Nonlinear size-dependent behaviour of single-walled carbon nanotubes
This paper examines the nonlinear size-dependent behaviour of single-walled carbon nanotubes (SWCNTs) based on the von-Karman nonlinearity and the nonlocal elasticity theory capable of predicting size effects. To this end, based on Hamilton's principle in the framework of the nonlocal Euler-Bernoulli beam theory, the equation of motion and associated boundary conditions are derived. Then, with the aid of a high-dimensional Galerkin scheme, the nonlinear partial differential equation of motion of the SWCNT is recast into a reduced-order model. The dynamic response of the system is then investigated for two different types of excitation, namely primary and superharmonic excitations. Eventually, the effect of the slenderness ratio, forcing amplitude, and excitation frequency on the motion characteristics of the system is investigated.