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Advances in Nano Research Volume 6, Number 2, June 2018 , pages 163-182 DOI: https://doi.org/10.12989/anr.2018.6.2.163 |
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Nonlinear vibration analysis of an embedded multi-walled carbon nanotube |
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Chih-Ping Wu, Yan-Hong Chen, Zong-Li Hong and Chia-Hao Lin
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| Abstract | ||
| 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 Karman 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. | ||
| Key Words | ||
| foundations; multi-walled carbon nanotubes; nonlinear vibration; nonlocal Timoshenko beams; Reissner's mixed variational theorem; van der Waals interaction | ||
| Address | ||
| Department of Civil Engineering, National Cheng Kung University, Taiwan, ROC. | ||