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Chaotic Flexural Oscillations of Embedded Non-Local Nanotubes Subjected to Axial Harmonic Force

[+] Author Affiliations
Zia Saadatnia

University of Toronto, Toronto, ON, Canada

Ebrahim Esmailzadeh

University of Ontario Institute of Technology, Oshawa, ON, Canada

Paper No. DETC2017-68317, pp. V008T12A004; 10 pages
doi:10.1115/DETC2017-68317
From:
  • ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 8: 29th Conference on Mechanical Vibration and Noise
  • Cleveland, Ohio, USA, August 6–9, 2017
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5822-6
  • Copyright © 2017 by ASME

abstract

Chaotic behavior of an embedded carbon nanotube subjected to an external excitation and the combinational static-dynamic axial loads is investigated. Mathematical formulation has been developed based on the non-local theory in order to reflect the small-scale effects. The tube is supported by the Kelvin-Voigt viscoelastic foundation and the Galerkin method is utilized to solve the governing nonlinear differential equations. The vibration behavior of the system for the parameters of a real model is studied and different vibration responses of the nanotube such as the periodic, quasi-periodic and the chaotic behaviors are detected. The bifurcation diagrams for several critical parameters, including the amplitude of external excitation and the axial applied load are presented. The time history diagram, phase-plane trajectories, and the Poincaré map are presented as the three appropriate techniques for diagnosing the system behavior under various conditions.

Copyright © 2017 by ASME

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