Journal of Mechanical Science and Technology

, Volume 29, Issue 3, pp 1207–1215 | Cite as

Application of the differential transformation method for nonlocal vibration analysis of functionally graded nanobeams

  • Farzad EbrahimiEmail author
  • Majid Ghadiri
  • Erfan Salari
  • Seied Amir Hosein Hoseini
  • Gholam Reza Shaghaghi


In this study, the applicability of differential transformation method (DTM) in investigations on vibrational characteristics of functionally graded (FG) size-dependent nanobeams is examined. The material properties of FG nanobeam vary over the thickness based on the power law. The nonlocal Eringen theory, which takes into account the effect of small size, enables the present model to be effective in the analysis and design of nanosensors and nanoactuators. Governing equations are derived through Hamilton’s principle. The obtained results exactly match the results of the presented Navier-based analytical solution as well as those available in literature. The DTM is also demonstrated to have high precision and computational efficiency in the vibration analysis of FG nanobeams. The detailed mathematical derivations are presented and numerical investigations performed with emphasis placed on investigating the effects of several parameters, such as small scale effects, volume fraction index, mode number, and thickness ratio on the normalized natural frequencies of the FG nanobeams. The study also shows explicitly that vibrations of FG nanobeams are significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG nanobeams.


Differential transformation method Functionally graded material Nanobeam Nonlocal elasticity Vibration 


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Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Farzad Ebrahimi
    • 1
    Email author
  • Majid Ghadiri
    • 1
  • Erfan Salari
    • 1
  • Seied Amir Hosein Hoseini
    • 2
  • Gholam Reza Shaghaghi
    • 1
  1. 1.Department of Mechanical Engineering, Faculty of EngineeringImam Khomeini International UniversityQazvinIran
  2. 2.Department of Mechanical EngineeringUniversity of ZanjanZanjanIran

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