Nonlinear vibrations of embedded multi-walled carbon nanotubes using a variational approach

Analytical and computational studies of the nonlinear vibrations of SWCNTs embedded in viscous elastic matrix using KBM method

The forced vibration analysis of single wall carbon nanotubes (SWCNTs) embedded in the viscous elastic matrix subjected to axial parametric excitation has been investigated. The Euler Bernoulli beam model of the non-local continuum theory is used. The resonant and non-resonant solutions are analytically studied using the Krylov Bogoliubov and Mitropolsky method. It has been seen that the amplitude remains constant up to the second order of approximation. The resonant solutions are also found to analyze the possibility of chaos in the neighborhood of resonance. The computational techniques are used, and plots of time series, phase plot, and Poincaré surface of section are also drawn to confirm the chaotic behavior for certain values of parameters of SWCNTs, which may lead the aging process in the SWCNTs after a long time.