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Resonant and Non-resonant Solutions of the Non-linear Vibration of SWCNTs Embedded in Viscous Elastic Matrix Using KBM Method

  • Ayub Khan
  • Monika Tyagi
  • Mushahid Husain
  • Samina HusainEmail author
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 215)

Abstract

The vibrational analysis of single wall carbon nanotube embedded in viscous elastic matrix has been investigated. The Euler Bernoulli model of non-local continuum theory is used and theoretical dynamic response under parametric excitation is studied. The resonant and non-resonant solutions in the response are analytically studied using Krylov Bogoliubov and Mitropolsky method.

References

  1. 1.
    S. Iijima, Helical microtubules of graphitic carbon. Nature 354, 56–58 (1991). LondonADSCrossRefGoogle Scholar
  2. 2.
    A.C. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54(9), 4703–4710 (1983)ADSCrossRefGoogle Scholar
  3. 3.
    Q. Wang, Y. Shindo, Nonlocal continuum models for carbon nanotubes subjected to static loading. J. Mech. Mater. Struct. 1(4), 663 (2006)CrossRefGoogle Scholar
  4. 4.
    B. Arash, Q. Wang, A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes. J. Comput. Mater. Sci. 51, 303–313 (2012)CrossRefGoogle Scholar
  5. 5.
    Y.Z. Wang, Y.S. Wang, L.L. Ke, Nonlinear vibration of carbon nanotube embedded in viscous elastic matrix under parametric excitation by nonlocal continuum theory. Phys. E 83, 195–200 (2016). Elsevier, North HollandCrossRefGoogle Scholar
  6. 6.
    A. Khan, S. Husain, Dynamical response of the nonlinear vibration of single walled carbon nanotubes. J. Comput. Theor. Nanosci. 9, 1–10 (2012). American Scientific Printers, USACrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ayub Khan
    • 2
  • Monika Tyagi
    • 1
  • Mushahid Husain
    • 3
  • Samina Husain
    • 1
    Email author
  1. 1.Centre for Nanoscience and NanotechnologyJamia Millia IslamiaNew DelhiIndia
  2. 2.Department of MathematicsJamia Millia IslamiaNew DelhiIndia
  3. 3.Department of PhysicsJamia Millia IslamiaNew DelhiIndia

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