Non-local free and forced vibrations of graded nanobeams resting on a non-linear elastic foundation

Sami El-Borgi, Ralston Fernandes, J. N. Reddy

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33 Citations (Scopus)


We consider in this paper the free and forced vibration response of simply-supported functionally graded (FG) nanobeams resting on a non-linear elastic foundation. The two-constituent Functionally Graded Material (FGM) is assumed to follow a power-law distribution through the beam thickness. Eringen?'s non-local elasticity model with material length scales is used in conjunction with the Euler-Bernoulli beam theory with von Kármán geometric non-linearity that accounts for moderate rotations. Non-linear natural frequencies of non-local FG nanobeams are obtained using He?'s Variational Iteration Method (VIM) and the direct and discretized Method of Multiple Scales (MMS), while the primary resonance analysis of an externally forced non-local FG nanobeam is performed only using the MMS. The effects of the non-local parameter, power-law index, and the parameters of the non-linear elastic foundation on the non-linear frequency-response are investigated.

Original languageEnglish
Pages (from-to)348-363
Number of pages16
JournalInternational Journal of Non-Linear Mechanics
Publication statusPublished - 1 Dec 2015



  • Eringen?'s non-local model
  • Graded nanobeam
  • Method of Multiple Scales (MMS)
  • Variational iteration method (VIM)

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Applied Mathematics

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