Free vibration analysis of functionally graded size-dependent nanobeams

M. A. Eltaher, Samir A. Emam, F. F. Mahmoud

Research output: Contribution to journalArticlepeer-review

387 Citations (Scopus)


This paper presents free vibration analysis of functionally graded (FG) size-dependent nanobeams using finite element method. The size-dependent FG nanobeam is investigated on the basis of the nonlocal continuum model. The nonlocal elastic behavior is described by the differential constitutive model of Eringen, which enables the present model to become effective in the analysis and design of nanosensors and nanoactuators. The material properties of FG nanobeams are assumed to vary through the thickness according to a power law. The nanobeam is modeled according to Euler-Bernoulli beam theory and its equations of motion are derived using Hamilton's principle. The finite element method is used to discretize the model and obtain a numerical approximation of the equation of motion. The model is validated by comparing the obtained results with benchmark results. Numerical results are presented to show the significance of the material distribution profile, nonlocal effect, and boundary conditions on the dynamic characteristics of nanobeams.

Original languageEnglish
Pages (from-to)7406-7420
Number of pages15
JournalApplied Mathematics and Computation
Issue number14
Publication statusPublished - Mar 15 2012


  • FG nanobeam
  • Finite element method
  • Nonlocal elasticity
  • Vibration analysis

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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