Nonlinear vibration and chaotic motion of uniform and non-uniform carbon nanotube resonators.
Year: 2014
Type: dissertation
Abstract: Vibration analysis of carbon nanotubes (CNTs) is very essential field owing to\ntheir many promising applications in tiny instruments. The unique and interesting\nproperties of CNTs, particularly their mechanical and electrical features, have fascinated\nindustries and researchers to implement CNTs for production of different\nelectromechanical devices. Research on vibration behavior of CNTs has been done for a\nfew decades. Accordingly, a number of mathematical theories have been developed to\nanalyze the vibration of CNTs. Most of the articles on the vibration of CNTs are focused\non the linear and free vibrations and also, CNTs are supported by linear foundations. The\nmain goal of this research is to develop nonlinear vibration analysis of CNTs having\ngeometrical nonlinearity and being rested on nonlinear Winkler and Pasternak\nfoundations. The nonlinear vibrations of the curved CNTs are developed using the\nEringen theory in conjunction with the Euler-Bernoulli beam model and the thermal\neffect is also considered for the vibration of CNTs. The effects of fluid conveying flow,\ngeometrical nonlinearities and Winkler and Pasternak foundations are studied. Nonlinear\nequations of CNTs vibration postulating the longitudinal electromagnetic effect is also\nmodeled. Furthermore, a new method is developed for the nonlinear vibrations of\nfreeform carbon nanotube based on the Euler-Bernoulli beam theory in conjunction with\nNon-Uniform Rational B-Spline (NURBS). The proposed model is quite straightforward\nfor the vibrational analysis of the curved structures. Moreover, the chaotic motions of the\nfluid conveying carbon nanotube rested on a Winkler and Pasternak foundation are\nstudied. The bifurcation and time history diagrams, phase-plane trajectories and Poincar??\nsections are presented to examine the dynamical behavior of carbon nanotubes. The\nGalerkin 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.
Author: H.R. Askari
Language: English
Subfield: Mechanical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2724205993