Nonlinear vibration and chaotic motion of uniform and non-uniform carbon nanotube resonators.
Date
2014-07-01
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Vibration analysis of carbon nanotubes (CNTs) is very essential field owing to
their many promising applications in tiny instruments. The unique and interesting
properties of CNTs, particularly their mechanical and electrical features, have fascinated
industries and researchers to implement CNTs for production of different
electromechanical devices. Research on vibration behavior of CNTs has been done for a
few decades. Accordingly, a number of mathematical theories have been developed to
analyze the vibration of CNTs. Most of the articles on the vibration of CNTs are focused
on the linear and free vibrations and also, CNTs are supported by linear foundations. The
main goal of this research is to develop nonlinear vibration analysis of CNTs having
geometrical nonlinearity and being rested on nonlinear Winkler and Pasternak
foundations. The nonlinear vibrations of the curved CNTs are developed using the
Eringen theory in conjunction with the Euler-Bernoulli beam model and the thermal
effect is also considered for the vibration of CNTs. The effects of fluid conveying flow,
geometrical nonlinearities and Winkler and Pasternak foundations are studied. Nonlinear
equations of CNTs vibration postulating the longitudinal electromagnetic effect is also
modeled. Furthermore, a new method is developed for the nonlinear vibrations of
freeform carbon nanotube based on the Euler-Bernoulli beam theory in conjunction with
Non-Uniform Rational B-Spline (NURBS). The proposed model is quite straightforward
for the vibrational analysis of the curved structures. Moreover, the chaotic motions of the
fluid conveying carbon nanotube rested on a Winkler and Pasternak foundation are
studied. The bifurcation and time history diagrams, phase-plane trajectories and Poincaré
sections are presented to examine the dynamical behavior of carbon nanotubes. The
Galerkin approach in conjunction with the multiple time scales method is chosen to study the nonlinear vibrations of the proposed models. The effects of different parameters on the primary and secondary resonant cases and also the nonlinear and linear frequencies of CNTs are examined.
Description
Keywords
Nonlinear vibration, Chaos, Non-uniform carbon nanotube resonators