Journal of Engineering Mathematics

, Volume 109, Issue 1, pp 85–111 | Cite as

Vibration and buckling analysis of nanotubes (nanofibers) embedded in an elastic medium using Doublet Mechanics

  • U. Gul
  • M. Aydogdu
  • G. Gaygusuzoglu


In the present study, vibration and buckling of nanotubes (nanofibers) embedded in an elastic medium are studied. A length scale-dependent theory called Doublet Mechanics (DM) is used in the formulation. In this theory, discrete microstructure of solids is considered in the formulation and using a bottom-up approach macro level strains and stresses are obtained from microlevel strains and stresses. Taylor series expansion of the microlevel displacement is used in the definition of the micro strains. The number of terms in the Taylor series describes the microstructure of the considered solids. In this study, nanotube fibers are assumed as an Euler–Bernoulli beam embedded in an elastic medium. Simply supported and clamped boundary conditions are considered at the edges of the beams. Free vibration frequencies and critical buckling loads are obtained and compared with the classical elasticity results. It is shown that scale-dependent DM can be used at the nanolength scale.


Buckling Doublet Mechanics Elastic medium Nanotube Vibration 



The constructive comments of the editor and reviewers are gratefully acknowledged.


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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringTrakya UniversityEdirneTurkey
  2. 2.Department of Civil EngineeringNamik Kemal UniversityCorluTurkey

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