Nonlinear vibration analysis of an embedded multi-walled carbon nanotube

Chih Ping Wu, Yan Hong Chen, Zong Li Hong, Chia Hao Lin

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


Based on the Reissner mixed variational theorem (RMVT), the authors present a nonlocal Timoshenko beam theory (TBT) for the nonlinear free vibration analysis of multi-walled carbon nanotubes (MWCNT) embedded in an elastic medium. In this formulation, four different edge conditions of the embedded MWCNT are considered, two different models with regard to the van der Waals interaction between each pair of walls constituting the MWCNT are considered, and the interaction between the MWCNT and its surrounding medium is simulated using the Pasternak-type foundation. The motion equations of an individual wall and the associated boundary conditions are derived using Hamilton's principle, in which the von Kármán geometrical nonlinearity is considered. Eringen's nonlocal elasticity theory is used to account for the effects of the small length scale. Variations of the lowest frequency parameters with the maximum modal deflection of the embedded MWCNT are obtained using the differential quadrature method in conjunction with a direct iterative approach.

Original languageEnglish
Pages (from-to)163-182
Number of pages20
JournalAdvances in Nano Research
Issue number2
Publication statusPublished - 2018

All Science Journal Classification (ASJC) codes

  • Biotechnology
  • Catalysis
  • Electronic, Optical and Magnetic Materials
  • Ceramics and Composites
  • Atomic and Molecular Physics, and Optics
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes
  • Electrical and Electronic Engineering


Dive into the research topics of 'Nonlinear vibration analysis of an embedded multi-walled carbon nanotube'. Together they form a unique fingerprint.

Cite this