Vibration Analysis of Nonuniform Single-Walled Carbon Nanotube Resting on Winkler Elastic Foundation Using DQM

  • Subrat Kumar JenaEmail author
  • S. Chakraverty
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


This study present frequency parameters and mode shapes of nonuniform Single-Walled Carbon Nanotube (SWCNT) placed on Winkler elastic foundation. Eringen’s nonlocal theory is implemented in the Euler–Bernoulli beam to inquire size-dependent behavior of single-walled carbon nanotube. Here flexural stiffness is assumed to vary exponentially which is responsible for making it nonuniform since many nanoelectromechanical systems acquire geometrically nonuniform model. Differential Quadrature Method (DQM) is adopted and MATLAB code has been developed to explore the tabular and graphical results for different scaling parameters. All the standard boundary condition, viz, S-S, C-S, C-C, and C-F are taken into consideration, and obtained results are compared with the well-known results available in the literature showing excellent agreement. Also, the effects of various scaling parameters like nonuniform parameter, the nonlocal parameter, aspect ratio, and Winkler modulus parameter on frequency parameters are demonstrated using numerical as well as graphical results.


SWCNT DQM Flexural stiffness Winkler elastic foundation Eringen’s theory 



The authors would like to thank Defence Research & Development Organization (DRDO), Ministry of Defence, New Delhi, India (Sanction Code: DG/TM/ERIPR/GIA/17-18/0129/020) for the funding to carry out the present research work smoothly.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of MathematicsNational Institute of TechnologyRourkelaIndia

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