STUDY ON THE NONLINEAR VIBRATION OF SWCNTs WITH INITIAL AXIAL STRESS BASED ON THE BIFURCATION THEORY OF DYNAMICAL SYSTEMS.

The nonlinear dynamical behaviors of single-walled carbon nanotubes (SWCNTs) with the initial axial stress are investigated based on Donnell's cylindrical shell model. By using the bifurcation theory of dynamical systems on a vibration equation of SWCNTs, the existence of centers, saddles, families of periodic orbits, homoclinic orbits and/or heteroclinic orbits is shown. Under different initial conditions, various sufficient conditions to guarantee the existence of the above solutions are given and the dynamical behaviors of SWCNTs are well-known. [ABSTRACT FROM AUTHOR]