Euler beam theory, the nonlinear dynamic stability of single-walled carbon nanotubes (SWCNTs) embedded in an elastic medium including the thermal effects is presented. The nonlinear dynamic equations and the boundary conditions of the SWCNTs are obtained by using the Hamilton variation principle. By adopting the Galerkin procedure, the governing nonlinear partial differential equation is converted into a nonlinear ordinary differential equation, and then the incremental harmonic balance method is applied to obtain the principal unstable regions of the SWCNTs. In the numerical examples, the effects of the thermal loads, the non-local parameters and the elastic medium on the nonlinear dynamic stability, respectively, are discussed.