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Radial Nonlocal Effect on the Vibration Characteristics of Carbon Nano-tube Supported in Winkler Type Elastic Foundation

[ Vol. 1 , Issue. 2 ]


Utpal Mandal and Suresh C. Pradhan   Pages 139 - 144 ( 6 )


Background: In the upcoming era carbon nanotubes have proved to be the most promising material in the field of science and technology. In the analysis of carbon nanotube, nonlocal elasticity is found to be highly effective as it regards the small scale effects in the analysis. The small scale effect is found to be considered via nonlocal elasticity in both axial and radial direction.

Objective: In the present article, radial nonlocal effect on the vibration of carbon nanotubes supported in Winkler type elastic foundation is studied.

Method: In the analysis, Timoshenko beam theory is employed to derive the governing differential equations. Finite element model is developed.

Results: It is observed radial nonlocal effect has a dominating effect over Winkler modulus parameter and at higher diameter, the effect of Winkler modulus disappears.

Conclusion: The observation indicates that radial scale effect has significant influence in the vibration analysis of carbon nanotubes supported on Winkler foundation.


Carbon nanotubes, finite element method, radial nonlocal effect, timoshenko beam theory, vibration analysis, winkler type elastic foundation.


Department of Aerospace Engineering, Indian Institute of Technology Kharagpur, West Bengal, 721 302-India.

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