Vibration analysis of multi-walled carbon nanotubes embedded in elastic medium

Abstract

We propose a method to estimate the natural frequencies of the multi-walled carbon nanotubes (MWCNTs) embedded in an elastic medium. Each of the nested tubes is treated as an individual bar interacting with the adjacent nanotubes through the inter-tube Van der Waals forces. The effect of the elastic medium is introduced through an elastic model. The mathematical model is finally reduced to an eigen value problem and the eigen value problem is solved to arrive at the inter-tube resonances of the MWCNTs. Variation of the natural frequencies with different parameters are studied. The estimated results from the present method are compared with the literature and results are observed to be in close agreement.

Keywords

natural frequencies / multi-walled carbon nanotubes (MWCNTS) / elastic medium

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Acknowledgments

PR Budarapu thankfully acknowledges the financial support through the project “MultiFrac” under the International Research Staff Exchange Scheme (IRSES), FP7-PEOPLE-2010-IRSES.

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg