(NTU "KhPI", 2016) Strozzi, Matteo; Manevitch, Leonid I.; Smirnov, Valeri V.; Pellicano, Francesco
In this paper, the nonlinear vibrations and energy exchange of single-walled carbon nanotubes (SWNTs) are
investigated. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of
finite amplitude of vibration. The SWNT deformation is described in terms of longitudinal, circumferential and
radial displacement fields. Simply supported boundary conditions are considered. The circumferential flexural
modes (CFMs), radial breathing modes (RBMs) and beam-like modes (BLMs) are studied. A numerical model
of the SWNT dynamics is proposed. The three displacement fields are expanded in the nonlinear field by using
approximate linear eigenfunctions. An energy method based on the Lagrange equations is used to reduce the
nonlinear partial differential equations of motion to a set of nonlinear ordinary differential equations, which is
solved using the implicit Runge-Kutta numerical method. The nonlinear energy exchange along the SWNT axis
is analysed for different initial excitation amplitudes. The internal resonances between CFMs, RBMs and BLMs
are investigated. The transition from energy beating to energy localization in the nonlinear field is studied.
